Answer:
Whe we have two functions, f(x) and g(x), the composite function:
(f°g)(x)
is just the first function evaluated in the second one, or:
f( g(x))
And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:
f(x) = 1/(x + 1)
where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.
Now, we have:
f(x) = x^2
g(x) = x + 9
then:
(f ∘ g)(x) = (x + 9)^2
And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:
x ∈ (-∞, ∞)
(g ∘ f)(x)
this is g(f(x)) = (x^2) + 9 = x^2 + 9
And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:
x ∈ (-∞, ∞)
(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4
And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:
x ∈ (-∞, ∞)
(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18
And again, there are no values of x that cause a problem here, so the domain is:
x ∈ (-∞, ∞)
ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=1). write your answer as a fraction.
Explanation:
P(T = 1) is the notation that means "The probability of getting exactly one tail". The table shows 3/8 in the bottom row, under the "1" in the top row. So that's why P(T = 1) = 3/8
Or it might make more sense to say P(one tail) = 3/8 so we don't have too many equal signs going on.
Which of the following represents the solution to the inequality 215-2xl-3315?
O (-60,-2) (7.00)
O (-0,1.5) (7.5.00)
O 1-2, 7]
O [1.5, 7.5]
9514 1404 393
Answer:
(c) [-2, 7]
Step-by-step explanation:
We can solve the inequality for an expression in x.
2|5 -2x| -3 ≤ 15
2|5 -2x| ≤ 18 . . . . . . add 3
|5 -2x| ≤ 9 . . . . . . . . divide by 2
We prefer a positive coefficient of x, so we'll multiply inside the absolute value by -1. This does not change the absolute value. (|-1| = |1|, for example)
|2x -5| ≤ 9
Now, we can "unfold" this to get the compound inequality ...
-9 ≤ 2x -5 ≤ 9
-4 ≤ 2x ≤ 14 . . . . . add 5
-2 ≤ x ≤ 7 . . . . . . . divide by 2
The solution interval is [-2, 7].
__
The graph shows the equation of the given form f(x) ≤ c converted to the form f(x)-c ≤ 0. The graphing calculator highlights x-intercepts easily, so we take advantage of that to show the solution interval bounds. The graph is less than zero between the bounds.
Can I get an awnser to both of these questions? Thank you!
Answer:
y+1=7(x+4) for first one
y-4=5(x-0) for second one
Step-by-step explanation:
point slope form for both of those questions.
the formula for point slope form is
y-y1(y coordinate) = slope(x+x2(x coordinate))
y+1=7(x+4)
Second question:
-1,-1 to 0,4
change in x +1, change in y +5.
5/1 = 5
slope is 5
y-4=5(x-0)
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per
year, compounded monthly. Give your answer accurate to 2 decimal places.
Preview
years.
Answer:
The time required is of 17.53 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.
This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0033} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
The time required is of 17.53 years.
State whether the data described below are discrete or continuous and explain why?
The distance between cities in a certain contry.
a. The data are discrete because the data can only take on specific values.
b. The data are discrete because the data can take on any value in an interval.
c. The data are continuous because the data can take on any value in an interval.
d. The data are continuous because the data can only take on specific values.
Answer:
c. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
Discrete data are those which can take up only specific values. Discrete data values may include the number of children in a particular school, the number of visitors received per day. All this values are specific and cannot just take up any number one f values within an interval. Continous data on the other hand can take up any number of data values between an interval. Continous data types are usually height temperature, length(distance data). There can be infinite number of possible data within interval values.
what is 2+2+3+3+5+6
Answer:
21
Step-by-step explanation:
21
21
21
Answer:
Simple addition the answer is 21.
1. My number has two digits.
2. Double my number is less than 150.
Follo
ther
3. I am not divisible by 12.
4. My digits are different from each other.
5. The second digit in my number is divisible
by an odd number.
6. My first digit is less than my second digit.
7. My digits add up to 14.
way.
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {Your\:answer\:is\:59.}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
1. My number has two digits.
59 is a two-digit number. ✔2. Double my number is less than 150.
Double of 59 is 118, which is less than 150. ✔3. I am not divisible by 12.
Since 59 is an odd number, hence it is not divisible by 12. ✔4. My digits are different from each other.
The digits 5 and 9 are different. ✔5. The second digit in my number is divisible by an odd number.
9 is divisible by an odd number, i.e. 3. ✔6. My first digit is less than my second digit.
5 is less than 9. ✔7. My digits add up to 14.
5 + 9 gives us 14. ✔Therefore, the required number is [tex]\sf\pink{59}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Answer:
59
Step-by-step explanation:
two digits, 59=118, unable to divide by twelve since its an odd number, 9÷3=3, 5<9, 5+9=14
Do 5, 5, and 5 form a right triangle?
Which graph has a slope of 4/5
Answer: whichever graph that goes up 4 and over 5
Step-by-step explanation:
rise over run, 4 up, 5 right
to find it just look at two points on the line and count how many up and how many horizontal units there are between them :)
a housewife spent 3/7 of her money to buy yams and 1/2 of the remainder to buy rice what is the fraction of her money left
Answer:
Fraction of money spent on calculator = 2/5
Find the fraction of money left:
1 - 2/5 = 3/5
Find the fraction of money spent on a book:
4/7 x 3/5 = 12/35
Answer: She spent 12/35 of the money on a book
------------------------------------------------------------------------------------------------
To find the fraction of saving:
Fraction of money saved = 1 - calculator - book
Fraction of money saved = 1 - 2/5 - 12/35 = 9/35
Fraction of the money saved = 9/35
Step-by-step explanation:
write 145,567 in expanded notation
Answer:
100000+45000+500+60+7
if 100% = Rs 120,then. A.120% = Rs 84 B. 20% = Rs 84 C. 70% = Rs 84 D. 30% = Rs 84
Answer:
70% is Rs 84
just use the formula
x% of 120= 84
and you will get the answer
Butch will miss an important TV program while taking his statistics exam, so he sets
both his VCRs to record it. The first one records 70% of the time, and the second one
records 60% of the time. What is the probability that he gets home after the exam and
finds? (We assume that events A and B are independent, so with P(A)=0.7 and
P(B) = 0.6 respectively.)
(a) No copies of his program?
(b) One copy of his program?
Answer:
b
Step-by-step explanation:
this because both VCSs were recording on the same time hence Butch will have two copies of record and the A vcr having an Extra of what B vcr will
NEED HELP ASAP!!!!!!
Answer:
It's a rhombus (if you can check more than one answer, it's also a parallelogram).
Step-by-step explanation:
A rhombus is a flat shape with 4 straight sides that are all equal length.
Also opposite sides are parallel and opposite angles are equal.
It is a type of parallelogram.
Answer:
It's a rhombus
Step-by-step explanation:
because all the 4 sides are equal
And it's like a square that it's top has been pushed
geumath malah 17.pdf
1/21
* 16 The diagram shows a swimming pool in the shape of a prism.
10 m
Sm
Diagram NOT
accurately drawn
וו 1
2 m
4m
DO NOT WRITE IN THIS AREA
2 m
The swimming pool is empty.
Water from 3 water tankers is going to be put into the pool.
There are 20000 litres of water in each water tanker.
Sam thinks that the surface of the water in the pool will be 10 cm below the top of the pool.
Is Sam correct?
You must show how you get your answer.
(lm - 1000 litres)
TE IN THIS AREA
Answer:
He is wrong.
In my answer I found the complete volume of the pool and then what the volume would be 10 cm empty. You probably only need to find the 10 cm emptied to answer, just a heads up. if you have any questions though let me know.
Step-by-step explanation:
To most easily figure out the volume of the empty pool I think it is easiest to break it up into four parts..
First break off that skinny end bit so it will have 1 m in height, 4 m in length and 5m in width. Width is never going to shange because of how we are breaking this up, and the width is the distance from you into the paper, if that makes sense. Basically not up and down or left and right.
Next another rectangular prism from the right side with 2 height, 2m length and again 5m width.
Now you have a trapezoidal prism with one base of length 1m, another of base 2m and a height of length 4m.
To fond the volume of prisms you want to find the area of their bases then multiply it by their heights. In this instance height is going to be the width again, and the bases are th parts facing us on the picture.
For a rectangular prism area of the base is easy, just multiply length by height. a trapezoid is taking the two bases (b1 and b2) ading them together and dividing that sum by 2, THEN taking this new number and multiplying it by what would be the height of the trapezoid. the trapezoid has its bases as two heights, and its height then would be the horizontal length of the pool. Sorry if that is confusing. Here are the three volumes though.
Rectangular 1: 4*1*5 = 20 m^3
Rectangular 2" 2*2*5 = 20m^3
Trapezoidal: = ([1+2]/2)*4*5 = 30 m^3
So total it is 70 m^3
The question then says each cubic meter can contain 1,000 liters of water. 70 m^3 then is 70,000 liters
The question also says there are three barrels of 20,000 liters each, so combined that's 60,000 liters.
Finally it wants to know if Sam is right saying if you dump all of the 60,000 liters into the pool the surface of the water will not reach the top of the pool by 10 cm. 60,000 is less than 70,000, but we don't know how much lower it is in cm.
The trick here is to know that we are lowering a specific dimension of each prism to a certain amount to be lower by 10cm
In the 4x1x5 rectangular prism the 1m side is lowering.
In the 2x2x5 rectangular prism the 2m side representing the vertical length is getting some amount taken away.
int he trapezoidal prism both of the "bases" are getting an amount taken.
So the trick here is to set up the math again, except this time with 10 cm less being subtracted from each part, then solving t and see if it gets us the 60,000 liters or 60 m^3. Since we are measurng in meters, 10 cm less is the same a subtracting .1, or if you prefer subtracting a decimeter.
4*1*5 becomes 4(.9)5 = 18
2*2*5 becomes 2(1.9)5 = 19
Trapezoidal: = ([1+2]/2)*4*5 becomes ([(.9)+(1.9)]/2)*4*5 = 28
Adding this all together gets us 65 or 65,000 liters. This means that if the pool is filled 10 cm from the top the volume would be 65,000 liters, still more than if the three tankers are emptied completely into it.
You could have probably just done the second part, where we sbtracted 10 cm from each of the dimensions, but I am going to leave it all since I wrote it.
9514 1404 393
Answer:
Sam is not correct.
Step-by-step explanation:
As shown in the attachment, the "base" (front face) of this prism can be divided into a rectangle and a trapezoid. The relevant area formulas are ...
A = LW . . . . area of a rectangle of length L and width W
A = 1/2(b1 +b2)h . . . . area with parallel bases b1 and b2 and height h
__
The rectangle portion of the "base" of the pool has area ...
A = (10 m)(1 m) = 10 m²
The trapezoid portion of the "base" of the pool has area ...
A = 1/2(6 m +2 m)(1 m) = 4 m²
Then the "base" area is ...
B = 10 m² +4 m² = 14 m²
__
The volume of the prism is given by ...
V = Bh . . . . where B is the base area and h is the distance between bases
V = (14 m²)(5 m) = 70 m³
We are told that 1 m³ = 1000 L and that 3 tankers of 20,000 L each are emptied into the pool. That leaves an unfilled volume of ...
70 m³ -3×(20 m³) = 10 m³ . . . . unfilled volume
__
The surface area of the pool is ...
A = LW = (10 m)(5 m) = 50 m²
So the unfilled volume has a height of ...
V = Bh
10 m³ = (50 m²)h
h = (10/50) m = 20/100 m = 20 cm . . . . . the height of the unfilled space
The water in the pool will be 20 cm below the top, not 10 cm. Sam is not correct.
Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r<b
Step-by-step explanation:
Correct option is
C
0≤r<b
If r must satisfy0≤r<b
Proof,
..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..
clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.
Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,
a−bq=r
=>a=bq+r
As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b
Thus, we have
a=bq1+r1, 0≤r1≤b
If ⅔ of a number is 20 what is ½ of the number?
Answer:
15
Step-by-step explanation:
2/3 of 30 is 20, so 1/2 of 30 is 15
the answer is in the image above
Noel and Casey both start at the same place. Noel walks due south and Casey walks due east. After some time has passed, Noel is 6 miles south and Casey is 8 miles east. At this time, Noel is walking at a rate of 2 mph and Casey is walking at a rate of 1 mph. How fast is the distance between them increasing at this time
Answer:
2.04 miles per hour
Step-by-step explanation:
Given
Noel
[tex]n_1 =6miles[/tex]
[tex]r_1 = 2mph[/tex]
Casey
[tex]c_1 = 8miles[/tex]
[tex]r_2 =1mph[/tex]
Required
The rate at which the distance increases
Their movement forms a right triangle and the distance between them is the hypotenuse.
At [tex]n_1 =6miles[/tex] and [tex]c_1 = 8miles[/tex]
The distance between them is:
[tex]d_1 = \sqrt{n_1^2 + c_1^2}[/tex]
[tex]d_1 = \sqrt{6^2 + 8^2}[/tex]
[tex]d_1 = \sqrt{100}[/tex]
[tex]d_1 = 10miles[/tex]
After 1 hour, their new position is:
New = Old + Rate * Time
[tex]n_2 = n_1 + r_1 * 1[/tex]
[tex]n_2 = 6 + 2 * 1 = 8[/tex]
And:
[tex]c_2 = c_1 + r_2 * 1[/tex]
[tex]c_2 = 8 + 1 * 1 = 9[/tex]
So, the distance between them is now:
[tex]d_2 = \sqrt{n_2^2 + c_2^2}[/tex]
[tex]d_2 = \sqrt{8^2 + 9^2}[/tex]
[tex]d_2 = \sqrt{145}[/tex]
[tex]d_2 = 12.04[/tex]
The rate of change is:
[tex]\triangle d = d_2 -d_1[/tex]
[tex]\triangle d = 12.04 -10[/tex]
[tex]\triangle d = 2.04[/tex]
what is the answered
pp lssss answer
[tex]\boxed{ \underline{ \bf \: Categorical}} \sf \: data \: set \: is \: the \: data \: set \\ \sf \: that \: deals \: with \: only \: non \: numerical \: values.[/tex]
Optoion C. Categorial data set is the right answer of the question given.
RaonbowSalt2222
help me please it’s timed !!!
While
AB is A. 5Welcome :)Which fact is not used to prove that ABC is similar to DBE?
the angles of a triangle is 2x,3x and 5x find the value of x
Here,
2x+3x+5x = 180 (sum of all angles of triangle are equal to 180)
or, 10x = 180
or, x = 180/10
x = 18
Therefore, the value of x is 18.
Hope this solution may help you☺
Answer:
2x + 3x + 5x = 180(sum of all the interior angles of a triangle is 180° )
10x = 180°
x=180/10
x = 18°
(07.04 LC)What is the solution to the equation ax = 2?
Ox= 1
Ox=1
- کی
Ox= 3
O x = 12
Plz helppp
Answer:
x=12 .
Step-by-step explanation:
See image below:)
16. Rachael teaches at the college and it pays $3000 per month. She spends $50 on groceries per
week. Netflix costs $9 per month. She pays $50/month for internet. Utilities cost $200 per
month. Rachael's phone bill is $82 per month. Find the net monthly cash flow. (assume 1 month
= 4 weeks).
Answer: Rachel gets a total of 2459 dollars to save each month.
Step-by-step explanation:
200+9+50+200+82=541
3000-541=2459
6+t=1 pls help.............
6+T=1
Try T=-5
6+(-5) = 1
Correct, So...
T=-5
find slope from the pair of points (2,-2) (-5,4)
Answer:
-6/7
Step-by-step explanation:
If we have two points, we can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 4 - -2)/( -5 -2)
= ( 4+2) /(-5-2)
= 6/-7
= -6/7
what is the average rate of change between:
x=1 and x=2
x=2 and x=3
x=3 and x=4
Rate of change = RΔ = (y2-y1)/(x2-x1) = Δy/Δx
(X1,Y1)(X2,Y2)
(1, 2) (2, 4)
RΔ = Δy/Δx
= (4-2)/(2-1)
RΔ = 2
(2, 4) (3, 8)
RΔ = (8-4)/(3-2)
RΔ = 4
(3, 8) (4, 16)
RΔ = (16-8)/(4-3)
RΔ = 8
How do I solve this and answer?
Step-by-step explanation:
at first solve first triangle with Pythagorean solving witch it c²=a²+b²
you have to change a bit so it will be c²-b²=a²
you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²
This holiday season, Ms. Bastarache organized to give each 9th grader a $10 Dunkin Donuts gift card. Because she bought a lot of cards, Ms. Bastarache tipped the Dunkin Donuts employee $20.
This function represents the relationship between the number of gift cards, c, and T(c), the total cost of the cards.
T(c) = 10c + 20
Be sure to answer BOTH questions below.
1. Determine the total cost, in dollars, for Ms. Bastarache to give out 93 gift cards.
2. Last year, Ms. Bastarache spent $820, how many cards did she purchase?
need help asap plzzzzzz
Answer:
1. $950
2. 80
Step-by-step explanation:
I don't understand plz help
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.
(3x +24)° = 30°
3x = 6 . . . . . . . . . divide by °, subtract 24
x = 2 . . . . . . . . . . divide by 3
__
Additional comment
What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)
Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.
