Answers
Answer:
19 m
Step-by-step explanation:
This is Geometric progression with
[tex]\left \{ {{u_1=1,\: u_2 =2} \atop {u_n=2^{n-1}u_1} \right.[/tex]
Then the fomular of sum is
[tex]S=u_1\frac{2^n-1}{2-1} =1\times(2^n-1)=2^n-1\\To\: save\: 1 \:million\: then \; our \:sum \: will \: be\: 1000000\\Hence,\\2^n-1=1000000\\2^n=1000001\\n=log_{2}{1000001}\approx19,9\\Thus, it\:would \;be \:19 \:months \:before\: we\: saved \:1000000 \:pounds[/tex]
Related Questions
Could anyone help me with this please?
Answers
Answer: Yes, it does. Because each input value has one and only output value.
Step-by-step explanation:
By definition, a relation is a function when each input value has one and only output value.
Then, to know if the table represents a function, you need to observe if each input value (in other words, each value of the variable "x") has only one output value (the output values are the values of the variable "y").
You can observe that each value of "x" has only one value of "y", therefore, you can conclude that the given table represents a function.
You are dealt one card from a 52-card deck. Find the probability that you are dealt a three or a red card.
Answers
16 is the amount of red cards and 3’s in a pack of 52 cards since one four has to be red it would 13 then add three since one of the three’s is a red u don’t count that and u get 16/52
Answer:
7/13
Step-by-step explanation:
26 cards are red. 2 are black threes. So the probability that a card is a three or red is 28/52, which reduces to 7/13.
Which set of ordered pairs represents a function?
O {(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)}
O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}
O {(6, 8), (5,2), (-2,-5), (1, -3), (-2, 9)}
O {(-3, 1), (6,3), (3, 2), (-3, -3), (1, -1)}
Answers
Answer:
{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}
Step-by-step explanation:
Any relation having repetitive x-coordinates, is NOT a function.
{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}, is the set of ordered pairs represents a function. So, the option B is correct.
Here, we have,
A set of ordered pairs represents a function if each input (x-value) is associated with exactly one output (y-value).
Let's examine the given options:
O {(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)}: This set does not represent a function because the input value 1 is associated with both 5 and -3.
O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}: This set represents a function since each input value is associated with a unique output value.
O {(6, 8), (5,2), (-2,-5), (1, -3), (-2, 9)}: This set does not represent a function because the input value -2 is associated with both -5 and 9.
O {(-3, 1), (6,3), (3, 2), (-3, -3), (1, -1)}: This set does not represent a function because the input value -3 is associated with both 1 and -3.
Therefore, the set of ordered pairs that represents a function is:
O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}
Hence, {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}, is the set of ordered pairs represents a function. So, the option B is correct.
To learn more on function click:
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URGENT
Which of the following is the graph of y=0.5sec (x+pi/3)-2?
Answers
Answer:
See attachment.
Step-by-step explanation:
The given function is
[tex]y=0.5\sec(x+\frac{\pi}{3})-2[/tex]
This is the graph of [tex]y=\sec(x)[/tex] that is shifted down 2 units and shifted to the left [tex]\frac{\pi}{3}[/tex] units.
When x=0, [tex]y=0.5\sec(0+\frac{\pi}{3})-2[/tex]
[tex]y=0.5\sec(\frac{\pi}{3})-2[/tex]
[tex]y=1-2=-1[/tex]
The y-intercept is -1.
The correct choice is shown in the attachment
Answer:
The attached graph is the answer
Step-by-step explanation:
* Lets revise the trigonometry translation
- If the equation is y = A sec(B(x + C)) + D
# Amplitude is A
- The Amplitude is the height from the center line to the peak .
Or we can measure the height from highest to lowest points and
divide that by 2
# period is 2π/B
- The Period goes from one peak to the next
# phase shift is C (positive is to the left)
- The Phase Shift is how far the function is shifted horizontally
from the usual position.
# vertical shift is D
- The Vertical Shift is how far the function is shifted vertically from
the usual position.
- If y = sec(x)
∴ A = 1 , B = 1 , C = 0 , D = 0
- That means the amplitude is 1, the period is 2π, no phase shift
or vertical shift
* Now lets solve the problem
∵ y = 0.5 sex(x + π/3) - 2
∴ A = 0.5
- The 0.5 tells us it will be half times taller than usual,
so Amplitude = 0.5
∴ B = 1
- The period is 2π
∴ C = π/3
- The π/3 means it will be shifted to the left by π/3
∴ D = -2
- The -2 tells us the vertical Shift = -2
* Lets calculate the y-intercept
- To find the y-intercept put x = 0
∴ y = 0.5 sec(0 + π/3) - 2
∵ sec(π/3) = 2
∴ y = 0.5(2) - 2 = 1 - 2 = -1
* Now lets look to the graphs to find the correct answer
- Only one graph has y-intercept is -1
- Look to the attached graph
- There is a vertical shift down 2 units
- There is a horizontal shift to the left by π/3 units
- The amplitude is 1/2 ⇒ (-1.5 - -2.5)/2 = 1/2, where -1.5 and -2.5
are the peak points
- The y-intercept is -1
* The attached graph is the answer
- For more understand look to the attached color graph
- The blue graph is y = sec(x)
- The red graph is y = 0.5 sec(x + π/3) - 2
The length of segment AB is 9 mm.
Which statements regarding triangle ABC are correct? Check all that apply.
AB is the shortest segment in △ABC.
BC = 18mm
AC = 2AB
AC = BC is the longest segment in △ABC
Answers
Answer:
1 and 3
AB is the shortest segment in △ABC.
AC = 2AB
Step-by-step explanation:
Enjoy!!
Answer:
1. AB is the shortest segment in △ABC.
3. AC = 2AB
Step-by-step explanation:
edge24
A pole that is 2.8 m tall casts a shadow that is 1.21 m long. At the same time, a nearby tower casts a shadow that is 48.75 m long. How tall is the tower? Round
Answers
Answer:
112.81 m.
Step-by-step explanation:
The pole and the tower and their shadows form 2 similar triangles so their corresponding sides are in the smae ratio.
Therefore we have the relation:
1.21 / 48.75 = 2.8 / x where x is the height of the tower.
Cross multiplying:
x = 2.8 * 48.75 / 1.21
= 112.81 m
Final answer:
To find the height of the tower, we use the proportion 2.8 m / 1.21 m = H / 48.75 m. After cross-multiplication and division, the height of the tower is calculated to be approximately 112.81 meters.
Explanation:
The student's question involves using similar triangles to determine the height of a tower based on the shadow it casts. To solve this problem, we can set up a proportion because the pole and tower will cast shadows at the same angle due to the sun's position. The proportional relationship is formed by the height of the pole over its shadow length being equal to the height of the tower over its shadow length.
Let's designate the height of the tower as H. The proportion will then be:
2.8 m / 1.21 m = H / 48.75 m
Cross-multiplying to solve for H, we get:
2.8 m \\times 48.75 m = H \\times 1.21 m
136.5 m = 1.21 m \\times H
To find H, divide both sides by 1.21 m:
H = 136.5 m / 1.21 m
H = 112.8099 m
So, the height of the tower is approximately 112.81 meters after rounding to two decimal places.
Look at this table.
Hours of
Training
10
20
30
40
50
Monthly
Pay
1220
1420
1620
1820
2020
2220
2420
60
70
According to the table, how many hours of training would you need to have a
monthly pay of $2620?
Answers
Answer:
you need 8 hours of training
what is the leading coefficient of the polynomial when written in standard form 8x^2+9+5x^3
Answers
Answer:
5
Step-by-step explanation:
To write the polynomial in standard form you need to write it in descending order of degree.
Standard form is:
5x^3 + 8x^2 + 9
The leading coefficient is the coefficient of the first term, the highest degree term.
Answer: 5
Therefore, the leading coefficient of the polynomial [tex]\(8x^2 + 9 + 5x^3\)[/tex] is [tex]\(5\)[/tex].
To write the polynomial [tex]\(8x^2 + 9 + 5x^3\)[/tex] in standard form, we arrange the terms in descending order of their degree:
[tex]\[ 5x^3 + 8x^2 + 9 \][/tex]
In this polynomial, the term with the highest degree is [tex]\(5x^3\)[/tex]. The coefficient of this term, which is the number multiplied by [tex]\(x^3\)[/tex], is the leading coefficient.
Robert earns $512.75 less than the salary earned by Noel. John earns three times Robert's salary. If the total salary earned by them is $47,645.25, how much salary do Robert earn?
Answers
Answer:
$9426.50
Step-by-step explanation:
let noel's salary = x, robert's salary = y and john's salary = z
y = x - 512.75 ..........(1)
z = 3y = 3(x - 512.75) = 3x - 1538.25 ...............(2)
x + y + z = 47645.25..........................(3)
substitute for y and z
x + (x - 512.75) + (3x - 1538.25) = 47645.25
x + x - 512.75 + 3x - 1538.25 = 47645.25
5x = 47645.75 + 512.75 + 1538.25
5x = 49696.25
divide both sides by 5
x = 9939.25 ..... noel's salary
to get robert's salary substitute x in equation 1
y = 9939.25 - 512.75 = 9426.50
y = $9426.50..... robert's salary
which products result in a difference of squares?
Answers
Answer:
is there an equation?
Which of the following is the equivalent to f(x)?
Answers
Answer:
2(25)x
Step-by-step explanation:
F(X) = 2(5)^2x two times five equals 10. 10 to the power of two equals 100 because it's ten times ten. So F(X) = 100^x because that means it's just 100. Also F(x) = 4(25)^x because four times 25 equals 100.
a large storage container in the shape of a rectangular prism has the dimensions of the following: length 16.5m width 18.2m height 12m .how many 1 cubic m boxes can fit in the storage container?
Answers
Answer:
3603 boxes.
Step-by-step explanation:
Rectangular Prism is actually a cuboid.
Volume of cuboid = length * width * height.
It is given that length = 16.5 m, width = 18.2 m, and height = 12 m. Therefore:
Volume = 16.5 * 18.2 * 12 = 3603.6 cubic meters.
Volume is actually the capacity of the shape. If the box has the volume of 1 cubic meters, then the number of boxes that can fit in the rectangular prism will be:
Number of boxes to be fit = Volume of Large container/Volume of Small Container.
Number of boxes = 3603.6/1 = 3603 boxes.
Therefore, 3603 boxes will fit the rectangular prism and 0.6 cubic meters will be the spare space!!!
ara buys two items that cost d dollars each. She gives the cashier $20. Which expression represents the change she should receive?
Question 8 options:
a 20 - 2d
b 20 - d
c 20 + 2d
d 2d - 20
Answers
Answer:
D
Step-by-step explanation:
write down the next term in each following sequence
83,77,71,65...
Answers
Answer:
59,53,47,41,35 and many more
Step-by-step explanation:
substract 6
Answer:
59
Step-by-step explanation:
Each of them are subtracting 6 each time.
David wants to complete a hypothesis test with the least amount of probability for error. If he sets the significance level to 1%, assuming his sample is truly random, what else could he adjust in the test in order to reduce error? He could change the population mean. He could increase the sample size. He could change the population standard deviation. He could decrease the sample size.
Answers
Answer:
He could increase the sample size
Step-by-step explanation:
In hypothesis testing, the error associated with the test is affected by a number of factors. The first factor is the level of significance, alpha. This is the probability of type 1 error. The probability of rejecting the null hypothesis when it is indeed true.
The second factor is the size of the sample used. The larger the sample, the smaller the error since the characteristics of the sample will be closer to those of the entire population on which inference is being made
Answer:
B is correct just took the test.
Step-by-step explanation:
Mixed Applications
8. Fernando bought a new watch set
- that includes 5 watch faces and 7
colored bands. From how many
different watches can he choose?.
Answers
each watch face has 7 choices of band so 5 times 7 is 35
Using the counting principle, Fernando can choose from a total of 35 different watch combinations, as he has 5 watch faces and 7 colored bands which can be selected independently.
Explanation:The question asks about combinations resulting from 5 watch faces and 7 colored bands, this comes from a mathematical concept known as the counting principle. The counting principle states that if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events together can occur in m × n ways.
So, Fernando can choose from 5 watch faces and 7 colored bands independently. Therefore, the total different combinations of watches he can make is 5 × 7 = 35. Thus, Fernando has 35 different watch combinations to choose from.
Learn more about Counting Principle here:https://brainly.com/question/29594564
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Ben has 100.00 in his savings account. He wants to save more money. He is looking at two investment plans. Under Plan A, he will increase his account balance by 20.00 per year. Under Plan B, he will increase his account balance by 15% per year. How much more will he save under Plan B in 10 years?
Answers
Answer:
The correct answer is 104.55
Step-by-step explanation:
From the given information we can write,
Principle amount = 100
To find the amount after 10 years in plan A
Now total = 100
Under plan A increase his account balance by 20.00 per year
Amount increased = 10 *20 = 200
Total = 100 + 200 = 300
To find the amount after 10 years in plan B
Total = 100
Amount after 10 yeras = 100[1 + 15/100]¹⁰
= 100 * 1.15¹⁰ = 100 * 4.04 = 404.55
To find the difference
Difference = 404.55 - 300
= 104.55
The correct answer is 104.55
Help! Can someone please explain how to do this. I have my final in one hour.
Answers
Answer:
n= -3 and n= -6
Step-by-step explanation:
[tex]n^2 = -18 -9n[/tex]
We need to solve this equation to find the value of n.
Rearranging:
[tex]n^2 +9n +18 =0[/tex]
This is a quadratic equation and we can solve by using factorization method.
We need to make factors of 18n^2 such that their sum is equal to 9n.
So solving,
[tex]n^2 + 9n +18 =0\\n^2 + 6n + 3n +18 =0\\n(n+6) + 3(n+6)=0\\(n+3)(n+6) =0\\=> n+3 =0 \,\, and n+6 =0\\n= -3 \,\,and \,\,n=-6[/tex]
Identify the transformation that carries the figure onto itself.
A) rotate 540° clockwise about (5, 3) and reflect across the line y = 3
B) rotate 540° clockwise about (5, 3) and reflect across the line x = 3
Eliminate
C) rotate 450° clockwise about (5, 3) and reflect across the line y = 3
D) rotate 450° clockwise about (5, 3) and reflect across the line x = 3
Answers
Answer: a
hope this helps
Answer:
The answer is A) rotate 540° clockwise about (5, 3) and reflect across the line y = 3 HOPE I HELP :)
Step-by-step explanation:
What is (2x-3y) (4x-y)
Answers
8x²+3y²-14xy
ANSWER
[tex](2x-3y) (4x-y) = 8 {x}^{2} -14xy + 3 {y}^{2} [/tex]
EXPLANATION
We want to expand (2x-3y) (4x-y)
We use the distributive property to obtain,
[tex](2x-3y) (4x-y) = 2x(4x-y) -3y(4x-y)[/tex]
We expand to get,
[tex](2x-3y) (4x-y) = 8 {x}^{2} -2xy -12xy + 3 {y}^{2} [/tex]
Combine the middle terms to obtain,
[tex](2x-3y) (4x-y) = 8 {x}^{2} -14xy + 3 {y}^{2} [/tex]
At a high school, 18% of the students play football and 6% of the students
play football and baseball. What is the probability that a student plays
baseball given that he plays football?
OOO
O A. 1.1%
O B. 10.8%
O C. 33.3%
O D. 3%
SUBMIT
Answers
D or B Step-by-step explanation:
Ann needs 3/4 of a book in 2 days. At this rate how many books can she read in 4 1/3 days.
Answers
Answer: 1 5/8 or 13/8. They are the same.
Step-by-step explanation to find the amount of books she reads in 4 1/3 says, first you need to find how much she reads in 1 day.
3/4 divided by 2 = 3/4 x 1/2=3/8.
Now you need to multiply 3/8 by 4 1/3 to find how many books she can reed in a day. 4 1/3= 13/3. 13/3 x 3/8= 39/24 = 13/8 = 1 5/8
Answer: 2.888889
Step-by-step explanation:
3/4 book 4 1/3 book
------------- = ---------------
2 days x days
4 1/3= 13/3
3/4= 0.75
1.5x= 13/3
--------- -------
1.5 1.5
x= 2.888889 books
50 points!!! please have serious answers
Use the data in the following table to answer the 3 questions below. Please show all calculations needed.
Daily Earnings $25 $26.50 $20 $23.50 $20
Find:
1: Median
2: Mean
3: Mode
PLEASE SHOW ALL STEPS
Answers
Median: Put the list in order from least to greatest.
$20, $20, $23.50, $25, $26.50
$20, $23.50, $25
$23.50 is the median. I took one from each side until I had one left.
Mean: Get the sum of them all and then divide by the number of earnings ( in this case )
$25 + $26.50 = $51.50 $51.50 + $20 = $71.50 $71.50 + $23.50 = $95
$95 + $20 = $115 $115/5 = $23
$23 is the mean.
Mode: Is the one that finds the frequency or in lamen terms it is the number which appears most often.
There's no steps for finding the expect counting how many times that number appeared.
$20 is the mode.
Answer:
He's correct
Step-by-step explanation:
There are 11 basketball teams in a league. Of the teams, 4 will end up in the semifinals of the tournament. How many different combinations of teams could end up in the semifinals?
1,663,200
330
7,920
44
Answers
Answer:I’m thinking 330 but I’m not sure
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer: 330
Solution:
= (11x10x9x8 / 4x3x2x1)
= 7920 / 24
= 330
nathan solved this problem anya cut a ribbon into 5 equal pieces that measured 6.9in how long was the orignal length of the ribbon nathan thought the anwser was 350in
Answers
Answer:
34.5 inches
Step-by-step explanation:
To find the length of the original piece of ribbon, multiply 6.9 inches by 5, obtaining 34.5 inches.
By the way, it appears that your problem statement is not complete. Nathan thought ... what? Please be sure to share the entire problem next time.
A football is kicked at ground level with an initial velocity of 64 feet per second
Find the height after 3 second and use one of the three forms and say which one would be the best to use and why
y= -16t^2+64t
y= -16(t-2)^2 + 64
y= -16t(t-4)
Answers
Answer:
The height of the football is 48 feet after 3 seconds
The first equation y = -16t² + 64t is the best
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation of motion of an object on air without any
external force is y = ut + 1/2 at², where y is the height of the
object from the ground, u is the initial velocity, a is the
acceleration of gravity and t is the time
* Lets solve the problem
- A football is kicked at ground level with an initial velocity of
64 feet per second
∴ u = 64 feet per seconds
∵ The football is kicked upward
∴ a = -32 feet per seconds²
∵ y = ut + 1/2 at²
∴ y = 64t + 1/2 (-32)t²
∴ y = 64t - 16t²
* We will use the first equation y = -16t² + 64t
∵ y = -16t² + 64t
- We need to find the height of the football after 3 seconds
∵ t = 3 seconds
∴ y = -16(3)² + 64(3)
∴ y = 48
∵ y represents the height of the football
∴ The height of the football is 48 feet after 3 seconds
What is the approximate circumference of a circle with a diameter of 40 inches? (careful you need radius so 40/2)
(Use π = 3.14)
(C= 2 *π*r)
(A.) 125.6 in.
(B.) 63 in.
(C.) 251 in.
Answers
Answer:
A. ) 125.6 in.
Step-by-step explanation:
We are given the diameter of the circle, which is 40, and we are aware that radius=diameter÷2.Therefore, the radius = (40÷2) =20.The formula for the circumference of a circle is 2×pi (which in this case is 3.14) × radius, therefore:2×3.14×20 gives you your answer.When you do this calculation in your head or a calculator or whatever, it equals to 125.6. Therefore A.) is the correct answer.Hope I helped :)
Answer:
(A.) 125.6 inStep-by-step explanation:
The formula of a circumference of a circle:
[tex]C=d\pi[/tex]
d - diameter
We have d = 40in. Substitute:
[tex]C=40\pi\ in[/tex]
[tex]\pi\approx3.14\to C\approx(40)(3.14)=125.6\ in[/tex]
If AB = 2x–8 and AC = x+9, What is the length of BC?
Answers
Answer:
17
Step-by-step explanation:
2x-8=x+9
x=17
ANSWER
BC=17 units
EXPLANATION
The given triangle is an isosceles triangle.
We have
AC=AB
This implies that,
[tex]x + 9 = 2x - 8[/tex]
Group similar terms and simplify to get:
[tex]2x - x = 9 + 8[/tex]
[tex]x = 17[/tex]
Side BC is x units. But x=17
Therefore BC is 17 units.
The dot plot shows the time trials of an experiment. Each number on the dot plot represents the amount of time, in seconds, it took to complete a trial.
How many time trials were recorded during the experiment?
Enter the answer in the box.
Answers
Answer:
There were 18 trials recorded
Step-by-step explanation:
Each dot is a trial, the numbers under them is how long each that trial took.
Hope this helps.
The number of times trials were recorded during the experiment are:
18
Step-by-step explanation:We know that the dot plot is nothing but the representation of outcomes of a experiment where the dots represent the value of each outcome.
and the total number of dots represent the total number of items which are studied or recorded.
Here, the total number of trials that are recorded is equal to the total number of dots in the dot plot i.e. the total frequency of the set.
The data frequency table is as follows:
Value Frequency
15 2
17 3
19 2
20 2
21 1
23 4
24 1
25 3
Total frequency= 2+3+2+2+1+4+1+3=18
Hence, the answer is: 18
URGENT PLEASE HELP
How many 4-letter passords can be made using the letters A thought Z if...
a) Repetition of letters is allowed?
b) Repetition of letters is not allowed?
Answers
a) The answer will be 456976 because you multiply 26 and 4.
b) The answer will be 358800 bacause you multiply 26*25*24*23