Answer:
Step-by-step explanation:
f(x)=3x+15
let f(x)=y
y=3x+15
flip x and y
x=3y+15
3y=x-15
y=1/3 x-5
or f^{-1}x=1/3 x-5
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
Enter a range of values of x
Answer:
[tex]-5<x<26[/tex].
Step-by-step explanation:
We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.
Angle opposite to larger side is larger.
Since, 14 < 15, therefore
[tex]2x+10<62[/tex]
[tex]2x<62-10[/tex]
[tex]2x<52[/tex]
[tex]x<26[/tex] ...(1)
We know that, angle can not not negative.
[tex]2x+10>0[/tex]
[tex]2x>-10[/tex]
[tex]x>-5[/tex] ...(2)
From (1) and (2), we get
[tex]-5<x<26[/tex]
Therefore, the range of values of x is [tex]-5<x<26[/tex].
PLEASEEEEE HELPPOO
For Individual or Group Explorations
Maximizing the Total Profit
Payles at The Christmas Store very periodically with a high ef 550.000 in December
the Christmas Stove also comes the Powe, where profits reach a high of $80,000
in Aurust and a few of $20,000 in February Assume that the profit function for
Crm Store
Save
40
20
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
a) Write the profit function for The Christmas Store as a function of the month
and sketch its graph
b)
Write the profit function for The Pool Store as a function of the month and
sketch its graph.
are are length
Write the total profit as a function of the month and sketch its graph. What is
the period?
are inside the
est enth of a
Use the maximum feature of a graphing calculator to find the owner's maxi-
mum total profit and the month in which it occurs.
Find the owner's minimum total profit and the month in which it occurs.
We know that y -a sin x + bcos x is a sine function. However, the sum of
two arbitrary sine or cosine functions is not necessarily a sine function. Find an
example in which the graph of the sum of two sine functions does not look like
a sine curve.
Explain.
is tangent to one
Answer:
what
Step-by-step explanation:
Of the cartons produced by a company, % have a puncture, % have a smashed corner, and % have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing%. (Type an integer or a decimal. Do not round.)
Full Question
Of the cartons produced by a company, 10% have a puncture, 6% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing ____%. (Type an integer or a decimal. Do not round.)
Answer:
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Step-by-step explanation:
Given
[tex]Puncture\ Corner = 10\%[/tex]
[tex]Smashed\ Corner = 6\%[/tex]
[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]
Required
[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]
For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;
[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]
Substitute:
10% for P(Puncture Corner),
6% for P(Smashed Corner) and
0.4% for P(Punctured and Smashed Corner)
[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]
[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]
Convert % to fraction
[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]
Convert to decimal
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Using Venn probabilities, it is found that:
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.In this problem, the events are:
Event A: Puncture.Event B: Smashed corner.The "or" probability is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
10% have a puncture, hence [tex]P(A) = 0.1[/tex]6% have a smashed corner, hence [tex]P(B) = 0.06[/tex].0.4% have both a puncture and a smashed corner, hence [tex]P(A \cup B) = 0.004[/tex].Then:
[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.
To learn more about Venn probabilities, you can check https://brainly.com/question/25698611
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
find the values of x and y that make k ll j and m ll n
Answer:
x = 80
y = 130
Step-by-step explanation:
The 2 angles are supplementary. so, x-30 + x+50 = 180.
We solve and get 2x = 180-20
x = 80
y = x+50, because of parallel rules.
y = 130
Answer:
x = 80
y = 130
Step-by-step explanation:edge 2020
Which parent function is represented by the graph?
A. The quadratic parent function
B. The absolute value parent function
C. An exponential parent function
D. The linear parent function
Answer:
D. The linear parent function
Step-by-step explanation:
Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.
Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;
m= gradient of the straight line graph
x= the independent variable
y= the dependent variable
c= the vertical intercept
Answer:
The linear parent function :)
Step-by-step explanation:
what other numbers can you square that result in 9 ?
Step-by-step explanation:
I'm not sure what your answers are, but you can only square 3 and -3 to get 9.
Answer:
3, -3
Step-by-step explanation:
3*3 = 9
-3 * -3 = 9
These are the only two numbers that square to 9
What is 25÷5what is 25 / 5
Answer:
5
Step-by-step explanation:
25/5
=5✖️5=25
=5/1
Answer:
25÷5 = 5 and 25/5 = 125
Step-by-step explanation:
hope this helps!
PLEASE HELP ASAP!! Write a polynomial f(x) that satisfies the following conditions. Polynomial of lowest degree with zeros of -4 (multiplicity of 1), 2 (multiplicity of 3), and with f(0)=64
Answer:
See below.
Step-by-step explanation:
So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.
Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.
Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.
Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:
In other words, we will have:
[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.
Let's determine n first. We know that f(0)=64, thus:
[tex]f(0)=64=4(-2)^3\cdot n[/tex]
[tex]64=-32n, n=-2[/tex]
Now, let's expand:
Expand:
[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]
[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]
[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]
[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]
This is the simplest it can get.
How does the frequency of f(x) = cos(2x) relate to the frequency of the parent function cos x?
Answer:
The frequency of f(x) is two times the frequency of the parent function.
Step-by-step explanation:
We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.
Then, for the parent function, we get:
[tex]1 = 2\pi f_1[/tex]
or solving for [tex]f_1[/tex]:
[tex]f_1=\frac{1}{2\pi }[/tex]
At the same way, for f(x), we get:
[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]
But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:
[tex]f_2=2f_1[/tex]
It means that the frequency of f(x) is two times the frequency of the parent function.
Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
explain square roots
Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)
Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hoursand notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoeyexpect from the iPad on a full battery charge?
Answer:
8 hours
Step-by-step explanation:
25%= 2 hrs
100%=8 hrs
brainliest plsssssssssssssssssssss
-zylynn
In Sparrowtown, the use of landlines has been declining at a rate of 5% every year. If there are 20,000 landlines this year, how many will there be in 15 years? If necessary, round your answer to the nearest whole number.
Answer:
5,000
Step-by-step explanation:
If it decreases by 5% a year, it'll decrease by 75% in 15 years
i.e 1 year = 5%
15 years = x
Cross multiply
x = 75%
Therefore, since it decreases by 75%
100 - 75 x 20,000 = 5,000
100
what is the value of this expression when a = 2 and b = -3 ? a^3 - b^3 / 5
Answer:
13 2/5
Step-by-step explanation:
a = 2 and b = -3
so the question asks whats.... a^3 - b^3/5
First we plug in the values of a and b
(2)^3 - (-3)^3 /5
Now we solve the ones in paranthesis first
(2)^3 = 8 because 2×2×2 and
-(-3)^3 forget about the - outside the parenthesis so
(-3)^3 = (-27) because (-3)×(-3)×(-3)
now we put it back together
8 -(-27)/5
the two minus become plus so
8 + 27/5
Now we solve it like fractions
8 and 27/5
simplify
13 and 2/5
Hope that helps!
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
simplify (3+3 / x(x+1) )(x-3 / x(x-1) )
Answer:
I think it is [tex]\frac{6x-18}{x^{4} }[/tex]
Step-by-step explanation:
One number is 2 more than another. The difference between their squares is 52. What are the numbers?
Answer:
The aprox, numbers:
4.1633 and 8.3266
Step-by-step explanation:
a = 2b
a² - b² = 52
then:
(2b)² - b² = 52
4b² - b² = 52
3b² = 52
b² = 52/3
b² = 17.333
√b² = √17.333
b = 4.1633 aprox.
a = 2b
a = 2*4.1633
a = 8.3266
Check:
8.3266² - 4.1633² = 52
69.333 - 17.333 = 52
Need help finding the length
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
What is the image of (-8, 10) when reflected in the y-axis?
Answer:
if you're just reflecting the point over the y-axis it just becomes (8,10)
Answer: (8, 10)
Explanation and Example:
I have a trick that I use. I'm not sure if it will make sense to you but I'll explain it. When the question asks you to reflect over the x-axis, then keep the x in (x,y) the same and just flip the sign for the y. If the question asks you to reflect over the y-axis, then keep y the same and flip the sign for x.
Reflect over x-axis:
(-2, 6) -----> (-2, -6)
Reflect over y-axis:
(-4, -8) -----> (4, -8)
PLZ IM ON THE CLOCK!!!!! A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month? $457.50 $460.00 $462.50 $572.50
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
PLEASE ANSWER FAST PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
sin = -√2 / 2
cos = √2 / 2
tan = -1
Step-by-step explanation:
Θ is in quad IV
sin = -√2 / 2
cos = √2 / 2
tan = -1
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]
Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
What value of x is I the solution set of 3(x-4)>5x+2
Answer:
-7 > x
Step-by-step explanation:
3(x-4)>5x+2
Distribute
3x-12>5x+2
Subtract 3x from each side
3x-12-3x>5x-3x+2
-12 > 2x+2
Subtract 2 from each side
-12-2>2x+2-2
-14 > 2x
Divide by 2
-14/2 > 2x/2
-7 > x
Answer:
[tex]\boxed{x<-7}[/tex]
Step-by-step explanation:
3(x-4)>5x+2
Expand brackets.
3x - 12 > 5x+2
Subtract 3x and 2 on both sides.
-12 - 2 > 5x - 3x
-14 > 2x
Divide both sides by 2.
-7 > x
Switch sides.
x < -7
What is 4sqrt7^3 in exponential form?
Answer:
[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]
Step-by-step explanation:
[tex]4 (\sqrt{7} )^3[/tex]
Square root can be written as a power.
[tex]4(7^{\frac{1}{2} })^3[/tex]
Multiply the exponents.
[tex]4(7^{\frac{3}{2} })[/tex]
Answer:
A (7^3/4)
Step-by-step explanation:
ed 2020
Solve the simultaneous equations 2x-y=7 3x+y=3
Answer:
( 2 , - 3 )Step-by-step explanation:
Using elimination method:
2x - y = 7
3x + y = 3
--------------
5x = 10
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{10}{5} [/tex]
Calculate
[tex]x = 2[/tex]
Now, substitute the given value of X in the equation
3x + y = 3
[tex]3 \times 2 + y = 3[/tex]
Multiply the numbers
[tex]6 + y = 3[/tex]
Move constant to R.H.S and change it's sign
[tex]y = 3 - 6[/tex]
Calculate
[tex]y = - 3[/tex]
The possible solution of this system is the ordered pair ( x , y )
( x , y ) = ( 2 , -3 )---------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex]2 \times 2 - ( - 3) = 7[/tex]
[tex]3 \times 2 - 3 = 3[/tex]
Simplify the equalities
[tex]7 = 7[/tex]
[tex]3 = 3[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( 2 , - 3 )Hope this helps..
Best regards!!
a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.