The expression (4 + 5i)(4 - 5i) simplifies to 41, as the multiplication of complex conjugates yields a real number.
The expression (4 + 5i)(4 - 5i) is a product of two complex conjugates. When multiplied, the product of complex conjugates results in a real number because the imaginary parts cancel out. The multiplication proceeds as follows:
Multiplying the real parts: 4 * 4 = 16.
Multiplying the outer terms: 4 * (-5i) = -20i (but this will cancel out with the next step).
Multiplying the inner terms: 5i*4 = 20i (which cancels out the -20i from the outer multiplication).
Multiplying the imaginary parts: 5i * -5i = -25[tex]i^2[/tex]. Remembering that i^2 = -1, we simplify this to -25 * -1 = 25.
Adding the results from steps 1 and 4, we get 16 + 25 = 41.
Therefore, the simplified expression is 41.
Sarah has 2/3 gallon of blue paint and 7/12 gallon of red paint. If she has a total of 2 1/8 gallons of paint, how many gallons are neither red nor blue?
Select all of the following that are equivalent to 1/8. 0.125 0.18 12.5% 1.25%
Answer:
Hi, my friend! The answer to this questions are "0.125" and "12.5%"
Step-by-step explanation:
First, if you divide 1 by 8 using a calculator, you will see that the result will be 0.125. Also, the option 12,5% is correct because de symbol "%" means "divided by 100". If you check in the calculator, 12.5 divided by 100 will also be 0.125.
Hoping to be clear! Good luck!
Final answer:
Only 0.125 and 12.5% are equivalent to the fraction 1/8. This is because they both reflect a '125-like' number pattern which is crucial when identifying representations of 1/8 in decimal or percentage form.
Explanation:
The fraction 1/8 is equivalent to a few different representations in decimal and percentage forms.
To identify which options among 0.125, 0.18, 12.5%, and 1.25% are equivalent to 1/8, we should look for a number pattern resembling '125' as it indicates a connection to the fraction 1/8 or its reciprocal nature.
So, 0.125 is exactly 1/8 as a decimal, and 12.5% represents 1/8 in percentage form because 12.5% is 12.5 parts per 100, which can be equated to 125 parts per 1000, resembling the multiplication of 1000 by the reciprocal of 8, that is 0.125.
Therefore, the options 0.125 and 12.5% are equivalent to 1/8.
PLEASEEEE
In a school of 2000 students, the ratio of teachers to students is 3:80.
Some teachers join the school and the ratio changes to 1:20.
Find the number of teachers who joined the school.
Answer:
The answer to your questions is: 25 new teachers
Step-by-step explanation:
Data
# of students = 2000
ratio = 3:80 teachers to students
New teachers = ?
Process
I suggest to use rule of three to solve this problem
3 teachers ---------------- 80 students
x ---------------- 2000 students
x = (2000 x 3) / 80 = 75 teachers
Number of initial teachers = 75
The ratio change to 1:20
1 teacher ------------------- 20 students
x ------------------- 2000 students
x = (2000 x 1) / 20
x = 100 teachers
Number of new teachers = 100 - 75 = 25
Mr. Johnson has his newspaper delivered every day. He determines the probability the newspaper is on his front porch is 0.64. The rest of the time he finds the newspaper somewhere on his lawn. What is the probability that Mr. Johnson finds his newspaper on his lawn?
Answer:
Step-by-step explanation:
Probability of getting the newspaper on his front porch = P(A) = 0.64
Probability of finding the newspaper on his lawn = P(B) =? (We don't know, this is what we have to find.)
Total probability = 1
Formula, P(A) + P(B) = 1
Let's put all values in this formula,
0.64 + P(B) = 1
P(B) = 1 - 0.64
P(B) = 0.36
Thus, the probablity that Mr. Johnson finds his newspaper on his lawn is 0.36 or 36%.
Find the intersection of the three sets: A = {–4, 3, 10}, B = {3, 6, 10, 15}, C = {–4, 10, 20}. {–4, 10} {10} {–4, 3, 6, 10, 15, 20} {–4, 3, 10}
Answer:
The intersection is 10
Step-by-step explanation:
You just have to look at them and see what number is in all the sets.
Answer:
the answer is 10
Enter an inequality that represents the graph in the box.
Help please?
Answer:
Step-by-step explanation:
Easy. its [tex]x^{2} \int\limits^a_b {x} \, dx \\ \\ \left \{ {{y=2} \atop {x=2}} \right. \\ \neq \frac{x}{y} \beta \al\left \{ {{y=2} \atop {x=2}} \right. pha \neq \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \geq \\ \left \{ {{y=2} \atop {x=2}} \right. \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
The inequality that represents the graph is:
[tex]y\geq x+3[/tex]
Step-by-step explanation:By looking at the graph we observe that the graph is a solid line which passes through the point (-1,0) and (1,2).This means that the inequality is a inequality with a equality sign(i.e. not strict)
This means that the equation of line is:
[tex]y-2=\dfrac{2-0}{1-(-1)}\times (x-(-1))\\\\y-2=\dfrac{2}{2}\times (x+1)\\\\y-2=x+1\\\\y=x+1+2\\\\y=x+3[/tex]
The shaded region is away from the origin.
This means that the inequality does not pass the zero test.
Hence, the inequality is:
[tex]y\geq x+3[/tex]
I'd appreciate it if you were to help me! (20 pts)
Your first two tests add up to:
85 + 89 = 174
To average 87 for 3 tests, the tests need to add up to : 87 x 3 = 261
To average 91, the 3 tests need to equal: 91 x 3 = 273
So to average 87, the third test needs to be: 261 - 174 = 87
To average 91, the third test needs to be: 273 - 174 = 99
Your score needs to be between 87 and 99
A salesperson obtained a systematic sample of size 25 from a list of 500 clients. To do so, he randomly selected a number from 1 to 20, obtaining the number 13. He included in the sample the 13th client on the list and every 20th client thereafter. List the numbers that correspond to the 25 clients selected.
A.. 25, 45.......500
B. 20, 33,.., 332
C. 13, 33, , 488
D. 13, 33, ..., 493
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
First term = 13
Increase each time = 20
Number of clients = 25
So, it forms an arithmetic progression:
So, 25 th term would be
[tex]a_{25}=a+(n-1)d\\\\a_{25}=13+(25-1)\times 20\\\\a_{25}=13+24\times 20\\\\a_{25}=13+480\\\\a_{25}=493[/tex]
Hence, list would look like 13,33,............493.
Therefore, Option 'D' is correct.
A map of a rectangular park has a length of 4 inches and a width olo and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. a. What is the actual area of the park? Show how you know.
Answer:
The actual area of the park is 21,600 miles square.
Step-by-step explanation:
Step 1: Calculate the area of the park
Area of rectangle = Length x width
Length = 4 inches
Width = 6 inches
Scale factor is given as, 1 inch = 30 miles.
So, converting the length and width in miles by using the scale factor, we get
Length = 4 * 30 = 120 miles
Width = 6 * 30 = 180 miles
The formula of finding the area of an rectangle is:
Area = length x width
By putting the values in equation, we get
Area = 120 x 180
Area = 21,600 miles square
Therefore, the actual area of the park is 21,600 miles square.
An automobile accelerates from rest at 1.7 m/s 2 for 22 s. The speed is then held constant for 29 s, after which there is an acceleration of −5.8 m/s 2 until the automobile stops. What total distance was traveled? Answer in units of km.
After 22 s, the car has velocity
[tex]v=\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)=36.4\dfrac{\rm m}{\rm s}[/tex]
In this time, it will have traveled a distance of
[tex]\dfrac12\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)^2=411.4\,\mathrm m[/tex]
Over the next 29 s, the car moves at a constant velocity of 36.4 m/s, so that it covers a distance of
[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(29\,\mathrm s)=1055.6\,\mathrm m[/tex]
so that after the first 51 s, the car will have moved 1467 m.
After the 29 s interval of constant speed, the car's negative acceleration kicks in, so that its velocity at time [tex]t[/tex] is
[tex]v(t)=36.4\dfrac{\rm m}{\rm s}+\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)t[/tex]
The car comes to rest when [tex]v(t)=0[/tex]:
[tex]36.4-5.8t=0\implies t=6.3[/tex]
That is, it comes to rest about 6.3 s after the first 51 s. In this interval, it will have traveled
[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(6.3\,\mathrm s)+\dfrac12\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)(6.3\,\mathrm s)^2=114.2\,\mathrm m[/tex]
so that after 57.3 s, the total distance traveled by the car is 1581.2 m, or about 1.6 km.
A solar water heater costs about $6240 to install (after rebates). A traditional gas water heater costs about $850 and costs about $320 per year to run. The average annual cost to run the solar water heater is about $75
Create total cost functions for each of the water heaters as a function of the number of years that the heater is used
Answer:
For solar: [tex]S(x)=6240+75x[/tex]
For traditional: [tex]T(y)=850+320y[/tex]
Step-by-step explanation:
Cost to install solar water heater = $6240
The average annual cost to run the solar water heater is about = $75
Total cost to run x years : [tex]S(x)=6240+75x[/tex]
A traditional gas water heater costs about = $850
The average annual cost to run = $320
Total cost to run y years : [tex]T(y)=850+320y[/tex]
1. The total cost of a solar water heater, including installation and annual running costs, can be calculated as $6240 + ($75 * years).
2. The total cost of a traditional gas water heater, including installation and annual running costs, can be calculated as $850 + ($320 * years).
Given that,
Solar water heater:
Installation cost: $6240 (after rebates)
Annual running cost: $75
Traditional gas water heater:
Installation cost: $850
Annual running cost: $320
Let's create the total cost functions for each water heater as a function of the number of years.
For the solar water heater, the total cost (TC) can be calculated as:
TC_solar(years) = installation cost + (annual running cost * years)
Given the installation cost of $6240 and annual running cost of $75,
The total cost function for the solar water heater becomes:
TC_solar(years) = $6240 + ($75 * years)
For the traditional gas water heater, the total cost (TC) can be calculated as:
TC_gas(years) = installation cost + (annual running cost * years)
Given the installation cost of $850 and annual running cost of $320,
So, The total cost function for the gas water heater becomes:
TC_gas(years) = $850 + ($320 * years)
These equations allow you to determine the total cost of each water heater based on the number of years they are used.
To learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ3
Tomatoes are 5 for $2.keith spent $8 on tomatoes. How many tomatoes did he get
Answer:
20
Step-by-step explanation:
8/2 = 4
4 * 5 = 20
Which is the graph of f(x) = Square root of x?
On a coordinate plane, a parabola opens up with a vertex at (0, 0).
On a coordinate plane, an absolute value graph starts at (0, 0) and goes up through (2, 4).
On a coordinate plane, a parabola opens to the right with a vertex at (0, 0).
On a coordinate plane, an absolute value graph starts at (0, 0) and goes up through (4, 2).
Answer:
Third option given
Step-by-step explanation:
On a coordinate plane, a parabola opens to the right with a vertex at (0, 0).
use the following x values to plot the associated y values on the x-y plane:
If x = 0, then [tex]y=\sqrt{0} =0[/tex]
If x = 1, then [tex]y=\sqrt{1} =1[/tex]
If x = 4, then [tex]y=\sqrt{4} =2[/tex]
If x = 9, then [tex]y=\sqrt{9} =3[/tex]
Join the points and you will find a branch of a parabola opening to the right.
Answer:
The Answer is D
Step-by-step explanation:
on e2020 its the last graph
The Dulac Box plant produces 500 cypress packing boxes in two-10 hour shifts. Due to higher demand, Dulac has decided to operate three eight-hour shifts instead. Dulac is now able to produce 600 boxes per day. What has happened to production:a. It has increased by 50 sets/shiftb. It has increased by 20 percentc. It has increased by 37.5 sets/hrd. It has decreased by 8.3 percente. It has decreased by 9.1 percent.
Answer:
Production has increased 20/day
Step-by-step explanation:
In the first scenario production is 500/day and productivity 25 set/hour. After the changes, production is 600/day and 25 set/hour.
So productivity remains the same, nevertheless, as there are more productive hours per day, production raises, in this case the can be calculated as (New Production-Old Production)/Old Production=(600-500)/500=100/500=0.2=20%.
As productivity remains the same, you do not ge more sets/shift, as shifts are shorter (8 instead of hours, so you get 200/shift instead of 250/shift). The rest of the option is false as productivity remains constant
Genghis Khan organized his men into groups of 10 soldiers under a "leader of 10." Ten "leaders of 10" were under a "leader of 100." Ten "leaders of 100" were under a "leader of 1000." *(a) If Khan had an army of 10,000 soldiers at the lowest level, how many men in total were under him in his organization? (b) If Khan had an army of 5763 soldiers at the lowest level, how many men in total were under him in his organization? Assume that the groups of 10 should contain 10 if possible, but that one group at each level may need to contain fewer.
Genghis Khan's army organizational structure can be used to calculate the total number of men under him: For an army of 10,000 soldiers, the total is 11,110 men; for an army of 5,763 soldiers, it is 6,404 men.
To solve both parts of the student's question, we use the military organizational structure implemented by Genghis Khan that is based on the 'decimal' system. We start with the lowest level groups of 10 soldiers and move up in orders of magnitude (10, 100, 1,000, and 10,000).
Part (a): Army of 10,000 soldiers
Groups of 10: There are 1,000 groups of 10 in an army of 10,000 soldiers.
Leaders of 10: Each group of 10 has 1 leader, resulting in 1,000 leaders of 10.
Groups of 100: 1,000 leaders of 10 make up 100 groups of 100 (because 1,000/10 = 100).
Leaders of 100: There are 100 leaders of 100.
Groups of 1,000: 100 leaders of 100 make up 10 groups of 1,000 (because 100/10 = 10).
Leaders of 1,000: There are 10 leaders of 1,000.
Adding it all together: 10,000 soldiers + 1,000 leaders of 10 + 100 leaders of 100 + 10 leaders of 1,000 = 11,110 total men under the command of Khan for an army of 10,000.
Part (b): Army of 5,763 soldiers
Groups of 10: There are 576 full groups of 10 and 1 incomplete group (with 3 soldiers), resulting in 577 groups.
Leaders of 10: There are 577 leaders of 10.
Groups of 100: 577 leaders of 10 make up 57 full groups of 100 and 1 incomplete group (with 7 leaders of 10), resulting in 58 groups.
Leaders of 100: There are 58 leaders of 100.
Groups of 1,000: 58 leaders of 100 make up 5 full groups of 1,000 and 1 incomplete group (with 8 leaders of 100), resulting in 6 groups.
Leaders of 1,000: There are 6 leaders of 1,000.
Adding it all together: 5,763 soldiers + 577 leaders of 10 + 58 leaders of 100 + 6 leaders of 1,000 = 6,404 total men under the command of Khan for an army of 5,763 soldiers.
If the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets and the theater took in $584, how many of each ticket were sold?
Answer:
The number of child tickets sold was 43 and the number of adult tickets sold was 20
Step-by-step explanation:
Let
x ----> the number of child tickets sold
y ----> the number of adult tickets sold
we know that
[tex]x=3y-17[/tex] -----> equation A
[tex]8x+12y=584[/tex] ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (43,20)
see the attached figure
therefore
The number of child tickets sold was 43 and the number of adult tickets sold was 20
Answer:
Number of child tickets sold = 43
Number of adult tickets sold = 20
Step-by-step explanation:
Let the number of child ticket be c and number of adult ticket be a,
Given that the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets,
c = 3a - 17
3a - c = 17 ----------------------eqn 1
The theater received $584
That is
8 c + 12 a = 584 ----------------------eqn 2
eqn 2 /4
2 c + 3 a = 146 ----------------------eqn 3
eqn 3 - eqn 1 gives
2 c + 3 a - (3a - c) = 146 - 17
3 c = 129
c = 43
Substituting in eqn 1
3 x a - 43 = 17
3a = 60
a = 20
Number of child tickets sold = 43
Number of adult tickets sold = 20
A news service conducted a survey of 1019 adults ages 18 years or older in a certain country, August 31 September 2, 2015. The respondents were asked, "Of every tax dollar that goes to the federal government, how many cents of each dollar would you say are wasted?" Of the 1019 individuals surveyed, 36% indicated that 51 cents or more is wasted. The news service reported that 36% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 6% and a 99% level of confidence. Complete parts (a) through (e) below (a) What is the research objective?
A. To determine the number of adults in the country paying their taxes to the federal government
B. To determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar
C. To determine the number of adults in the country (b) What is the population? O A. The country's federal government O B. The 1019 adults in the country that were surveyed OC. Adults in the country aged 18 years or older O D. Adults in the world aged 18 years or older
c) What is the sample?
A. Adults in the country aged 18 years or older.
B. The country's federal government.
C. Adults in the world aged 18 years or older.
D. The 1019 adults in the country that were surveyed.
Answer:
(a) What is the research objectives?
B. To determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar.
(b) What is the population?
C. Adults in the country aged 18 years or older.
(c) What is the sample?
D. The 1019 adults in the country that were surveyed.
D. The 1019 adults in the country that were surveyed. The research objective is to determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar. The population is adults in the country aged 18 years or older. The sample is the 1019 adults in the country that were surveyed.
Explanation:The research objective of the survey conducted by the news service is B. To determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar.
The population in this study is C. Adults in the country aged 18 years or older.
The sample in this study is D. The 1019 adults in the country that were surveyed.
Ryan claims that any fraction located between 1/5 and 1/3 on a number line must have a denominator of 4. Enter a fraction that shows Ryan's Claim is incorrect.
let's firstly convert both fractions with the same denominator, by simply multiplying one by the denominator of the other, let's proceed,
[tex]\bf \cfrac{1}{5}\cdot \cfrac{3}{3}\implies \cfrac{3}{15}~\hspace{7em}\cfrac{1}{3}\cdot \cfrac{5}{5}\implies \cfrac{5}{15} \\\\[-0.35em] ~\dotfill\\\\ \boxed{\cfrac{3}{15}}\rule[0.35em]{10em}{0.25pt}~~\cfrac{4}{15}~~\rule[0.35em]{10em}{0.25pt}\boxed{\cfrac{5}{15}}[/tex]
well, low and behold, 4/15 doesn't simplify further and is right between those two, and its denominator is not 4.
What is the congruence statement for the given triangles?
Answer:
A triangle with three sides that are each equal in length to those of another triangle, for example, are congruent. This statement can be abbreviated as SSS. Two triangles that feature two equal sides and one equal angle between them, SAS, are also congruent.
Step-by-step explanation:
PLEASE I BEG U NOW!!
£130 is divided between Henry, Gavin & Jim so that Henry gets twice as much as Gavin, and Gavin gets three times as much as Jim. How much does Henry get?
Answer:
The answer to your question is: Henry gets £ 78
Step-by-step explanation:
Data
Henry = H
Gavin = G
Jim = J
Henry + Gavin + Jim = £ 130
H = 2G
G = 3J
Process
Write an equation in terms of G
H + G + J = 130
2G + G + G/3 = 130
Solve it for G
3( 2G + G + G/3 = 130)
6G + 3G + G = 390
10G = 390
G = 390 / 10
G = £39
H = 2G = 2(39)
H = £78
J = G/3
J = 39/3
J = £13
Final answer:
By setting up and solving algebraic equations, we find that Henry receives £78, which is twice the amount that Gavin receives and six times the amount that Jim receives from the total sum of £130.
Explanation:
Let's solve the problem by denoting Jim's share of the money as x. According to the problem, Gavin gets triple the amount of money that Jim gets, which means Gavin gets 3x. Henry gets twice as much as Gavin, so he gets 2(3x) or 6x. The total amount of money is £130 and the sum of their shares is x + 3x + 6x = 10x. Setting up the equation:
10x = £130,
we find that x, Jim's share, is £130/10 = £13. Gavin's share is 3 times Jim's: 3 × £13 = £39, and Henry's share is 6 times Jim's: 6 × £13 = £78. So Henry gets £78.
solve for m.
4+|7-m|=5
Answer:
m= 6 or m= 8. I'm not sure if its multiple choice, but that's what I got.
Answer:
m=6,8
Step-by-step explanation:
I am a number between 7 000 000 and 8 000 000 all my digits are odd all the digits in my thousands period are the same all the digits in my units period are the same the sum of my digits is 31 what number am i ?
Answer:
Any of 7,111,777 or 7,333,555 or 7,555,333 or 7,777,111.
Step-by-step explanation:
The first digit must be 7. The sum of the unknown digits is then 31-7 = 24. Since this represents 3 pairs of digits (a thousands period digit and a units period digit), each pair must total 24/3 = 8.
There are two ways that odd numbers can total 8: 1+7 = 3+5 = 8. Since there is no restriction on the digits other than they must be the same in any period and they must be odd, there are 4 ways the 2 pairs of digits can be arranged into a number:
7,111,7777,333,5557,555,3337,777,111Can anyone help me with these two problems? I found the distance to one. Please, assignment is due tonight. Thank you.
Answer:
32 mi @ N77°E
Step-by-step explanation:
The route of travel forms legs of a right triangle, so the final distance (d) from harbor can be found using the Pythagorean theorem:
d² = 28² +16² = 784 +256 = 1040
d = √1040 ≈ 32.249 . . . miles
___
The angle (α) added to the original N47°E bearing can be found using the fact that opposite and adjacent sides are given. So, they can tell you the tangent of the angle:
tan(α) = 16/28
α = arctan(16/28) ≈ 29.74°
Then the bearing to the final position is ...
47° +29.74° = 76.74° . . . . . east of north
Rounded to whole numbers, the final position from harbor is ...
32 miles @ N 77° E
The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take. A. Solve the equation for x.
Answer:
[tex]x=(c-60)/85[/tex]
Step-by-step explanation:
we have
[tex]c=85x+60[/tex]
Solve for x
That means -----> isolate the variable x
subtract 60 both sides
[tex]c-60=85x+60-60\\c-60=85x[/tex]
Divide by 85 both sides
[tex](c-60)/85=85x/85\\(c-60)/85=x[/tex]
Rewrite
[tex]x=(c-60)/85[/tex]
What is a purpose of a financial institution?
A.
buying back video games
B.
giving away money
C.
selling groceries
D.
lending money
Answer:
B
Step-by-step explanation:
Giving away money because individuals loan dollars to other entitles at a a cost
Answer:
D. lending money
Step-by-step explanation:
It depends on the institution. A "for profit" financial institution has the purpose of making money for its investors. To do that, it offers a variety of money-oriented services, some involving payments to customers (interest) and some involving charging customers for the service (fees or interest).
A service offered in the latter category is "lending money."
__
A "not for profit" financial institution has the purpose of providing financial services to its members. Again, some of these services may involve payments to customers, and others may involve collecting interest or fees from customers. These institutions, too, offer the service of "lending money."
__
Among the services a financial institution may offer that do not involve lending money are ...
checking accountssafe deposit boxesnotary servicebrokerage serviceConsider the three functions below.
f(x) = Negative StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript x g(x) = StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript negative x h(x) = Negative StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript negative x
Which statement is true?
The range of h(x) is y > 0.
The domain of g(x) is y > 0.
The ranges of f(x) and h(x) are different from the range of g(x).
The domains of f(x) and g(x) are different from the domain of h(x).
Answer:
The range of g(x) is y > 0
The ranges of f(x) and h(x) are different from the range of g(x)
Step-by-step explanation:
we have
[tex]f(x)=-(\frac{6}{11})^{x}[/tex]
[tex]g(x)=(\frac{6}{11})^{-x}[/tex]
[tex]h(x)=-(\frac{6}{11})^{-x}[/tex]
Using a graphing tool
see the attached figure
Verify each statement
case A) The range of h(x) is y > 0.
The statement is false
The range of h(x) < 0
case B) The range of g(x) is y > 0. (Note the statement is The range of g(x) is y > 0 instead of The domain of g(x) is y > 0)
The statement is true (see the attached figure)
case C) The ranges of f(x) and h(x) are different from the range of g(x)
The statement is true (see the attached figure)
Because
The ranges of f(x) and h(x) are y < 0
and
The range of g(x) is y > 0
case D) The domains of f(x) and g(x) are different from the domain of h(x)
The statement is false
The domain of the three functions is the same
Answer:
OPTION C.The ranges of f(x) and h(x) are different from the range of g(x).
Step-by-step explanation:
Today a typical family of four spends $897.20/ month for food. If inflation occurs at the rate of 3%/ year over the next 6 years, how much should the typical family of four expect to spend for food 6 years from now?
Answer:
1071.30 per month
Step-by-step explanation:
The multiplier each year is 1 + .03 = 1.03. After 6 years, the cost has been multiplied by that factor 6 times, so has been multiplied by 1.03⁶ ≈ 1.194052.
$897.20 × 1.194052 ≈ $1071.30
The typical family of four should expect to spend $1,056.27 per month for food six years from now.
1. Calculate the inflation factor using the formula: [tex]\( (1 + \text{inflation rate})^{\text{number of years}} \).[/tex]
- Inflation rate = 3% or 0.03
- Number of years = 6
- Inflation factor = [tex]\( (1 + 0.03)^6 = 1.191016 \)[/tex]
2. Multiply the current monthly food expenditure by the inflation factor to find the expected expenditure six years from now.
- Current expenditure = $897.20/month
- Expected expenditure = $897.20 × 1.191016 = $1,056.27/month
Therefore, the typical family of four should expect to spend $1,056.27 per month for food six years from now if inflation occurs at a rate of 3% per year.
An equation of the secant line containing (4, h(4)) and (6, h(6)) is
Answer:
y= (h(6)-h(4))/2x +C
Where C=-2*h(6)+3*h(4)
Step-by-step explanation:
The secant line is the line that meets a function (in this case h(x) ) in two points, so we have to apply the ecuation of a straigt line that meets two points:
y-y1 = (y2-y1)/(x2-x1) * (x-x1)
In this case X1=4 , x2=6, y1 = h(4) and y2= h(6)
So
y-h(4)= 1/2 (h(6)-h(4)) * (x-4)
y-h(4)= 1/2 (h(6)-h(4)) x- 2 *(h(6)-h(4))
y-h(4)= 1/2 (h(6)-h(4)) x- 2 (h(6) + 2h(4))
y= 1/2 (h(6)-h(4)) x- 2 h(6) + 2h(4) + h(4)
y= 1/2 (h(6)-h(4)) x- 2 h(6) + 3h(4)
Good Luck!
*****************************************************************************
Dont forget to rate my answer if it was helpful!
Chocolates costing $8 per pound are to be mixed with chocolates costing $3 per pound to make a 20 pound mixture. If the mixture is to sell for $5 per pound, how many pounds of each chocolate should be used? Which of the following equations could be used to solve the problem? 8x + 3x = 5(20) 8x + 3(20) = 5(x + 20) 8x + 3(20 - x) = 5(20)
Answer:
8x + 3(20 - x) = 5(20)
Step-by-step explanation:
If x represents the number of pounds of $8 chocolates, then (20-x) is the number of pounds of $3 chocolates. The cost of the mix attributable to the $8 chocolates will be 8x, and the cost associated with the $3 chocolates will be 3(20-x). The sum of these costs is the cost of the 20 pounds of mix: $5×20.
In equation form, this is ...
8x + 3(20-x) = 5(20)
_____
The solution is x=8, so 8 lb of $8 chocolates should be mixed with 12 lb of $3 chocolates to make a mix worth $5 per pound.
Final answer:
The correct equation to determine the pounds of each type of chocolate for the mixture is 8x + 3(20 - x) = 5(20), where x represents the pounds of the $8 chocolate.
Explanation:
To solve for how many pounds of each type of chocolate should be used in the mixture, let's designate x as the number of pounds of the $8 chocolate and 20-x as the number of pounds of the $3 chocolate. The total cost of the $8 chocolate will be 8x dollars, and the total cost of the $3 chocolate will be 3(20-x) dollars. The total sales price for the 20-pound mixture must be $5 per pound, which equals $100 (since 20 pounds × $5 per pound = $100). Therefore, the correct equation that represents the situation is 8x + 3(20 - x) = 5(20).
Let's break down this equation:
The $8 chocolate: 8x dollars
The $3 chocolate: 3(20 - x) dollars
Total cost: 8x + 3(20 - x)
The mixture sells for: $5 × 20
The equation balances the cost of both chocolates with the selling price of the mixture.
Many states have programs for assessing the skills of students in various grades. The Indiana Statewide Testing for Educational Progress (ISTEP) is one such program. In a recent year, 76,531 tenth-grade Indiana students took the English/language arts exam. The mean score was 572 and the standard deviation was 51. Use the fact that the ISTEP scores are approximately Normal, N(572, 51). Find the proportion of students who have scores between 500 and 650.
Answer:
P ( 500<X<650 ) = 0.8577
Step-by-step explanation:
Since μ=572 and σ=51 we have:
P ( 500<X<650 ) = P ( 500−572< X−μ<650−572 )
[tex]\RightarrowP ( \frac{500-572}{51} < \frac{x-\mu}{\sigma} < \frac{650-572}{51})[/tex]
⇒ P ( 500<X<650 ) = P ( −1.41<Z<1.53 )
Now, Using the standard normal table to conclude that:
P ( −1.41< Z <1.53 ) = 0.8577
Final answer:
Approximately 85.77% of Indiana tenth-grade students scored between 500 and 650 on the English/language arts ISTEP exam, as calculated by converting the given scores to z-scores and finding the proportion within the standard normal distribution.
Explanation:
To find the proportion of Indiana tenth-grade students who scored between 500 and 650 on the English/language arts exam, given that the ISTEP scores are approximately normal with a mean (μ) of 572 and a standard deviation (σ) of 51, we can use the standard normal distribution.
First, we'll convert the scores to z-scores using the formula z = (X - μ) / σ where X is the score.
For X=500, the z-score would be (500 - 572) / 51 ≈ -1.41.For X=650, the z-score would be (650 - 572) / 51 ≈ 1.53.Then we'll look up these z-scores in a standard normal distribution table or use a calculator with normal distribution functions to find the proportion of students whose scores fall between these two z-scores. The table or calculator will provide us with the areas under the curve to the left of each z-score.
Let's assume the area to the left of z=-1.41 is approximately 0.0793 (7.93%) and to the left of z=1.53 is approximately 0.937 (93.7%). To find the proportion between 500 and 650, we'll subtract the smaller area from the larger one:
Proportion = Area to the left of z=1.53 - Area to the left of z=-1.41 = 0.937 - 0.0793 = 0.8577 or 85.77%
Therefore, approximately 85.77% of the students scored between 500 and 650 on the ISTEP English/language arts exam.