Given data:
[tex]F(x)=\sqrt[3]{x-2}+3[/tex]A. The domain of cube root function is all the real numbers because it is possible for three negatives to equal a negative. But this cannot apply for square functions.
B. For range put F(x) = y
[tex]\begin{gathered} y=\sqrt[3]{x-2}+3 \\ y-3=\sqrt[3]{x-2} \end{gathered}[/tex]Now, taking cube both sides we get
[tex](y-3)^3=x-2[/tex][tex]x=2+(y-3^{})^3[/tex]Thus, the range for the function is also all real numbers because value of x will be defined for every value of y.
The Spanish Club is washing cars as a fundraiser. The graph below shows the amount of money earned, y, based on the number of cars washed, x. Which equation will calculate the amount of money earned, y, after washing x cars?
Answer:
Explanation:
The points are all on a straight line, we determine the equation of the line.
The slope-intercept form of a line is:
[tex]undefined[/tex]You order 15 DVD's at S8 a DVD and 24 books at $5 a book. What is the cost of the order?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
DVD price = $8
Book price = $5
Step 02:
total cost = 15 dvd * $8 + 24 book * $5
= 120 + 120 = $240
The answer is:
The total cost of the order is $240
Suppose y varies directly with x, and y=8 when x=4. Find x when y=10.
Since y varies directly with x, we have the following relation:
[tex]\frac{y}{x}=k[/tex]Where k is a constant.
For y = 8 and x = 4, we have:
[tex]\begin{gathered} \frac{8}{4}=k \\ k=2 \end{gathered}[/tex]Then, for y = 10, we have:
[tex]\begin{gathered} \frac{10}{x}=2 \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]So for y = 10 we have x = 5.
Give the correct numerical response.The odds against obtaining a 4 when a single fair die is tossed aretoThe odds against obtaining a 4 when a single fair die is tossed are(Type whole numbers.)
Answer:
[tex]1\text{ to 5}[/tex]Explanation:
Here, we want to compare odds
In a single toss of a die, the probability of obtaining a 4 is 1/6
This is because there are 6 possible results and only one of these could be 4
The probability of not obtaining a 4 is 5/6
This is because the sum of the probability of obtaining a 4 and not obtaining a 4 is 1
Now, let us compare the odds
We have that as:
[tex]\begin{gathered} \frac{1}{6}\text{ to }\frac{5}{6}\text{ } \\ \\ which\text{ is:} \\ 1\text{ to 5} \end{gathered}[/tex]Hi, can you help me answer this question please, thank you!
Step 1:
You wish to test the following claim at a significance level of
α = 0.05
Step 2:
Null hypothesis
[tex]H_0\colon\mu\text{ = 87.8}[/tex]Step 3:
Alternative hypothesis
[tex]H_a\text{ : }\mu\text{ < 87.8}[/tex]May I please get some help with this The question asks Which lines are Perpinduicular?It may take me a while to understand this
For this question, we need to calculate the slope
For G
[tex]\begin{gathered} m=\frac{-3+2}{2+2} \\ m=\frac{-1}{4} \end{gathered}[/tex]For R
[tex]\begin{gathered} m=\frac{5-1}{3-2} \\ m=\frac{4}{1} \end{gathered}[/tex]For B
[tex]\begin{gathered} m=\frac{5-0}{1-0} \\ m=5 \end{gathered}[/tex]R is perpendicular to B
x Complete the table for each equation. 5. d=rt when r = 5 d=5t 3 4 5 6 á t d
We have the following expression:
[tex]d=r\cdot t[/tex]we are given that r = 5, then, the equation is:
[tex]d=5t[/tex]then, if we want to make a table for the values of t = 3,4,5,6, we have:
[tex]\begin{gathered} t=3 \\ \Rightarrow d=5\cdot3=15 \\ t=4 \\ \Rightarrow d=5\cdot4=20 \\ t=5 \\ \Rightarrow d=5\cdot5=25 \\ t=6 \\ \Rightarrow d=5\cdot6=30 \end{gathered}[/tex]then, the table would be the following:
write a number of terms in a trinomial.
Given statement-
Write a number of terms in a trinomial.
To find- the number of terms.
Explanation-
A trinomial is a polynomial with three terms (with single or multiple variables).
An example with one variable is mentioned below.
[tex]x^2+6x+9[/tex]Similarly, with multiple variables is mentioned below.
[tex]a^2+b^2+ab[/tex]suppose you find six articles related to the topic of your research paper. in how many ways can you choose four articles to read
Given
Number of articles you have to read = 6
Find
Number of ways to choose four articles to read.
Explanation
here , we apply permutations,
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]so ,
[tex]\begin{gathered} ^6P_4=\frac{6!}{(6-4)!} \\ \\ ^6P_4=\frac{6!}{2!} \\ \\ ^6P_4=\frac{6\times5\times4\times3\times2!}{2!} \\ \\ ^6P_4=360 \end{gathered}[/tex]Final Answer
Hence , the number of ways to choose four articles to read is 360
Need help with this because I don’t know this and I need jt
Given
[tex]\begin{gathered} 2(x+\frac{5}{2})=20 \\ \\ \end{gathered}[/tex]Solution
[tex]\begin{gathered} 2x+5=20 \\ 2x=20-5 \\ 2x=15 \\ divide\text{ both sides by 2} \\ \frac{2x}{2}=\frac{15}{2} \\ x=7.5 \end{gathered}[/tex]The final anwer
[tex]\frac{15}{2}\text{ or 7.5}[/tex]Given u = 35i − 12j, what are the magnitude and direction of −3u? Round to the nearest whole number.
Solution
For this case we have the following number:
u= 35i -12j
And we want to find the magnitude and direction of -3u so we have this:
-3 u = -105i + 36j
Then the magnitude is given by.
[tex]M=\sqrt[]{(-105)^2+(36)^2}=111[/tex]And the angle can be founded using this:
[tex]\theta=\tan ^{-1}(\frac{36}{-105})=-18.92[/tex]Therefore the angle is:
-18.92 + 360 º= 341º
The answer is:
111, 341º
10. A contractor has 16 gallons of paint which will cover 2,912 square feet. Which of the following rates best represents the relationship between the number of square feet and the number of gallons of paint?
okwe need to calculate tge rate of the relation so must do a divison the area between the gallons so
[tex]\begin{gathered} \frac{2912}{16} \\ =182 \end{gathered}[/tex]so, you have 182 square feet per gallon
the answer is C
21 Use properties of operations to find the quotient. 4 2/4÷6A.3 2/3B.26 2/5C.2/3D.11/15
first transform the mixed number
[tex]4\frac{2}{5}\longrightarrow\frac{(4\times2)+2}{5}=\frac{22}{5}[/tex]now do the division
we can represent the 6 as 6/1 to use the following method
where the red multiplication is the numerator and green the denominator
so
[tex]\begin{gathered} \frac{22\times1}{6\times5} \\ \\ \frac{22}{30}=\frac{11}{15} \end{gathered}[/tex]then the answer is 11/15
Can someone please answer this calculus question
The numeric value of the derivative of the function at x = -1 is given by:
f'(-1) = -12.
Derivative of product ruleA function defined by the multiplication of two functions is as follows:
f(x) = g(x)h(x)
The derivative of this function is given as follows:
f'(x) = g'(x)h(x) + h'(x)g(x).
In this problem, the function is:
f(x) = x^6h(x).
The parameters are as follows:
g(x) = x^6.g'(x) = 6x^5.The derivative is given by:
f'(x) = x^6h'(x) + 6h(x)x^5
At x = -1, the numeric value of the derivative of the function is:
f'(-1) = (-1)^6 x (6) + 6 x 3 x (-1)^5 = 6 - 18 = -12.
We just took the general derivative calculated, and for the numeric value at x = -1, only the data given on the exercise for function h(x) was needed.
More can be learned about derivatives at https://brainly.com/question/5313449
#SPJ1
Estimator bias occurs when a sample is not random and does not accurately represent the population being studied?
We say that an estimator is biased when it does not represent accurately the population being studied
mixture 1there is 1 1/2 teaspoons and 1 cupmixture 2there is 1/2 teaspoons and 2 cupsmixture 3 there is 1/4 teaspoons and 1 cup
Mixture 1 would taste different
Explanation
the taste is given by the proportion of teaspoons and cups in eeach mixture, let's find them
Step 1
mixture 1
[tex]\begin{gathered} 1\frac{1}{2}=\frac{(1\cdot2)+1}{2}=\frac{3}{2}=1.5 \\ \text{then} \\ 1.5\text{ teaspoons }\rightarrow1\text{ cup} \\ \text{the proportion is} \\ \frac{1.5}{1}=1.5\frac{teaspoon}{\text{cup}} \end{gathered}[/tex]mixture 2
[tex]\begin{gathered} \frac{1}{2}=0.5 \\ \text{then} \\ 0.5\text{ teaspoonss}\rightarrow2\text{ cups} \\ \text{the proportion is} \\ \frac{0.5\text{ teaspoons}}{2\text{ cups}}=0.25\frac{teaspoons}{\text{cup}} \end{gathered}[/tex]mixture 3
[tex]\begin{gathered} \frac{1}{4}=0.25 \\ \text{then} \\ 0.25\text{ teaspoons}\rightarrow1\text{ cup} \\ \text{the proportion is} \\ \frac{0.25}{1}=0.25\text{ }\frac{teaspoons}{\text{cup}} \end{gathered}[/tex]Step 3
compare the proportions
[tex]\begin{gathered} \text{mixture 1=1.5} \\ \text{mixture 2=0}.25 \\ \text{mixture 3=0.25} \\ \end{gathered}[/tex]Hence
Mixture 1 would taste different.
I hope this helps you
Use a unit multiplier to perform the following rate conversion 440 yards per minute to yards per second
EXPLANATION
Using a unit multiplier give us the following relationship:
[tex]440\frac{yards}{\text{minute}}\cdot\frac{1\text{ minute}}{60\text{ seconds}}=\frac{22}{3}\frac{yards}{s}=7.3\text{ yards/s}[/tex]How many snake man and red chrome books were sold all together .
You multiply each yellow book in the diamgram for 10 to find the total number of books sold:
Snake man books that were sold: 3 x 10 = 30
Red crow books that were sold: 5 x 10 = 50
Number of snake man abd red crow that were sold all together: 30 + 50 =80
A rare stamp in Lings collection is now worth $280. it's value has been increasing by 8% each year. the value of the stamp to continue increasing at this rate, so the function V(t) =280(1.08)^t estimates the value of GLing expects after t years.Ling graphed the function to find the number of years, to the nearest whole number, that he must wait before the stamp is worth approximately double it's current value.How many years will it take for the stamp to double in value?
9 years
1) Gathering the data
now worth $280
increasing by 8% each year.
V(t) =280(1.08)^t
2) Since we want to know how long it'll take for that stamp to double its value then we can write:
[tex]\begin{gathered} 280\times2=560 \\ 560=280(1.08)^t \\ \frac{560}{280}=\frac{280(1.08)^t}{280} \\ 2=(1.08)^t \\ \log _{1.08}(1.08)^t=\log _{1.08}2 \\ t\log _{1.08}(1.08)^{}=\log _{1.08}2 \\ t=\log _{1.08}2 \\ t\approx9.00 \end{gathered}[/tex]Notice that we had to apply the logarithms on both sides and we chose an appropriate base so that we can get rid of that 1.08 on the left side.
3) So, in approximately 9 years that stamp will have its current value doubled.
Find the volume of a cylinder with a radius 28 and height 18
Given:-
Radius of cylinder is 28 and Height of cylinder is 18.
To find:-
The volume of the cylinder.
So now we use the formula of cylinder,
[tex]v=\pi r^2h[/tex]Substituting the known values. we get,
[tex]v=\pi r^2h=\pi\times28\times28\times18=14112\pi[/tex]So the required solution is 14112pi.
which of the following best described the nature of roots if the discriminant is 2.a. roots are unreal and unequal. b.roots are real and equal.c.roots are not real and unequal. d.roots are not real.
hello
to find the discriminant of a root, i'll write down the formula for you
[tex]d=b^2-4ac[/tex]now there are six nature of roots
1.
QuestionGiven the following frequency table of values, is the mean or the median a better measure of the center of the data set?
From the frequency table provided;
The median takes the exact value that is atthe middle of the data set, while the mean also does this but uses every one of the data provided in the process of doing this.
Hence, the Mean is a better measure of central tendency in this case
Plans for a new school call for classrooms directly across the hall from each other to be congruent. This computer printout shows a biology classroom. If the vertices of a history classroom are located at (x1, -3y1) , (x2, -3y2) , (x3, -3y3) , and (x4, -3y4) , will the history classroom be congruent to the biology classroom ?
According to the given information, the class must be congruent and symmetric towards the hallway. To do that, we need to use the same transformation on each vertex in order to have symmetry.
Therefore, the right answer would be Yes, because the same transformation was applied to all the vertices.
Answer:
No, because the transformation applied was not a rigid motion.
Step-by-step explanation:
The y values are decreased by a scale factor of -3, which makes the classroom a different size than the biology classrom.
What is the relative frequency of the revenue earned by B&B Motors from sales of mini trucks compared to the total sales revenue earned by all four companies? OA 0.02 B. 0.16 OC. 0.26 OD. 0.55
From the table we can derive the following :
Revenue earned by B&B from the sale of mini trucks = 9
The total sales revenue earned by all four companies = 431
Recall that relative frequency is calculated using the formula:
[tex]R\mathrm{}F=\text{ }\frac{frequency}{Sum\text{ of frequency}}[/tex]Hence:
[tex]\begin{gathered} R\mathrm{}F\text{ = }\frac{9}{431} \\ =\text{ }0.02088 \\ \cong\text{ 0.02} \end{gathered}[/tex]
Fredward is buying juice and soda for his birthdayparty. He wants to buy 12 total bottles and can spend$29. If juice cost $3 per bottle and soda cost $2per bottle, how many bottles of each should he buy?Oj+s = 29j + s = 123j + 2s = 29j + s = 12Oj= 3S = 2O3 = 292s = 12
3j +2s = 29 ...eqn(1)
j + s = 12 .......eqn(2)
By elimination method of solving simultaneous equations, we have,
[tex]undefined[/tex]what is the solution of 3+5n=5(n+2)-7
this is
[tex]\begin{gathered} 3+5n=5(n+2)-7 \\ 3+5n=5n+10-7 \\ 3+5n=5n+3 \\ 3+5n-3=5n+3-3 \\ 5n=5n \\ 5n-5n=5n-5n \\ 0=0 \end{gathered}[/tex]solution: equation is true for all n
14. If I offered you one of the two accounts detailed below, which would you choose, and why? Account 1 $1,000.00 Account 2 $1,000.00 $1,050.00 Start $1,060.00 After 1 year $1,102.50 $1,120.00 After 2 years $1,180.00 After 3 years $1,157.63 $1,215.51 $1,240.00 After 4 years
Accounts with interests
Account 1 = $1000
Account 2 = $1000
Account 1 ,increases by $60 anually
Account 2 ,increases exponentially , not fixed
50, 52.5 ,55, 58 etc...
THEN ANSWER IS
If you need money in 4 years , ill choose Account 1
BUT
if you can wait more time, say 10 years ,ill choose Account 2
Then
Account 1
After 5 years =$ 1300
After 10 years =$ 1600
After 15 years = $ 1900
After 20 years= $ 2200
After 25 years= $ 2500
Account 2
After 5 years=$1276. 27
After 10 years=$ 1611.34
After 15 years=$ 1987.6 + $10.85 = $1998.45
After 20 years=$ 2382.95 + $33.635 = $ 2416.585
After 25 years= $2936.22 + $104.26 = $ 3040.48
The domain of the function given below is the set of all real numbers greater than 1.A.TrueB.False
Given:
[tex]f(x)=(\frac{1}{2})^x[/tex]To Determine: The domain of the given function
Solution
[tex]\begin{gathered} \:The\text{ }domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values\: \\ \:for\:which\:the\:function\:is\:real\:and\:defined \end{gathered}[/tex]For the given function
[tex]domain=-\inftyHence the domain is the set of all real numbers. The correct option is FALSE, OPTION BGiven mn, find the value of x. (10x-4) (x-14)
Step-by-step explanation:
please give the complete question
One section of the island - to be sampled by researchers to develop a census of tortoises- is a large square with a sade length of 1 kilometer. Researchers intend to place infrared cameras throughout, including around the diagonal of the square. what is the length of the diagonal of this square, expressed in kilometers (rounded to the nearest tenth of a kilometer).Formula used:Answer
The formula for the length of diagonal for the square of side a is,
[tex]d=\sqrt[]{2}a[/tex]Substitute 1 for a in the formula to obtain the length of diagonal.
[tex]\begin{gathered} d=\sqrt[]{2}\cdot1 \\ =1.414 \\ \approx1.4 \end{gathered}[/tex]So answer is 1.4 km.