Using the principle of proportional relationship, you can go 165km farther after the trip of 360km with 42L gasoline in the tank.
Consumption rate =[tex]8L[/tex] for [tex]100 km[/tex]
So, per number of Km per Litre is
[tex]8L = 100km[/tex]
[tex]1 L = x[/tex]
so,
[tex]8x = 100[/tex]
[tex]x=8 \div 100\\[/tex]
[tex]x= 12.5[/tex] kilometer per Litre
Number of kilometers for [tex]42 L[/tex]
[tex]12.5 km = 1 L[/tex]
[tex]y=42L[/tex]
On, Cross multiplying
[tex]y = 12.5\times42[/tex]
[tex]y = 525 km[/tex]
The difference in the distance [tex]= 525 - 360 = 165 km[/tex]
Therefore, the gas can go for a further [tex]165 km[/tex]
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In Linguistics 101, the ratio of the number of juniors to the number of seniors is $3:2$. When seven more juniors join the class, and two seniors drop the class, the ratio of the number of juniors to the number of seniors becomes $5:2$. How many students are in the class after these changes?
The number of students in the class after the changes here are 35.
What are ratios?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
The question tells us that 7 more juniors have joined this class, while 2 seniors have dropped the class. Then the ratio would be 5 : 2 from the question.
This would give us the ratios as
[tex]\frac{3x+7}{2x-2} = \frac{5}{2}[/tex]From here we would have to cross multiply
2(3x + 7) = 5(2x - 2)
6x + 14 = 10x - 10
6x - 10x = -10 - 14
- 4x = -24
x = 6
Put the value of x in both equations
3x + 7 = 3 x 6 + 7
= 25
2x - 2 = 2 x 6 - 2 = 10
25 + 10 = 35
The number of students that are in the class is given as 25
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algebra solution for tiffany had $330 in her account in 1999 and the value has been growing exponentially at a constant rate. the value of the account reached $590 in the 2007. what is the value in 2009?
The value of the account in the year 2009 will be $682.
The acount's balance, in t years after 1999, can be modeled by the following equation.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
$330 in an account in the year 1999This means that $590 in the year 20072007 is 8 years after 1999, so P(8) = 590.We use this to find r.Determine the value of the account, to the nearest dollar, in the year 2009.2009 is 10 years after 1999, so this is A(10).The value of the account in the year 2009 will be $682.learn more about solutions here:
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help meeeeeeeeeeeeeeeeee please
Answer:
Step-by-step explanation:
x² + (x + 2)² = (x + 3)²
x² + x² + 4x + 4 = x² + 6x + 9
x² - 2x - 5 = 0
[tex]x_{1}[/tex] = [tex]\frac{-(-2)+\sqrt{4+20} }{2}[/tex] = 1 + √6 ≈ 1 + 2.45 = 3.45 units
[tex]x_{2}[/tex] = [tex]\frac{-(-2)-\sqrt{4+20} }{2}[/tex] = 1 - √6 < 0 can not be solution of the given problem.
x ≈ 3.4 units
x + 2 ≈ 5.4 units
x + 3 ≈ 6.4 units
If a+4/a = 4 then find the value of a^5-1/a^5
pls answer this one as quick as possible.
Value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
What do you mean by algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression which is having only one term is known as a monomial.
Given expression:
a + 4/a = 4
We need to simplify the above expression and will find the value of a.
[tex]a+\frac{4}{a}=4[/tex]
⇒ [tex]\frac{a^2+4}{a}=4[/tex]
⇒ [tex]a^{2}+4=4a[/tex]
⇒ [tex]a^2-4a+4=0[/tex]
⇒ [tex]a^2-2a-2a+4=0[/tex]
⇒ a(a-2) -2(a-2) = 0
⇒ (a-2)(a-2) = 0
⇒ a = 2
Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]
[tex]2^5-\frac{1}{2^5}[/tex]
= 32 - 1/32
= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]
Therefore, value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
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In the graph below, find the coordinate of the image point. O is the origin and P is the point (4, 3). Ry and Rx are reflections around the x- and y- axes.
Complete the following:
HpHo : (3, 0) --- >
(3, 0)
(-5, -6)
(11, 6)
A school district telephone system has three-digit extensions. How many unique extensions are there with no
repeated digits, if the first digit cannot be zero and the last number is a nine?
A.72
B.64
C.504
E.None of the above
64 unique extensions are there with no repeated digits.
What is Combination?Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged.
For the 3-digit area code, the first digit can be any digit from 2 through 9, and each of the two digits that follow can be any digit from 0 through 9. That's a total of 8 × 10 × 10 = 800 different combinations.
Given:
A school district telephone system has three-digit extensions.
So, first digit cannot be zero then we have possibility of total 8 digits.
and the last number is a nine.
unique extensions are there with no repeated digits
= 8 x 8 x 1
= 64
Hence, 64 unique extensions are there with no repeated digits.
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What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
The remainder of the division problem given by the image at the end of the answer is as follows:
How to obtain the remainder of a division problem?When a division does not result in an exact term, we have that the quotient is added to the remainder.
A long division problem is represented as follows:
q(x) + (r(x)/b(x))
In which the terms are listed as follows:
q(x) is the quotient.r(x) is the remainder.b(x) is the divisor.In this problem, the division is given as follows:
(x + 1)/x.
Separating the division into two terms, we have that:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Hence:
The quotient is of x.The remainder is of 1.Missing InformationThe division in this problem is:
(x + 1)/x.
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Answer: B. 1
Step-by-step explanation:
edge 2023
Fig. 3.3 shows an equilateral triangle with the lengths of its sides given in terms of x and y. Find the values of x and y. A 4x cm B 3y cm C (x + y + 5) cm
The values of x and y are 3 and 4.
Given:
shows an equilateral triangle with the lengths of its sides given in terms of x and y.
A 4x cm B 3y cm C (x + y + 5) cm
In equilateral triangle all sides are equal:
4x = 3y = x+y+5
4x = 3y
4x - 3y = 0. ---------eq(1)
4x = x + y + 5
3x - y = 5. ----------eq(2)
solving eq 1 - eq 2*3 we get,
4x - 3y - 9x + 3y = 0 - 15
-5x = -15
x = 3
4x - 3y = 0
4*3 - 3y = 0
12 = 3y
y = 12/3
y = 4
Therefore The values of x and y are 3 and 4.
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Please help me!!!!!!!!
the two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a statistics course at a university. (a) based on these graphs, which of the two exams has the strongest correlation with the final exam grade? explain. (b) can you think of a reason why the correlation between the exam you chose in part (a) and the final exam is higher?
a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.
b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.
Define correlation.The link between variables is described by correlation. It can be characterized as strong or weak, as well as positively or negatively.
Given,
The two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a statistics course at a university.
a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.
b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.
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a bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900. a) what is the probability that a randomly selected credit card holder has a credit card balance less than $2500? b) you randomly select 25 credit card holders. what is the probability that their mean credit card balance is less than $2500? c) compare the probabilities from a) and b).
(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.
Let us pull out the critical elements
Population: Normally distributed with mean of 2870
population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180
As population sigma is known, we do not have apply any corrections
P(xbar < $2500) = ?
Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.
Ztest = (2500-2870 )/ 180 or -370/180 = -2.055
As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma being 95.44% to get a close estimate. If the area between -2 and 2 sigma = .9544 then the area outside = .0456. Half of this (the amount under the curve LESS THAN -2) would be .0228
Using a calculator or computer for an exact answer we find (using a TI-83/86):
nmcdf(-9E6,2500,2870,180) = .0199
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in developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. use a planning value for the population standard deviation of seven minutes. (round your answers up to the nearest integer.) how large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence?
A sample should be 47 to be taken if the desired margin of error is two minutes at a 95% level of confidence
Given information:
A medical facility wants to determine the average amount of time each patient spends with a staff member while creating patient appointment schedules. utilize a planned value of seven minutes for the population's standard deviation.
б=7, ME=2
95% Confidence (to the nearest whole number):
For 95% confidence interval z-critical value is z_{c}=1.96. So
n = (z * б /ME )² = (1.96* 7/ 2)= 47.05
The Requried sample size is 47
If the acceptable margin of error is two minutes at a 95% level of confidence, then a sample of 47 should be taken.
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Use the formula M = log10 T to find the magnitude M of an earthquake with a shock wave that measures
T = 1,000 on a seismograph.
The magnitude is
The magnitude of earthquake on seismograph will be 3 .
What is seismograph?
A seismograph is a device that measures and records crucial data concerning earthquakes. Electromagnetic sensors in seismographs convert ground vibrations into electrical voltages. Seismograms are records that a seismograph generates and displays .
Main Body:
formula given : M = ㏒₁₀T where T =1000
substituting the value of T in the formula
M = ㏒₁₀ 1000
M = ㏒₁₀10³
M = 3㏒₁₀ (㏒₁₀Xᵃ = a㏒₁₀)
M = 3 (㏒₁₀10 =1)
Therefore the magnitude of the earthquake is 3.
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I need help like asap !!!
only numbers and decimal points
Please help. ill give brainliest
Answer:
I believe the answer is number 2, which is 20 degrees.
Step-by-step explanation:
When I plugged that number in for x for both of them I got the numbers 81 and 99. Added them together ad they made 180 degrees. Which makes them supplementary.
A box is filled with black (B), white (W), red (R), green (G), and prink (P) phone cases. A phone case is selected at random. what is the sample space for this experiment? A) S={B,W,R,G,P} B) S={B,W,R} C) S={G,P} D) S={B,R,G,P}
Do You UNDERSTA
D?
1.? ESSENTIAL QUESTION Why is identifying
the domain and range important when
defining a function?
If Eof= 26 and FOG= 38, then what is the measure of BOG? The diagram is not to scale.
If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.
What is a measure of angle?
An angle is measured in degrees, thus the term "degree measure." Because one complete revolution equals 360 degrees, it is divided into 360 parts. Each stage of the revolution represents a degree.
The given data:
A measure of EOF = 26 and a measure of FOG = 38.
Then we can say that OF is an angle bisector of angle EOG.
Then the measure of BOG = EOF + FOG
= 26 + 38
= 64 degrees.
Hence, If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.
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Ben and Charlie had the same number of books at first. Ben gave away 16 of his books, Charlie gave away 28 books. The ratio of the number of books Ben had left to that of Charlie's is 3:1. How many books did each boy have at first.
The number of books each boy had based on the 3:1 ratio of the books remaining is 34 books
What is a ratio?A ratio is a quantitative expression of the relationship between two values that indicates the relative proportion of each amount.
The initial number of books Ben had = The initial number of books Charlie has
The number of books Ben gave away = 16 books
The number of books Charlie gave away = 28 books
The ratio of the number of books Ben and Charlie had left is 3:1
Let x represent the number of books each of them initially have. Representing the numbers as a ratio gives;
The number of books Ben had left = x - 16
The number of books Charlie had left = x - 28
[tex]\dfrac{x - 16}{(x - 16) + (x - 28)} = \dfrac{3}{3+1}[/tex]
Which gives; [tex]\dfrac{x - 16}{(2\cdot x - 44) } = \dfrac{3}{4}[/tex]
4 × (x - 16) = 3 × (2·x - 44)
6·x - 4·x = 3×44 - 4×16 = 68
2·x = 68
x = 68 ÷ 2 = 34
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Suppose that y varies directly with .x, and y=-8 when x=2.
(a) Write a direct variation equation that relates x and y.
Equation:
(b) Find y when x = 5.
OC
Answer:
y = -4x
b. y = -20.
Step-by-step explanation:
y = kx
-8 = 2k
k = -8/2
k = -4
y = -4x
y = kx
y = -4 × 5
y = -20
40 points bc im ducking struggling!!!! 5. Why is -x/y equivalent to x/-y? Explain..
-x/y is equivalent to x/-y according to the division rule a/b*d/c=a/b*c/d.
Describe division.In division, a number is divided, which is an easy operation. In mathematics, division is the division of a sum into equal parts. A group of 20 people, for instance, could be divided into four groups of 5, five groups of 4, and so on. Division's opposite is multiplication. If 3 groups of 4 add up to 12, then 4 are in each group when 12 is divided into 3 equal groups.
According to the division rule a/b/c/d=a/b*d/c,
=1/(y/-x)
=1*-x/y
=-x/y
-x/y is equivalent to x/-y according to the division rule a/b÷c/d=a/b*d/c.
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B. Determine the principal
1. √64
2. √100
3. √169
4. √196
5. √256
how please
The principal square root of √64 is 8, √100 is 10,√169 is 13, √196 is 14 and √256 is 16.
According to the question,
We have the following information:
1. √64
2. √100
3. √169
4. √196
5. √256
Now, in order to find the principal square root of these numbers, we will express these numbers in the form of the product of numbers then we will find the square root.
1) [tex]\sqrt{64}[/tex]
We have the following expression:
[tex]\sqrt{2*2*2*2*2*2}[/tex]
2*2*2
8
2) [tex]\sqrt{100}[/tex]
[tex]\sqrt{2*2*5*5}[/tex]
2*5
10
3) [tex]\sqrt{169}[/tex]
[tex]\sqrt{13*13}[/tex]
13
4) [tex]\sqrt{196}[/tex]
[tex]\sqrt{2*2*7*7}[/tex]
2*7
14
5) [tex]\sqrt{256}[/tex]
[tex]\sqrt{2*2*8*8}[/tex]
2*8
16
Hence, the principal square root of √64 is 8, √100 is 10,√169 is 13, √196 is 14 and √256 is 16.
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recipe requires 1 cup of sugar for every 6 cups of flour. How many cups of sugar will be required for 18 cups of flour?
Answer: 3 cups of sugar will be required for 18 cups of flour.
Step-by-step explanation:
1 cup of sugar - 6 cups of flour
2 cups of sugar - 12 cups of flour
3 cups of sugar - 18 cups of flour
I hope this make sense.
help meeeeeeeeeeeeeeeeee please
Answer:
I believe it's 4.5 seconds
shopper needs 48 hot dogs. The store sells identical hot dogs in 2 differently sized packages. They sell a six-pack of hot dogs for $2.10, and an eight-pack of hot dogs for $3.12.
The pack of hot dogs that the shopper should buy that would be cheaper is six - pack of hot dogs
How to find the pack to be bought?If the shopper decided to buy the six-pack of hot dogs for $2.10, their total cost to be able to get 48 hot dogs would be:
= Cost per six pack of hot dogs x ( Number of hot dogs needed / Number of hot dogs in pack)
=2.10 x (48 / 6)
= 2.10 x 8
= $16.80
The cost if the shopper wants the eight pack is:
= 3.12 x (48 / 8)
= $18.72
The shopper should pick the six - pack of hot dogs because it is cheaper.
The rest of the question is:
Which option would be cheaper to the shopper?
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Find the rate of change between the following points:
(2,-1)
(-6,-5)
The rate of change between (2,-1) and (-6,-5) is 1/2.
What is the rate of change?
The slope is the ratio of the rate of change between two points (also known as the "slope") to (the change in the x coordinate).
Let (x,y)=(2,-1), (m,n)=(-6,-5)
Rate of change=(n-y)/(m-x)=(-5-(-1))/(-6-2)=1/2.
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Wyatt is deciding between two different movie streaming sites to subscribe to. Plan A costs $19 per month plus $0.50 per movie watched. Plan B costs $13 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Wyatt watches x per month, and let B represent the monthly cost of Plan B if Wyatt watches a movies per month. Write an equation for each situation, in terms of x, and determine the number of monthly movies watched, x, that would make the two plans have an equal monthly cost.
Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.
Cost of both the plans will be equal for 6 movies.
What is a linear equation?A linear function is defined as a function that has either one or two variables without exponents.
Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.
According to question,
A = 19 + 0.50x and
B = 13 + 1.5x
For costs being equal, we have,
A = B
19 + 0.50x = 13 + 1.5x
x = 6
Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x
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Mark and Janet together have 10 pairs of jeans.
Janet has 6 more pairs of jeans than John.
How many pairs of jeans does John have?
Answer:
John has 4 pair of jeans.
Hope this helps : )
Step-by-step explanation:
Together they 10, so if Janet has 6 more, we have to subtract.
10 - 6 = 4
Check:
6 + 4 = 10 ✔
Jace's company has 17 employees who work full time. The company has a number of very dedicated
clients, and last year they generated $2 million in revenue. What type of software should Jace use?
The type of software should Jace use will be "Entry level accounting system" as his company has 17 employees who work full time. The company has a number of very dedicated clients, and last year they generated $2 million in revenue.
What is entry level accounting system?Entry-level accounting includes typical accounting operations such as accounts payables and receivables, as well as basic financial reporting. These are, predictably, among the most affordable items; some sellers even provide an entry-level bundle for free for a brief time as a trial period. Entry-level accounting jobs are the initial level of accounting positions for people who are just starting out in their careers. Accounting Representative, Accounting Executive, Accounting Assistant, Accounting Associate, Entry-Level Accounting Clerk, Staff Accountant, and Bookkeeper are examples of entry-level occupations.
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The town of Wattle has a population that is decreasing steadily.
It is found that the population is decreasing at a rate of 5.4% per year.
How long will it take for the population to be beneath 45% of what it is now?
Answer:
After 1 yr P1 = .946 Po
After 2 yrs P = .946 P1 = .946^2 Po
After n yrs P = .946^n Po
.45 = .946^n What is n needed to drop P to .45 P
log .45 = n log .946
n = log .45 / log .946 = -.347 /-.0241 = 14.4 years