math word problem: factions of a number

The total amount of money in the savings account using Student 1's equation is 100 + 8 = $108.

An account is a record of financial transactions that is kept to track the flow of money in and out of an individual or organization. It is a numerical record of a company's assets, liabilities, equity, revenue, and expenses, and is used to measure the overall financial health and performance of a business.

Student 1's equation: Savings = 100 + (0.08 x 10):
Using Student 1's equation, the total amount of money in the savings account is $108. This is because the original balance of $100 is increased by 8% (0.08) multiplied by 10, which is equal to $8. Therefore, the total amount of money in the savings account using Student 1's equation is 100 + 8 = $108.

Student 2's equation: Savings = 100 x 1.08
Using Student 2's equation, the total amount of money in the savings account is $108. This is because the original balance of $100 is multiplied by 1.08 which is equal to $108. Therefore, the total amount of money in the savings account using Student 2's equation is 100 x 1.08 = $108.

Student 3's equation: Savings = 100 + 8
Using Student 3's equation, the total amount of money in the savings account is $108. This is because the original balance of $100 is increased by 8, which is equal to $108. Therefore, the total amount of money in the savings account using Student 3's equation is 100 + 8 = $108.

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We need to find the probability that a student will winn a gift card of at leat $25.

We use probability formula:

In this case, the total number of events is: 8

this is because we have 8 possible triangles as the result.

The favorable events are the number of triangle that have a value of at least $25, which are the following:

The only two favorable events are $25 and $50, so

Favorable events = 2

Substituting this into our probability formula:

We can simplify this probability as 1/4, or as 0.25

Answer: 2/8=1/4=0.25

Answer:

20% increase

Step-by-step explanation:

To find the percent increase, use this formula

New value - original value

----------------------------------------

original value

114-95

-----------

95

19

---- = .2

95

.2 is 20%, so it is a20% increase

The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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Answer:

ill mark brainlist or whatever it is“In the period 1500- 1700 the main aim of changes to punishments was retribution” how far do you agree? explain ur answer.

hellllppppy9

shouldshould

Step-by-step explanation:

should

should

The expression 2 - 5(x - 1) is a linear expression

From the question, we have the following parameters that can be used in our computation:

2 - 5(x - 1)

The general rule is that

Using the above as a guide, we have the following:

2 - 5(x - 1) is a linear expression

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Answer:

x = -1

y = 7

Step-by-step explanation:

-7x = -3x +4

4x = -4

x = -1, y = 7

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.

given

Put this together using the conditions given: 319.14 / (1- 19%)

Determine the total or difference: 319.14 / 0.81

Diminish the fraction: 394

Response: 394

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

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The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.

solve the equation logₓ(64) + 5 = 2, we can follow these steps:

Step 1: Move the constant term to the other side of the equation:

logₓ(64) = 2 - 5

logₓ(64) = -3

Step 2: Rewrite the equation in exponential form:

x^(-3) = 64

Step 3: Rewrite 64 as a power of x:

x^(-3) = x^6

Step 4: Set the exponents equal to each other:

-3 = 6

The equation -3 = 6 is not true, which means there is no real solution to the given equation.

Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.

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As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

a e f and g I think this because it has to be then they say that then ya

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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Step-by-step explanation:

so, what's the problem ?

it's all there, we only need to take the calculator (or simply our heads) and do the calculation :

2×5 - 5×2 = 10 - 10 = 0

you see ? that was all that was needed.

put the given values for the variables into the places of these variables, and then calculate !

that is what variables are for : placeholders for actual values.

9514 1404 393

Answer:

  64

Step-by-step explanation:

Put the value where the variable is and do the arithmetic.

  -8u = -8(-8) = 64

Answer: 9e

Step-by-step explanation:

Answer: 4.037 × 10³

Step-by-step explanation:

If you simplify 4.037 × 10³, you get 4037

4.037 × 10³

4.037 × 1000

4037

Hope this helped!

The number of workers required = 15

Observe the given problem and find out the relation between the number of workers and the number of days.

In given two one quantity decreased and the other quantity increased then both quantities are said to be in inverse proportions.    

Here the product of two quantities will equal a constant.

Here we have

10 workers can complete a piece of work in 18 days

Let 'x' be the number of workers required to complete work in 12 days

Here when the number of days increases the number of workers will be decreased which shows the number of work is inversely proportional to the number of days

The relation can be represented as  

=> 10 worker × 18 days  = 12 days × x workers

=> 10 × 18 = 12x

=> x = 180/12

=> x = 15

Therefore,

The number of workers required = 15

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Answer: 30 5/12

Step-by-step explanation: 18 1/4/3=6 1/12. 6 1/12x5=30 5/12.

Answer:

a_n = 47 - 8n

Step-by-step explanation:

a_1 = 39

a_2 = 31

a_3 = 23

31 - 39 = -8

23 - 31 = -8

This is an arithmetic sequence with constant difference -8.

a_1 = 39

a_2 = 39 - 8

a_3 = 39 - 8 - 8 = 39 - 2(8)

a_4 = 39 - 8 - 8 - 8 = 39 - 3(8)

...

a_n = 39 - (n - 1)(8)

a_n = 39 - 8(n - 1)

a_n = 39 - 8n + 8

a_n = 47 - 8n

Answer:

\(a_n=47-8n\)

Step-by-step explanation:

Given sequence:

Calculate the differences between the terms:

\(39 \underset{-8}{\longrightarrow} 31 \underset{-8}{\longrightarrow} 23\)

As the differences are constant (the same), this is an arithmetic sequence with:

\(\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\end{minipage}}\)

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

\(\implies a_n=39+(n-1)(-8)\)

\(\implies a_n=39-8n+8\)

\(\implies a_n=47-8n\)

In mathematics, the value for x is 9.38 in Example 1 and 11.40 in Example 2.

What are the value signifies?

The value in mathematics refers to the numerical representation of a quantity or concept. It represents the numerical magnitude of a mathematical expression, equation, or quantity.

For example, in the expression 2 + 3 = 5, the value of 2, 3, and 5 all represent specific numerical magnitudes. The value of a variable, such as x or y, can change depending on the context or equation it is used in, but it still represents a specific numerical value.

Values can be represented in different forms, such as integers, fractions, decimals, or real numbers, and they are used to perform mathematical operations and solve mathematical problems.

a) Example 1

AB  is a diameter

PQ is a chord

AO = 13

AO is perpendicular to PQ (2AP=AQ)

In Δ APO

\((AO)^2 =(AP)^2+ (PO)^2\)

\((13)^2 = (9)^2 + X^2\)

\(169 = 81 +X^2\)

X^2 = 169-81

X^2 = 88

X = √88

X = 9.38

As a consequence, 9.38 is equal to x.

b) Example 2

LM = 18

KN = 7

LK = ?

LN = 9

In Δ LKN:

\(X^2 = (KN)^2 + (LN)^2\)

\(X^2 = (7)^2 + (9)^2\)

X^2 = 49 + 81

X^2 = 130

X =√ 130

X = 11.40

As a consequence, 11.40 is equal to x.

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Answer:

x ≤ 9

Step-by-step explanation:

Step 1: Write inequality

x - 9 ≤ 2(9 - x)

Step 2: Solve for x

Here we see that any solution less than or equal to 9 would work.

Answer:

x ≤ 9

Step-by-step explanation:

x -9 ≤ 2(9 -x)    

x -9 ≤ 18 -2x

+2x         +2x

3x -9 ≤ 18

    +9    +9

3x  ≤ 27

\(\frac{3x}{3}\) ≤ \(\frac{27}{3}\)

x  ≤ 9

the answer is (-8) because x=4, y=-6, z=11

These consists of more than 1 equation with unknown variables. The value that is not a solution in (x,y, z)is -8

These consists of more than 1 equation with unknown variables. Given the set of equations

x+y+z=9

x-y-z=-1

x-y+z= 21

Add 1 and 2

2x = 9 - 1

2x = 8

x = 4

Subtract 2 and 3

-2z = -22

z = 11

Determine the value of y

x +y + x = 9

4 + y + 11 = 9

y = 9 - 15

y = -6

Hence the value that is not a solution in (x,y, z)is -8

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Answer:

3. y=6x/5+7/5

4.y=2x+2

5.

Step-by-step explanation:

Answer:

3) m = 6/5

4) m = 2

5) y = 3x + 2

6) y = -2x - 3

Step-by-step explanation:

To find slope for questions 3 and 4, use formula below⤵⤵⤵

\( \frac{y _{2} - y _{1} }{x _{2} - x _{1}} \)

3) 5-(-1) ➡ 5+1 ➡ 6

3-(-2) ➡ 3+2 ➡ 5

4) -8-4 ➡ -12 ➡ 12 12÷6 = 2

-5-1 ➡ -6 ➡ 6

For questions 5 and 6, find the y-intercept first, which is the point in which the line crosses the y-axis. From then you can use rise/run to find the slope.

Hope this helps :)

Answer:

1/8, 2/8, 3/8, 4/8, 5/8, 6/8

Step-by-step explanation:

If i have interpreted correct. You want to know a fraction with a denonminator of 8 that is less than 5/6

5/6=0.8333

Multiple Answers

1/8, 2/8, 3/8, 4/8, 5/8, 6/8

Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

\(C(1) = C(0) * \frac{1 - 0.14}{1}\)

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * \(\frac{1 - 0.14}{1}\)

Substituting the formula for C(1), we get:

C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)

or, more generally:

\(C(n) = C(0) * (0.86)^n\)

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

\(C(0) * (0.86)^n < 0.09\)

Dividing both sides by C(0), we get:

\((0.86)^n < 0.09\)

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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Answer:

Explanation:

We must write this equation in the form

(

x

−

a

)

2

+

(

y

−

b

)

2

=

r

2

Where

(

a

,

b

)

are the co ordinates of the center of the circle and the radius is

r

.

So the equation is

x

2

+

y

2

−

10

x

+

6

y

+

18

=

0

Complete the squares so add 25 on both sides of the equation

x

2

+

y

2

−

10

x

+

25

+

6

y

+

18

=

0

+

25

=

(

x

−

5

)

2

+

y

2

+

6

y

+

18

=

0

+

25

Now add 9 on both sides

(

x

−

5

)

2

+

y

2

+

6

y

+

18

+

9

=

0

+

25

+

9

=

(

x

−

5

)

2

+

(

y

+

3

)

2

+

18

=

0

+

25

+

9

This becomes

(

x

−

5

)

2

+

(

y

+

3

)

2

=

16

So we can see that the centre is

(

5

,

−

3

)

and the radius is

√

16

or 4