Answer:
2/3
Hope this helps
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.
g(x) = f(x − 3) + 4
A.
The graph of function f is shifted left 3 units and up 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted right 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and down 4 units.
The graph of function f is shifted right 3 units and up 4 units.
Let f(x) be the parent function
Now use the Rule : f(x)→f(x-b) to find the shifting of graph
The graph shifts right by b units
So, shift the graph by 3 unit
So, f(x)→f(x-3)
So, the graph shifted right by 3 units
2nd rule used is Rule : f(x)→f(x)+b to find the another shifting of graph
The graph shifts up by b units
Now shift the obtained graph up by 4 units
So, f(x-3)→f(x-3)+4
So, the graph shifts up by 4 units
Thus, The graph of function f is shifted right 3 units and up 4 units.
Learn more about GRAPH here https://brainly.com/question/4025726
#SPJ1
Super confused need help
The Apollo space program lasted from 1967 until 1972 and included 13 missions.The missions lasted from as little as Z hours to as long as 30ours.The duration of each flight is listed below. 9 195 241 295 142% 142% 147 a.Expain why the flight times b.Find Mean and the Median of flight times c.Find range and the standard deviation of flight times
The mean and the median based on the information given will be 166.08 and 195.
How to calculate the value?It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.
The median is simply the middle number. This will be 195.
The range will be:
= 301 - 7
= 294
Learn more about mean on:
brainly.com/question/1136789
#SPJ1
The population of a city is modeled by the equation P(t)=232012e0.23t where t is measure in years. If the city continues to grow at this rate, approximately how many years will it take for the population to reach one million? Round your answer to two decimal places
In around 6.35 years, the population will be 1 million.
how many years will it take for the population to reach one million?
The population is modeled by the exponential equation:
[tex]P(t) = 232,012*e^{0.23*t}[/tex]
Then we just need to solve the equation for t:
[tex]P(t) = 232,012*e^{0.23*t} = 1,000,000[/tex]
Let's solve that:
[tex]232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\[/tex]
If we apply the natural logarithm to both sides:
[tex]ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35[/tex]
So in around 6.35 years, the population will be 1 million.
If you want to learn more about exponential equations:
https://brainly.com/question/11832081
#SPJ1
Question 3(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 6x +8=0 into the form (x-p)² =q?
[p and q are integers]
The correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
Vertex form of a quadratic equationThe vertex form of a quadratic equation is expressed as:
a(x-h)² + k
Given the quadratic equation
x^2 + 6x +8=0
Subtract 8 from both sides
x^2 + 6x +8 - 8 = 0 - 8
x^2 + 6x = -8
Complete the square
(x^2+6x+3^2) = -8 + 9
(x+3)² = -8 + 9
(x+3)² = 1
Hence the correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
learn more on completing the square here: https://brainly.com/question/13981588
#SPJ1
Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
When [tex]n=0[/tex], we have
[tex]5^{3^0} + 1 = 5^1 + 1 = 6[/tex]
[tex]3^{0 + 1} = 3^1 = 3[/tex]
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for [tex]n=k[/tex], that
[tex]3^{k + 1} \mid 5^{3^k} + 1[/tex]
Now for [tex]n=k+1[/tex], we have
[tex]5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)[/tex]
so we know the left side is at least divisible by [tex]3^{k+1}[/tex] by our assumption.
It remains to show that
[tex]3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1[/tex]
which is easily done with Fermat's little theorem. It says
[tex]a^p \equiv a \pmod p[/tex]
where [tex]p[/tex] is prime and [tex]a[/tex] is any integer. Then for any positive integer [tex]x[/tex],
[tex]5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3[/tex]
Furthermore,
[tex]5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3[/tex]
which goes all the way down to
[tex]5^{3^k} \equiv 5 \pmod 3[/tex]
So, we find that
[tex]\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3[/tex]
QED
Exponentiation is the raising of one number to the power of another. This operation is performed using two asterisks **. Let's use exponentiation to solve a known problem. You are offered a choice of either $1.000.000 or $0.01 (one penny) doubled every day for 30 days (the resulting amount is doubled every day). Task: Write a program to calculate the amount that will result from the doubling to understand which choice results in a larger amount. Hint: Let's see how exponentiation can be useful to perform the calculation. For example, if we want to calculate how much money we will have on the 5th day, we can use this expression: 0.01*(2**5) = 0.32 dollars (multiply the penny by 2 raised to the power of 5).
In math, Exponentiation refers to the operation of raising one quantity to the power of another. See the program running the exponentiation below.
What is the required code?The code is given below:
number_of_days = 30
amount_after_30days = 0.01 * (2 ** number_of_days)
# print the amount
print(amount_after_30days)
Learn more about exponentiation at;
https://brainly.com/question/11975096
#SPJ1
WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40
Answer:
20
Step-by-step explanation:
20+20=40
Find a12 given the geometric sequence 4, 8, 16, 32, ...
A. 32,768
OB. 8192
OC. 16,384
D. 4096
Reset Selection
The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)
How to find a determined element of a geometric sequence by exponential formulae
Sequences are series of elements generated according to at least one condition, usually equations. geometric sequences are generated according to a exponential formulas, whose form and characteristics are described below:
f(n) = a · bⁿ ⁻ ¹ (1)
Where:
a - First element of geometric sequenceb - Common ratio of the geometric sequencen - Element index within the geometric sequenceIf we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:
f(12) = 4 · 2¹² ⁻ ¹
f(12) = 4 · 2¹¹
f(12) = 4 · 2,048
f(12) = 4,096
The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)
To learn more on geometric sequences: https://brainly.com/question/4617980
#SPJ1
Represent the following situation using Venn diagrams and answer the questions that follow. In a survey of 100 students in the institute language studies at oxford university, the number of students studying various languages in last four years were found to be : Italian 28, German 30,French 42,Italian and French 10, Italian and German 8, German and French 5, all the three languages 3. (1 point each) a. Venn diagram. b. How many students are studying none of the languages? c. How many students had French as their only language? d. How many students are studying at least one of the languages?
There are 80 students studying at least one language
The Venn DiagramThe given parameters are:
Italian = 28German = 30French = 42Italian and French = 10Italian and German = 8German and French = 5Three languages = 3Using the above parameters, we have:
German and French only = 5 - 3 = 2
Italian and French only = 10 - 3 = 7
Italian and German only = 8 - 3 = 5
French only = 42 - 7 - 2 - 3 = 30
German only = 30 - 2 - 5 - 3 = 20
Italian only = 28 - 7 - 5 - 3 = 13
See attachment for the Venn diagram
Students studying none of the languagesThis is calculated as:
None + At least one = Total
Using the Venn diagram, we have:
None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100
This gives
None + 80 = 100
Subtract 80 from both sides
None = 20
Hence, there are 20 students studying none of the languages
Students studying French onlyThis is calculated as
French only = French - French and Italian - French and German + All three
So, we have:
French only = 42 - 10 - 5 + 3
Evaluate
French only = 30
Hence, there are 30 students studying French only
Students studying at least oneIn (b), we have:
None + At least one = Total ⇒ None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100
By comparing both equations, we have
At least one = 3 + 2 + 5 + 7 + 13 + 20 + 30
This gives
At least one = 80
Hence, there are 80 students studying at least one language
Read more about Venn diagram at:
https://brainly.com/question/4910584
#SPJ1
Identify all rays and lines in the picture below.
The rays and lines in the picture are as follows;
rays: BD, AC and AB
lines: AC
What are rays and lines?A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.
A ray is named using its endpoint first, and then any other point on the ray
A line segment has two endpoints.
Therefore, the rays and lines are as follows:
rays: BD, AC and AB
lines: AC
learn more on rays and lines here: https://brainly.com/question/13486760
#SPJ1
The coconut milk is in a can but he doesn’t know how much the can holds.
The can is 12 cm high and the diameter is 8 cm.
Using the formula V = π r2 h, work out how much coconut milk is in the can.
Use 3 as a value for π.
Give your answer using the correct units.
Fill in the blank 57.59 - ___=1.29
Answer: 57.59- 56.3=1.29
Step-by-step explanation:
57.59-x = 1.29
-x= 1.29-57.59
(—) -x= - 56.3
x=56.3
(-2) * n * (8) * n * (-n)
Answer:
16[tex]n^{3}[/tex]
Step-by-step explanation:
we evaluate from left side to right side
so -2*n =-2n
-2n *8 = -16n
-16n * n =-16n^2
-16 n * -n =16 n^3
hope this helps
Determine whether the relation represents y as a function x. x=y^2
It is false that x is a function of y
How to determine the true statement?The equation is given as:
x = y^2
Set y = 2
x = (2)^2
x = 4
Set y = -2
x = (-2)^2
x = 4
Different values of y give the same x value.
This means that x is not a function of y
Read more about functions at:
https://brainly.com/question/12431044
#SPJ1
PLEASE IF ANYONE CAN HELP I HAVE 35 MINUTES LEFT 1-8 ANSWERS ONLY WILL DO THANK YOU
Answer:
1. x=2 2.
y=1
Step-by-step explanation:
Im sorry I TRIED :(
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share. Thereafter, dividends are expected to growth at a constant rate of 6% per year. The discount rate for TYK is 10%. How much would you pay for one share in Company TYK?
14.11 is the price of one share in the company TYK.
How much would you pay for one share in Company TYK?Given:
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share.Dividends are expected to grow at a constant rate of 6% per year.The discount rate for TYK is 10%.Find:
How much would you pay for one share in Company TYK?Solution:
The dividend is the amount paid to the shareholders for their investment in the company.
Dividend at end of 7th year = $1 per share (given)
dividend expected growth rate = 6% (given)
the dividend will be paid from the end of seven years.
So find the price of the share at the end of the 6th year.
price at the end of the 6th year
= Dividend at the 7th year/discount rate growth rate
= 1/(10%-6%) = 1/4% = 25
price of the share at the end of the 6th year is $25
discount price 10% (given)
current price share = 25/(1+10%)^6
= 25/(1.1)^6
= 25/1.77
= 14.11
The current price of the share is $ 14.11
To learn more about rate percent, refer to:
https://brainly.com/question/21509987
#SPJ9
Teacher increases spatial awareness for children as they use position words and provide experience through mapping and manipulating shapes.
a. True
b. False
It is true teachers can increase spatial awareness as they use position words or implement mapping and shape manipulation.
Whatis spatial awareness?This refers to the ability to understand the position of one's body in relation to space and other objects as well as understanding how location and movement work.
How can spatial awareness be increased in children?In children spatial awareness can be increased through:
Positionoing wordsDancingMappingShape manipulationAmong othersLearn more about spatial awareness in: https://brainly.com/question/22442769
#SPJ1
I need to find the area for this shape I’ve tried several different ways and still no answer please help
Answer:
c) 212 sq ft
Step-by-step explanation:
I don't know which ways you tried, but I will show you three different ways, and the answer will be the same using all three ways.
1) The length of the upper horizontal side is 8 ft + 12 ft = 20 ft
Think of a rectangle 20 ft by 16 ft with a rectangle 12 ft by 9 ft missing at the lower right corner.
area = 20 ft × 16 ft - 12 ft × 9 ft
area = 320 ft² - 108 ft²
area = 212 ft²
2) Break up the shape into an upper horizontal rectangle 20 ft long by (16 ft - 9 ft) = 7 ft wide and a lower left rectangle 9 ft high and 8 ft wide.
area = 20 ft × 7 ft + 9 ft × 8 ft
area = 140 ft² + 72 ft²
area = 212 ft²
3) Break up the shape into an left vertical rectangle 16 ft high by 8 ft wide and an upper right rectangle 7 ft high and 12 ft wide.
area = 16 ft × 8 ft + 7 ft × 12 ft
area = 128 ft² + 84 ft²
area = 212 ft²
Answer: c) 212 sq ft
Answer:
Step-by-step explanation:
espero ter ajudado
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer:
all real values of x where x < -1
Step-by-step explanation:
See attached graph.
As seen in the diagram below, Shandra is building a walkway with a width of feet
to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the
pool and the walkway will be 168 square feet, how wide should the walkway be?
The walkway should be about 2.57feet.
What is the total surface area?
The total surface area of the building is the sum of the total faces of an object contains.
The formula is expressed as:
TSA = 2(lw + wh + lh)
where,
l is the length ,w is the width , h is the height
Calculation
Given the following parameters
TSA = 168 square feet
length = 8 feet and Height = 6 feet
Required
Width of the walkway, Substitute the given values in the formula
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
4w = 84 - 48
14w = 36
w = 2.57feet
The walkway should be about 2.57feet.
Learn more about total surface area here:
https://brainly.com/question/27537575
#SPJ1
(7)/(3) of it is 5 (5)/(6)
let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}[/tex]
What is the range of y = log Subscript 8 Baseline x?
The range of [tex]y =\log_8(x)[/tex] is the set of all real values
How to determine the range?The function is given as:
[tex]y =\log_8(x)[/tex]
The above function is a parent logarithmic function.
The parent logarithmic function have a range of the set of all real values
Hence, the range of [tex]y =\log_8(x)[/tex] is the set of all real values
Read more about range at:
https://brainly.com/question/10197594
#SPJ1
Answer:
D
Step-by-step explanation:
on edg
Jason’s utility and telephone bills for the month totaled $180. The utility bill was 3 times as much as the telephone bill. How much was each bill?
Answer:
telephone was $45, utility was $135
Step-by-step explanation:
Let the telephone bill be x, then the utility bill is 3x
3x+x = 180
4x = 180
x = 45
3x = 135
The following contingency table gives the results of a sample survey of Sowetan male and female respondents regarding their preferred mobile phone service provider.
What is the probability of selecting a respondent who does not prefer Cell C?
a.
0.2250
b.
0.50
c.
0.3750
d.
0.65
e.
0.7750
The probability of selecting a respondent who does not prefer Cell C is 0.775
How to determine the probability?The complete question is in the attached image
From the attachment, we have
Prefer cell C = 90
Total = 400
So, the number of respondents that do not prefer cell C is
Do not = 400 - 90
Do not = 310
The probability is then calculated as:
P = 310/400
Evaluate
P = 0.775
Hence, the probability of selecting a respondent who does not prefer Cell C is 0.775
Read more about probability at:
https://brainly.com/question/12090187
#SPJ1
Which function is graphed below?
The function that represents the given trigonometric graph is; f(x) = cos (x)
How to Interpret Trigonometric Graphs?From the given trigonometric Graph, we can see the following;
When x = 0, y = 1
When x = π/2, y = 0
When x = π, y = -1
When x = 2π, y = 1
Now, according to trigonometric functions in radians, we know that;
cos 0 = 1
cos π/2 = 0
cos π = -1
cos 2π = 1
These values correspond with what we have in the given trigonometric graph and as such we can say that the function that is graphed is;
f(x) = cos (x)
Read more about Trigonometric Graphs at; https://brainly.com/question/24329125
#SPJ1
Fill in the blank with a number to make the expression a perfect square. v^(2)-10v+
The number makes the expression a perfect square trinomial is 25.
Hence, we have v² - 10v + 25.
What number makes the expression a perfect square?
Given the expression; v² - 10v
To determine the number that makes the expression a perfect square trinomial, we divide the coefficient of v by 2 and square the result.
( -1 × 10/2 )²
(-1 × 5)²
( -5 )²
25
We add 25 to the expression to get a perfect square trinomial.
v² - 10v + 25.
Therefore, the number makes the expression a perfect square trinomial is 25.
Hence, we have v² - 10v + 25.
Learn more about perfect square here: https://brainly.com/question/385286
#SPJ1
Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]The composite function is of the given functions f(x) and g(x) is:
[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
[tex]x + 3 \geq 0[/tex]
[tex]x \geq -3[/tex]
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
[tex]\sqrt{x + 3} - 3 \neq 0[/tex]
[tex]\sqrt{x + 3} \neq 3[/tex]
[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]
[tex]x + 3 \neq 9[/tex]
[tex]x \neq 6[/tex]
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
More can be learned about composite functions at https://brainly.com/question/13502804
#SPJ1
Is this Network a HAMILTONIAN Circuit? If so write the path.
The path of the given Hamiltonian diagram is A, E, B, C, D, F. See explanation below.
What is a Hamiltonian Path?A Hamiltonian path, also known as a traceable path, is one that visits each vertex of the graph precisely once.
A traceable graph is one that contains a Hamiltonian path.
Hence, the path is given as;
A, E, B, C, D, F
Learn more about Hamiltonian Paths at;
https://brainly.com/question/15521630
#SPJ1
Sharon is planting tulip
bulbs in her garden. In the
catalog she sees a disclaimer that there is a 1/15 probability that a bulb will not flower. If Sharon plants 90 bulbs, how many tulips can she expect to see in her garden?
Answer:
84 flowers.
Step-by-step explanation:
We must multiply 90 by 1/15 to get 6 bulbs that will not flower. 90-6 is 84.