The total number of coins required to fill all the [tex]64[/tex] boxes are [tex]\boxed{\bf 18446744073709551615}[/tex].
Further explanation:
In a chessboard there are [tex]64[/tex] boxes.
The objective is to determine the total number of coins required to fill the [tex]64[/tex] boxes in chessboard.
In the question it is given that in the first box there is [tex]1[/tex] coin, in the second box there are [tex]2[/tex] coins, in the third box there are [tex]8[/tex] coins and it continues so on.
A sequence is formed for the number of coins in different boxes.
The sequence formed for the number of coins in different boxes is as follows:
[tex]\boxed{1,2,4,8,...}[/tex]
The above sequence can also be represented as shown below,
[tex]\boxed{2^{0},2^{1},2^{2},2^{3},...}[/tex]
It is observed that the above sequence is a geometric sequence.
A geometric sequence is a sequence in which the common ratio between each successive term and the previous term are equal.
The common ratio [tex](r)[/tex] for the sequence is calculated as follows:
[tex]\begin{aligned}r&=\dfrac{2^{1}}{2^{0}}\\&=2\end{aligned}[/tex]
The [tex]n^{th}[/tex] term of a geometric sequence is expressed as follows:
[tex]\boxed{a_{n}=ar^{n-1}}[/tex]
In the above equation [tex]a[/tex] is the first term of the sequence and [tex]r[/tex] is the common ratio.
The value of [tex]a[/tex] and [tex]r[/tex] is as follows:
[tex]\boxed{\begin{aligned}a&=1\\r&=2\end{aligned}}[/tex]
Since, the total number of boxes are [tex]64[/tex] so, the total number of terms in the sequence is [tex]64[/tex].
To obtain the number of coins which are required to fill the [tex]64[/tex] boxes we need to find the sum of sequence formed as above.
The sum of [tex]n[/tex] terms of a geometric sequence is calculated as follows:
[tex]\boxed{S_{n}=a\left(\dfrac{r^{n}-1}{r-1}\right)}[/tex]
To obtain the sum of the sequence substitute [tex]64[/tex] for [tex]n[/tex], [tex]1[/tex] for [tex]a[/tex] and [tex]2[/tex] for [tex]r[/tex] in the above equation.
[tex]\begin{aligned}S_{n}&=1\left(\dfrac{2^{64}-1}{2-1}\right)\\&=\dfrac{18446744073709551616-1}{1}\\&=18446744073709551615\end{aligned}[/tex]
Therefore, the total number of coins required to fill all the [tex]64[/tex] boxes are [tex]\boxed{\bf 18446744073709551615}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Sequence
Keywords: Series, sequence, logic, groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule., geometric sequence, common ratio, nth term.
Coins on the chessboard follow a doubling pattern. In the nth box, the coins can be expressed as [tex]\(2^{(n-1)}[/tex]. The total coins for all 64 boxes is [tex]2^{63}[/tex].
Certainly, let's break down the doubling pattern of coins in each chessboard box, expressed in exponential form:
1. **First Box (kotak pertama):
- Number of coins: [tex]\(2^0 = 1\)[/tex] (2 raised to the power of 0).
2. **Second Box (kotak kedua):
- Number of coins: [tex]\(2^1 = 2\)[/tex] (2 raised to the power of 1).
3. **Third Box (kotak ketiga):
- Number of coins: [tex]\(2^2 = 4\)[/tex] (2 raised to the power of 2).
4. **Fourth Box (kotak keempat):
- Number of coins: [tex]\(2^3 = 8\)[/tex] (2 raised to the power of 3).
The pattern continues, doubling the number of coins with each subsequent box.
For the n-th box, the number of coins is given by [tex]\(2^{(n-1)}[/tex], where n is the box number.
So, the exponential form for the number of coins in each chessboard box is [tex]\(2^{(n-1)}[/tex], where n is the box number ranging from 1 to 64.
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Que. A father challenges his child to calculate the total number of coins needed to fill a chessboard. In the first box, 1 coin is placed, 2 coins in the second box, 4 coins in the third, and so on, up to the 64th box. Help the child determine the doubling pattern of coins in each chessboard box, expressed in exponential form.
Triangle PQR lies in the xy-plane, and the coordinates of vertex Q are (2, –3). Triangle PQR is rotated 180° clockwise about the origin and then refected across the y-axis to produce triangle P′Q′R′, where vertex Q′ corresponds to vertex Q of triangle PQR. What are the coordinates of Q′?
Answer:
(2,3)
Step-by-step explanation:
We are given that triangle PQR lies in the xy-plane, and coordinates of Q are (2,-3).
Triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R',
We have to find the coordinates of Q'.
The coordinates of Q(2,-3).
180 degree clockwise rotation about the origin then transformation rule
[tex](x,y)\rightarrow (-x,-y)[/tex]
The coordinates (2,-3) change into (-2,3) after 180 degree clockwise rotation about origin.
Reflect across y- axis the transformation rule
[tex](x,y)\rightarrow (-x,y)[/tex]
Therefore, when reflect across y- axis then the coordinates (-2,3) change into (2,3).
Hence, the coordinates of Q(2,3).
After applying the sequence of transformations, the coordinates of Q′ are Q' (2, 3).
What is a rotation?In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Additionally, the mapping rule for the rotation of any geometric figure 180° clockwise or counterclockwise about the origin is represented by the following mathematical expression:
(x, y) → (-x, -y)
Q (2, -3) → Q" (-2, 3)
By applying a reflection over the y-axis to the coordinates of the point (4, -9), we have the following new coordinates for the image;
(x, y) → (-x, y)
Q" (-2, 3) → Q' (2, 3).
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Study designed 1: two hundred student were selected at random from those enrolled at large college in California each student in the simple was asked whether he or she ate sweet potatoes more than once in a typical week
The survey design described is a statistical study on college student eating habits, specifically focusing on sweet potato consumption, to obtain quantitative data about behaviour patterns.
Explanation:The student in question is surveying to gather data on a particular behavioural pattern, in this case, the frequency of sweet potato consumption among college students. To achieve results that reflect the larger student body of the college, a random sample of 200 students is selected to answer the survey question. Completing the survey comprises the collection of quantitative data, which can later be analyzed statistically. Surveys are a common method in statistics to investigate various questions and hypotheses. For example, a survey similar to this might be performed to evaluate the number of movies students watch in a week or determine the daily average study time for freshmen students. The effectiveness of the survey method relies on a representative sample accurately reflecting the population of interest.
A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
A. 0.20
B. 0.25
C. 0.50
D. 1.00
Answer: A. 0.20
Step-by-step explanation:
Let A be the event of employees needed corrective shoes and B be the event that they needed major dental work .
We are given that : [tex]P(A)=0.08\ ;\ P(B)=0.15\ ;\ P(A\cap B)=0.03[/tex]
We know that [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Then, [tex]P(A\cup B)=0.08+0.15-0.03= 0.20[/tex]
Hence, the probability that an employee selected at random will need either corrective shoes or major dental work : [tex]P(A\cup B)= 0.20[/tex]
hence, the correct option is (A).
The probability that an employee selected at random will need either corrective shoes or major dental work is 0.20.
Explanation:The subject of this problem is probability. To find the probability that an employee selected at random will need either corrective shoes or major dental work, you need to add the probabilities of each individual event and then subtract the probability of both events occurring, as this is counted twice.
So, the probability is calculated as:
P(Corrective Shoes or Major Dental Work) = P(Corrective Shoes) + P(Major Dental Work) - P(Both)
Substituting the values from the problem, we have:
P(Corrective Shoes or Major Dental Work) = [tex]0.08 + 0.15 - 0.03 = 0.20[/tex]
So, the probability that an employee selected at random will need either corrective shoes or major dental work is 0.20, matching answer choice A.
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2) Jose has a new job and earns a salary of $48,000. Victor has a new job and earns a salary of $59,000. Jose will receive a salary increase of $2,800 per year and Victor will receive a salary increase of $1,700 per year. Which equation can be used to find x, the number of years it will take Jose to earn the same salary as Victor?
Answer:
y = b + kn
Step-by-step explanation:
In any given year, the salary of each will be given by the equation
y = b + kn where
y = Salary
b= Initial salary before increment
k= Increment
n= is the year in question
Thus, this can be proven by equating the salaries of both workers.
Jose's salary will be $48,000 + $2800n
Victor's salary will be $59000 + $1700n
Thus, to get the particular year, we equate both as
$48,000 + $2800n = $59000 + $1700n
$2800n -$1700n =$59,000 - $48,000
$1100n =$11000
Canceling the dollar signs throughout, we get
n = 11000/1100 = 10 years.
If you worked his out, you will get that in the 10th year, both salaries will be $76,000.
Thus, the equation is
y = b + kn
with the variables as explained above.
Answer: 48,000 + 2,800x = 59,000 + 1,700x
Step-by-step explanation:
If f and t are both even functions, is the product ft even? If f and t are both odd functions, is ft odd? What if f is even and t is odd? Justify your answers.
Answer:
(a) If f and t are both even functions, product ft is even.
(b) If f and t are both odd functions, product ft is even.
(c) If f is even and t is odd, product ft is odd.
Step-by-step explanation:
Even function: A function g(x) is called an even function if
[tex]g(-x)=g(x)[/tex]
Odd function: A function g(x) is called an odd function if
[tex]g(-x)=-g(x)[/tex]
(a)
Let f and t are both even functions, then
[tex]f(-x)=f(x)[/tex]
[tex]t(-x)=t(x)[/tex]
The product of both functions is
[tex]ft(x)=f(x)t(x)[/tex]
[tex]ft(-x)=f(-x)t(-x)[/tex]
[tex]ft(-x)=f(x)t(x)[/tex]
[tex]ft(-x)=ft(x)[/tex]
The function ft is even function.
(b)
Let f and t are both odd functions, then
[tex]f(-x)=-f(x)[/tex]
[tex]t(-x)=-t(x)[/tex]
The product of both functions is
[tex]ft(x)=f(x)t(x)[/tex]
[tex]ft(-x)=f(-x)t(-x)[/tex]
[tex]ft(-x)=[-f(x)][-t(x)][/tex]
[tex]ft(-x)=ft(x)[/tex]
The function ft is even function.
(c)
Let f is even and t odd function, then
[tex]f(-x)=f(x)[/tex]
[tex]t(-x)=-t(x)[/tex]
The product of both functions is
[tex]ft(x)=f(x)t(x)[/tex]
[tex]ft(-x)=f(-x)t(-x)[/tex]
[tex]ft(-x)=[f(x)][-t(x)][/tex]
[tex]ft(-x)=-ft(x)[/tex]
The function ft is odd function.
An investment property now worth $180,000 was purchased seven years ago for $142,000. At the time of the purchase, the land was valued at $18,000. Using a 39-year life for straight-line depreciation purposes, the present book value of the property isa. $95,071.35.b. $113,071.00.c. $126,000.50.d. $119,743.59.
Answer:
d. $119,743.59
Step-by-step explanation:
actual value (AV)=$180,000
purchase price (PP) =$142,000
intial value (IV) =$18,000
useful live (UL)= 39 years
First, we subtract the value of the property from the purchase value or IV to know the value to be depreciated:
PP-IV= $142,000-$18,000 = $124,000
Then we find out the yearly depreciation by dividing $124,000 into useful live (UL) years:
$124,000/39 = $3,179.49 This is the amount that the property depreciates every year.
But after 7 years the depreciation is: $3,179.49*7= $22,256.41
We subtract the depreciation in the 7 years from the purchase price (PP) and that's the present book value of the property:
$142,000-$22,256.41=$119,743.6
To find the present book value of the property, subtract the land value from the purchase price to get the initial building value. Then, calculate the total depreciation over the seven years and subtract this from the initial building value. Finally, add back the land value.
Explanation:To find the present book value of the property, we need to first determine the value of the structure. We can do this by subtracting the value of the land ($18,000) from the purchase price of the property ($142,000), according to the details given. So, the initial value of the building is $124,000.
Since we use the straight-line method of depreciation, the structure depreciates at a constant amount each year over its useful life. So, the yearly depreciation expense is 124,000 / 39 = $3,179.49.
Then, we'll calculate the total depreciation over the seven years, which is 3,179.49 * 7 = $22,256.43.
Lastly, we'll subtract this total depreciation from the original building value ($124,000 - $22,256.43). This yields a present book value of $101,743.59 for the structure. When we add back the value of the land ($18,000) which does not depreciate, we obtain a total present book value of $119,743.59 for the property.
Therefore, the current book value of the property is d. $119,743.59.
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Greg was sharing his candy with his friends. He had 4 1/2 bags of candy. There are 6 friends total. If theg each get equal amounr how much will each person get
Answer:
3/4 bag
Step-by-step explanation:
4.5 divided 6 ways makes each part ...
4.5/6 = 0.75 = 3/4
Each person gets 3/4 bag.
solve 3/2x-4=16 please :)
Final answer:
Solve the equation 3/2x - 4 = 16 by adding 4 to both sides, simplifying to 3/2x = 20, and then multiplying both sides by 2/3 to find the solution, x = 40/3.
Explanation:
To solve the equation 3/2x - 4 = 16, you need to perform a series of algebraic manipulations.
Add 4 to both sides of the equation to isolate the term with the variable on one side: 3/2x = 16 + 4.
Combine like terms: 3/2x = 20.
To find x, multiply both sides by the reciprocal of 3/2, which is 2/3: x = 20 * (2/3).
Simplify the multiplication: x = 40/3 or x = 13.33 repeating.
Therefore, the solution to the equation is x = 40/3.
Krystal and 4 friends were going to the movies. Each ticket cost $12. They bought 2 buckets of popcorn at $4.50 each and then each person bought their own soda at $4.75 each. How much money did they spend in total?
Answer:
Step-by-step explanation:
First you would multiply 12 by four since each person has to have a ticket ($48) next you would multiply 4.50 by two since they bought two buckets of popcorn ($9) then you would multiply 4.75 by four since they each bought their own drink ($15) then you would all three of those totals together to get the final cost of everything ($72)
Hoped that answered your question!
Answer:
$92.75
Step-by-step explanation:
Krystal and 4 friends were going to the movies.
Total person = 5
The cost of each ticket = $12.00
They bought 2 buckets of popcorn at $4.50 each
They all bought soda at $4.75 each.
Total money they spent = (12 × 5) + (4.50 × 2) + (4.75 × 5)
= 60 + 9.00 + 23.75
= $92.75
They spent $92.75 in total.
In order to qualify for finals in racing event,a race car must achieve an average speed of 250km/hr on a track with a total length of 1600m.if a particular car covers the first half of the track at an average speed of 230km/hr,what minimum average speed must it have in the second half of the track in order to qualify?
Answer:
The minimum average speed needed in the second half is 270 km/hr
Step-by-step explanation
We can divide the track in two parts. For the first half of the track the average speed the car achieved was 230 km/hr and we need to make sure that the average speed of the full track is 250 km/hr. Then, we can calculate the average speed of the two parts of the track and force this to be equal to 250 km/hr. In equation, defining [tex]v_2[/tex] as the average speed of the second half:
[tex]\frac{230 + v_2}{2}=250[/tex]
Solving for [tex]x[/tex]
[tex]x=250*2-230\\x=500-230\\x=270[/tex]
Therefore, achieving a speed of 270 km/hr in the second half would be enough to achieve an average speed of 250 on the track.
Need help with Geometric Sequence Please and Explanation
Which pairs of triangles can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of triangles.
Congruent Not Congruent
△ABC and △DEF
△ABC and △JKL
△ABC and △QRS
△JKL and △DEF
△JKL and △QRS
△QRS and △DEF
Did you ever get the answer for this?
Answer:
The order is Congruent, not congruent, not congruent, not congruent,congruent, not congruent
Step-by-step explanation:
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One book has 84 pages. Another book has 210 pages. Which is the greatest common factor of the number of pages in the two books? CLEAR SUBMIT 14 21 42 84
42
42x2 is 84 and 42x5 is 210
Final answer:
The greatest common factor (GCF) of 84 and 210 is 42, which is found by listing the factors of each number and identifying the largest one they share.
Explanation:
The student is asking for the greatest common factor (GCF) of the number of pages in two books, one with 84 pages and another with 210 pages. To find the GCF, we need to list the factors of each number and then identify the largest factor they have in common.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. The common factors of 84 and 210 are 1, 2, 3, 6, 7, 14, 21, and 42. The largest of these is 42, so the GCF is 42.
How much more interest will maria receive if she invests 1000$ for one year at x % annual interest, compounded semianually, than if she invest 1000$ for one year at x percent annual interest, compounded annually?
A. 5x
B. 10x
C. x^2/20x220
D. x^2/40
E. (10x+x^2/40)
Answer:
D. [tex]\frac{x^{2} }{40}[/tex]
Step-by-step explanation:
Compound interest formula is:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
When compounded annually;
[tex]A=1000(1+\frac{x}{100})^{1}[/tex]
=> [tex]A=1000(1+\frac{x}{100})[/tex] ....(1)
When compounded semi annually means rate = x/2 and n = 2.
[tex]A=1000(1+\frac{x}{2\times100})^{2}[/tex]
=> [tex]A=1000(1+\frac{x}{200})^{2}[/tex] .... (2)
Now, subtracting 1 from 2 we get ;
[tex]1000(\frac{x^{2} }{40000} )[/tex]
= [tex]\frac{x^{2} }{40}[/tex]
Hence, option D is correct.
Given: BC bisects DBE. Prove: ABD is congruent to ABE
The proof that ∠ABD is congruent to ∠ABE would be detailed below to your understanding
What are Congruent Angles and Bisectors?
Congruent angles are angles that are equal and identical to each other when measured.
A Bisector is a line that divides another line or angle into two equal parts.
Given that;
Line BC divided angle DBE into two equal parts.
It is seen that line BC extends to point A while dividing the external angle DBE into two equal parts.
Therefore, ∠ABD is congruent to ∠ABE.
HELP ME PLEASE !!!!!!!!!
Andre has been offered an entry-level job. The company offered him $48,000 per year plus 3.5% of his total sales. Andre knows that the average pay for this job is $62,000. What would Andre’s total sales need to be for his pay to be at least as high as the average pay for this job?
Answer: 33 333,33 per month or 400 000 per year
Step-by-step explanation:
You need 48 000 + 0.035X = 62 000
So ( 62 000 - 48 000 ) / 0.035 = X
Then you can divide X per 12 (months in a year)
And you have your answer per month .
So 33 333,33 total sale per month to have at least as high as the average pay
An equation is formed of two equal expressions. Andre’s total sales need to be $400,000 for his pay to be at least as high as the average pay for this job.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Andrew will earn $48,000 per year plus 3.5% of his total sales, the average pay for this job is $62,000. Therefore, the amount of sales that Andrew needs to make in order to make his pay equal to the average pay is,
Average pay = Annual pay + 3.5% of sales
$62,000 = $48,000 + (3.5/100)x
$62,000 - $48,000 = 0.035x
$14,000 = 0.035x
$14,000 / 0.035 = x
x = $400,000
Hence, Andre’s total sales need to be $400,000 for his pay to be at least as high as the average pay for this job.
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Desde una altura de 3m un chico patea verticalmente hacia arriba una pelota con una velocidad de 18m/s cual es su posicion 1 seguendo despues de haberla pateado?
Answer: la altura es 13.1 m
Step-by-step explanation:
El movimiento descripto es de tipo rectilineo uniformemente variado, más precisamente tiro vertical.
Para calcular la posición al cabo de 1 seg utilizaremos la ecuacionecuación del movimiento descrita como:
y = v0.t - 1/2 g t^2
Donde y es la altura para cualquier momento
v0 es la velocidad inicial 18 m/s
g la aceleración de la gravedad 9.81 m/s2
y t el tiempo medido en segundos
Entonces para calcular la altura después de un segundo:
y = 18 m/s x 1 seg - 1/2 9.81 m/s2 (1 seg)^2 = 18 m - 4.9 m = 13.1 m
La posición de la pelota, que fue pateada verticalmente hacia arriba desde una altura de 3 metros con una velocidad inicial de 18 m/s, después de 1 segundo, es aproximadamente 11.1 metros por encima del punto de inicio.
Explanation:La pregunta trata sobre un problema de física relacionado con el movimiento vertical de un objeto. En este caso, una pelota es pateada verticalmente hacia arriba desde una altura de 3 metros con una velocidad inicial de 18 m/s. Para resolverla, podríamos usar la segunda ley del movimiento de Newton para el movimiento vertical, que se puede escribir de la siguiente manera: y = y0 + v0t - 1/2gt^2.
Aquí, y es la posición de la pelota después de un tiempo t, y0 es la posición inicial (3 metros en este caso), v0 es la velocidad inicial (18 m/s), g es la aceleración debido a la gravedad (9.8 m/s^2), y t es el tiempo (1 segundo).
Si sustituimos los valores correspondientes en la ecuación, obtenemos: y = 3m + 18m/s * 1s - 1/2 * 9.8m/s^2 * (1s)^2. Al hacer la respectiva operación, encontramos que la posición de la pelota después de 1 segundo es de aproximadamente 11.1 metros por encima del punto de inicio.
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Farmer Donald is selling two parcels of land together. One of the parcels is one square mile and the other parcel is five acres. The sale price is $2,100 per acre. What is the total sale price of the property Donald is selling?
a) $178,500
b) $793,475
c) $1,354,500
d) $10,500
The correct option is (c) $1,354,500 The total sale price of Farmer Donald's property is calculated by converting square miles to acres (1 square mile = 640 acres), adding the additional 5 acres, and then multiplying by the sale price per acre to get the total of $1,354,500.
To calculate the total sale price of the property Farmer Donald is selling, we need to find the total number of acres for both parcels of land and then multiply that by the price per acre.
First, we convert the one square mile to acres, knowing that one square mile equals 640 acres:
Parcel 1: 1 square mile = 640 acres
Parcel 2: 5 acres
Adding the two parcels together gives us:
Total acres = 640 acres + 5 acres = 645 acres
Next, we multiply the total acres by the price per acre:
Total sale price = 645 acres \\u00D7 $2,100 per acre
Total sale price = $1,354,500
Therefore, the total sale price of the property is $1,354,500.
Brianna has $25 and a $10 gift certificate to a clothing store she buys two T-shirts for $9.97 each what are the questions you must answer before you can find how much money she has left
Answer:
$15.06
Step-by-step explanation:
First you add $25.00 and $10.00 Then you multiply $9.97 by two and you would get $19.94 which you would then subtract $19.94 from $35
To find out how much money Brianna has left, we need to first calculate the total cost of the T-shirts, then determine how she paid for them and subtract this from her cash and gift certificate value.
Explanation:To find out how much money Brianna has left after her purchase, we need to answer a few important questions:
What is the total cost of the two T-shirts? We know each T-shirt costs $9.97, so we multiply this by two.How did Brianna pay for the T-shirts? Did she use her gift certificate, her cash, or a combination of both? If she used her gift certificate first, then we should subtract the total cost of the T-shirts from the value of the gift certificate first.How much money does Brianna have left after her purchase? If the total cost of the T-shirts is less than the value of the gift certificate, then she still has the remaining value of the gift certificate and her cash. If the total cost of the t-shirts is more than the gift certificate, she would need to also pay with some of her cash, so we should subtract the remaining cost from her cash to find out how much money she has left.Learn more about money here:https://brainly.com/question/32960490
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stephanie spent half of her weekly allowance playing arcade games. To earn more money her parents let her clean the oven for $7. what is her weekly allowance if she ended with $12?
Answer:
$10.00
Step-by-step explanation:
Let Stephanie's weekly allowance = x
She spent half of her weekly allowance playing arcade games = [tex]\frac{x}{2}[/tex]
Her parents let her clean the oven for = [tex]\frac{x}{2}+7[/tex].
She ended with $12
So the equation will be [tex]\frac{x}{2}+7=12[/tex]
[tex]\frac{x}{2}[/tex] = 12 - 7
[tex]\frac{x}{2}[/tex] = 5
x = 5 × 2
x = 10 dollars
Her weekly allowance would be $10.00
Final answer:
To find Stephanie's weekly allowance, we set up an equation where half of her allowance plus $7 equals $12, which results in a calculation showing that her weekly allowance is $10.
Explanation:
Stephanie spent half of her weekly allowance on arcade games and earned an additional $7 by cleaning the oven. We're told that after this, she ends up with $12. To find Stephanie's weekly allowance, let's denote her allowance as A. Since she spent half of it on games, she was left with A/2. By cleaning the oven, she received $7, so her total money became A/2 + $7 = $12. To find the allowance, we solve the equation:
Therefore, Stephanie's weekly allowance is $10.
which is the solution of the following system?
x-y=11
-x+y=-11
Answer: Infinite solutions. It is the same line
Step-by-step explanation:
Tom and David get their haircut at the barber shop on Saturdays.Tom gets his hair cut every 3 weeks. David gets his hair cut every 4 weeks. One Saturday, Tom and David got their hair cut at the same time. When will Tom and David get their hair cut on the same day again?
Answer:
On Saturday, when 12 weeks passed
Step-by-step explanation:
Tom gets his hair cut every 3 weeks.
David gets his hair cut every 4 weeks.
Find the least common multiple of numbers 3 and 4:
[tex]3=3\\ \\4=2\cdot 2\\ \\LCM(3,4)=3\cdot 2\cdot 2=12[/tex]
This means that Tom and David will get their hair cut on the same day at 12th week (if the first week when they started has number 0).
You can think in another way:
Tom gets his hair cut every 3 weeks. He got his hair cut after 3 weeks, after 6 weeks, after 9 weeks, after 12 weeks passed.
David gets his hair cut every 4 weeks. He got his hair cut after 4 weeks, after 8 weeks, after 12 weeks passed.
Use the conditional statement to answer the question.
If an angle is a right angle, then the angle measures 90°.
Are the statement and its contrapositive true?
A. Both the statement and its contrapositive are true.
B. Both the statement and its contrapositive are false.
C. The statement is true, but the contrapositive is false.
D. The statement is false, but the contrapositive is true
Answer: The correct option is
(A) Both the statement and its contrapositive are true.
Step-by-step explanation: We are given to check whether the following conditional statement and its contrapositive is true or false :
"If an angle is a right angle, then the angle measures 90°".
Let us consider that
p : an angle is a right angle
and
q : the angle measures 90°.
So, the conditional statement is p ⇒ q. This is true, because the measure of a right angle is 90°.
The contrapositive of "p ⇒ q" is "not q ⇒ not p".
That is, if the measure of an angle is not 90°, then the angle is not right angle.
This is also true, because only angles with measure 90° are right angles.
Thus, the given statement and its contrapositive are TRUE.
Option (A) is correct.
How to find the indicated probability? Please show your work. Thanks!
Total accidents = 400
Multiple vehicles would be both 2 and 3 or more columns.
Involved alcohol for 2 or more vehicles = 96 +19 = 115
Probability = 115 / 400 = 23/80
The travers are adding a new to their house. The room will be a cube with a volume 8,000ft cubed. They are going to put hardwood floors, and the contractor charges 10$ per square foot. How much will the hardwood floor cost?
Answer:
The answer to your question is: cost = $4000
Step-by-step explanation:
Data
Volume = 8000 ft³
cost = $10 / square foot
Process
It's a cube then we find the length of one side
Volume = l³ = 8000
l = ∛8000
I = 20 ft
Now, calculate the area of the floor,
Area = l x l
= 20 x 20
= 400
Finally, find the cost of the floor
cost = area x price
cost = 400 x 10
= $4000
Final answer:
To calculate the cost of the hardwood floor for a cubic room with a volume of 8,000ft³, we first find the length of one side of the cube (20ft), then calculate the floor area by squaring that length (400ft²), and multiply it by the contractor's charge ($10/ft²) to get the total cost ($4000).
Explanation:
The question involves calculating the cost of adding hardwood floors to a cubic room, with knowledge of its volume. First, we need to find the length of one side of the cube to determine the floor area. Since the volume of a cube is found by cubing the length of one side, we find the cube root of the room's volume:
∛(8,000ft³) = 20ft (this is the length of one side of the cube).
Then the area of the floor, which is a square, is calculated by squaring the length of the side:
Area = side² = (20ft)² = 400ft².
Finally, to find the cost, we multiply the area by the contractor's charge per square foot:
Cost = area × charge per square foot = 400ft² × $10/ft² = $4000.
Therefore, the hardwood floor will cost $4000.
Bill removed the ten of spades and the king of hearts from a deck of standard playing cards and threw them in the trash. There were originally fifty two cards in the deck. Three days later, his friend James picks up the same deck of cards. How many cards are in the deck now?
Answer:
Step-by-step explanation:
2 if you mean 1 of each so it would be 50 cards
The cards left are in the deck now is 38.
What are different types of card in a deck of standard playing cards ?A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.
According to the question
Total number of cards in deck = 52
Total number of spades of card in deck = 13
Bill removed the spades from deck of card = 10
Bill removed the king of hearts from a deck of cards = 4
Total cards removed from deck and thrown in trash = 10 + 4
= 14
Cards left in the deck of card = 52 - 14
= 38
Hence, the cards left are in the deck now is 38.
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In an editorial, the Poughkeepsie Journal printed this statement: "The median price minus the price exactly in between the highest and lowest minus..."Does this statement correctly describe the median? Why or why not?Choose the correct answer below. A.Yes. It correctly describes the median. B.No. It describes the midrange, not the median. C.No. It describes the mean, not the median. D.No. It describes the mode, not the median.
Answer:
B.No. It describes the midrange, not the median.
Step-by-step explanation:
Further,
The range is the difference between the least and largest value of data. It measures skewness using all data points.
Mean is calculated as the ratio of the sum of all the observations to the total number of observations.
Median is the middle value of the data after arranging them in ascending order.
In the lab, robyn has two solutions that contain alcohol and is mixing them with each other. Soultion A is 6% alcohol and Solution Bis 20% alcohol. She uses 400 milliliters of Solution A. How many milliters of Solution B does she use, if the resulting mixture is a 12% alcohol solution?
Answer:
She needs 300 mililiters of Solution B so that the resulting mixture is a 12% alcohol
Step-by-step explanation:
In this problem you have to take into account that when you are talking about solutions you can't just add the porcentaje because each percentaje represent how many mililiters of the total of the solution are, in this case of alcohol.
So for solving this problem we are first going to establish the variables, because it si solved using a system of equations. In that way we are going to say that:
VT: represents the total volume of the resulting mixture of solution A and solution B at 12% of alcohol
VA: represent the mililiters of solution A, in the problem they say that this value it equals to 400 ml
VB: Represent the mililiters of solution B, that is what we need to find.
From now on, we are just going to use this variables but always keep in mind what does they represent.
VaT: Represent the total volume of alcohol in the resulting mixture solution at 12%
VaA: Represent the volume of alcohol in solution A
VaB: Represent the volume of alcohol in solution B
What comes next? we need to describe the equations from the information we have so that we create a system that can be solve after.
What can we first say about the total volume (VT)? That it is the result of the adition of solution A and B so we can state the following equation:
VT = VA + VB
As we know that VA equals to 400ml we can replace to get:
1) VT = 400ml + VB
But what happens with the other information we have? We now need to take into account the concentration of each solution, so as we can´t add the percentages of alcohol but we can add the volumes of alcohol in each solution we can say that:
2) VaT = VaA + VaB
Now we are going to start to reduce the number of variables changing does that we don't know for those that we do to solve the problem, starting first with the volumes of alcohol.
A porcentaje represents a part of the total volume so to know how much alcohol does each of the solutions has we must do rules of three so that we can leave all the variables in terms of VT, VA and VB:
- VT → 100%
VaT → 12%
VaT = [tex]\frac{12.VT}{100}[/tex] = 0,12.VT
- VA → 100% In this case we know that VA = 400
VaA → 6%
VaA = [tex]\frac{6x400}{100}[/tex]
VaA = [tex]\frac{6x4}{1}[/tex]
VaA=24ml
VaB → 100%
VaB → 20%
VaB = [tex]\frac{20.VB}{100}[/tex] = 0,20.VB
Now we are going to replace this information in the equation number two to get the following expresion:
3) 0,12.VT = 24ml + 0.20VB
At this point we have a system of two equations (remember equation 1) with two variables VT and VB so we are going to do some algebra to clear the variables.
- Replace VT of equation 1 in equation 3
Remeber that VT = 400ml + VB so now we are going to put this information in equation 3) 0,12.VT = 24ml + 0.20VB to get:
4) 0,12 (400ml + VB) = 24ml + 0.20VB
- Use the distributive operation to solve the parentesis
0,12x400ml + 0.12.VB = 24ml + 0.20VB
5) 48ml + 0.12VB = 24ml + 0.20VB
- Organize the information in one side the ones with variables and in the other side just numbers:
0.12VB - 0.20VB = 24ml - 48ml
-0.08 VB = -24ml (do the operations)
As it is a minus in both sides we can divide it and cancel the sign to have:
0,08VB = 24 ml (to clear VB, we must divide in both sides by 0,08)
[tex]\frac{0,08.VB}{0,08} = \frac{24ml}{0.08}[/tex] after doing the division we get:
VB = 300mlwith this you already get the answer of how many mililiters of solution B does she use to get a resulting mixture of 12%.
To verficate we must do the following process:
VT = 300ml + 400ml = 700ml
The total volume of the solution is 700 ml of which 12% equals to:
VaT = 0,12. VT = 0,12(700ml) = 84 ml
VaA = 24ml (Volume of alcohol in solution A, we already calculated)
VaB = 0,20 VB = 0,20(300ml) = 60ml (Volume of alcohol in solution B)
VaT = VaA + VaB (Prove the equation with the values we obtain)
84ml = 24ml + 60ml
84 ml = 84ml
As the equation is the same we have verificated our result.
Robyn needs to use 300 mL of Solution B to achieve a 12% alcohol solution when mixed with 400 mL of Solution A. This was calculated by setting up an equation based on the concentrations and solving for the quantity of Solution B.
To solve this problem, we need to find out how much Solution B (20% alcohol) Robyn needs to add to 400 mL of Solution A (6% alcohol) to get a 12% alcohol solution.
Step-by-Step Solution
First, let's set up the equation assuming she uses x milliliters of Solution B:
Since Solution A is 6% alcohol, in 400 mL of Solution A, there is:
0.06 * 400 = 24 mL of alcoholNext, for Solution B, which is 20% alcohol, the amount of alcohol in x mL of Solution B is:
0.20 * x = 0.2x mL of alcoholWe need the resulting mixture to have a 12% concentration. The total volume of the mixture will be:
400 + x mLThe total amount of alcohol in this mixture will be 12% of the total volume:
0.12 * (400 + x) = 24 + 0.2xSimplify and solve for x:
0.12 * 400 + 0.12 * x = 24 + 0.2x48 + 0.12x = 24 + 0.2x24 = 0.08xx = 300So, Robyn needs to use 300 mL of Solution B.
The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the level of cobalt radiation in a certain region at 100 times the level acceptable for human habitation. How long will it be until the region is again habitable?
Answer:
35 years
Step-by-step explanation:
The proportion p that remains after y years is ...
p = (1/2)^(y/5.27)
In order for 1/100 to remain (the level decays from 100 times to 1 times), we have ...
.01 = .5^(y/5.27)
log(0.01) = y/5.27·log(0.5) . . . take logs
y = 5.27·log(0.01)/log(0.5) ≈ 35.01 ≈ 35 . . . . years
Given that the radioactive isotope cobalt-60 has a half-life of 5.27 years, it will take around 36.89 years for it to decay to a level that is safe for human habitation, assuming the initial level is 100 times the safe limit.
Explanation:The subject of this question is the half-life of radioactive substances, specifically cobalt-60. The half-life is the time it takes for half of the radioactive atoms to decay. Cobalt-60 has a half-life of 5.27 years. This implies that 50% of the cobalt-60 will remain after 5.27 years, 25% will remain after 10.54 years (two half-lives), 12.5% will remain after 15.81 years (three half-lives), and so forth.
Understanding this concept, we can calculate when the region will be habitable. Currently, the radiation level is 100 times the acceptable limit. We need to determine how many half-lives it will take for the radiation level to reduce to 1% i.e., 1/100 of its original level. Since each half-life reduces the radiation by half, this is equivalent to finding when the cobalt-60 will be reduced to a fraction of 1/(2^n), where 'n' is the number of half-lives. Using n = 7 gives us 1/128, which is less than 1/100 (it will need to be less to be within safe levels).
So, it will take approximately 7 half-lives for the area to become safe for human habitation again. Since the half-life of cobalt-60 is 5.27 years, it will therefore take about 7 * 5.27 = 36.89 years for the region to become habitable once more.
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In the game of billiards called 14.1, players lose points if they receive penalties. Find the difference in the scores of the winner with 50 points and the opponent with –17 points.
Answer:
67 points
Step-by-step explanation:
To find the difference between the winning and losing scores, subtract the losing score from the winning score:
50 -(-17) = 50 +17 = 67
The difference is 67 points.