A computer costs $1500, but on average, it loses 20% of its value each year. a.What is the start value?

The value of "n" is 6.

"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:

7(n+4) = 5(n+8)

Expanding the brackets, we get:

7n + 28 = 5n + 40

Simplifying, we get:

2n = 12

n=6

A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.

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The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

50 gallons

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i aint never seen two pretty best friends its always one of em gotta be ugly

\({ \qquad \qquad \huge \rm \underline{ \underline{ \Répondre}}} \)

lets find the equation of line in two point form, considering points (0 , 0) and (-3 , 4)

\(\qquad \rm\dashrightarrow \:y - 0= \dfrac{4 - 0}{ - 3 - 0} (x -0)\)

\(\qquad \rm\dashrightarrow \:y = - \dfrac{4 }{ 3 } x \)

That's the required equation ~

You can also simply it as :

\(\qquad \rm\dashrightarrow \:3y= - 4x\)

\(\qquad \rm\dashrightarrow \:4x + 3y = 0\)

9514 1404 393

Answer:

  $400

Step-by-step explanation:

If the price after taking 25% off is $300, then $300 is 75% of the original price.

  $300 = 0.75p

  $300/0.75 = p = $400

The original price was $400.

_____

Check

0.25 × $400 = $100

$400 -100 = $300 . . . . the price after taking 25% off

Subtract to find the amount you left as a tip:

24 - 20 = 4

The tip amount was $4

Now divide the amount of the tip by the amount of the bill before the tip was added:

4 / 20 = 0.2

Multiply by 100:

0.2 x 100 = 20%

Answer: the tip was 20%

The projection of vector w onto vector v is (-34/29)i + (85/29)j, and the decomposition of vector v into v1 parallel to w and v2 orthogonal to w is v1 = (-34/29)i + (85/29)j and v2 = (142/29)i - (60/29)j.

To find the projection of vector w onto vector v, we need to use the formula: proj_w(v) = (v · w) / ||w||^2 * w. Then, to decompose vector v into two vectors, v1 parallel to w and v2 orthogonal to w, we can use the formulas: v1 = proj_w(v) and v2 = v - v1.

Given vector v = 4i + 5j and vector w = -2i + 5j, let's find the projection of w onto v.

1. Calculating proj_w(v):

proj_w(v) = (v · w) / ||w||^2 * w

To find the dot product (v · w), we multiply the corresponding components and sum them up:

(v · w) = (4 * -2) + (5 * 5) = -8 + 25 = 17

The magnitude of w, ||w||, can be calculated as follows:

||w|| = √((-2)^2 + 5^2) = √(4 + 25) = √29

Now we can calculate proj_w(v):

proj_w(v) = (17 / 29) * (-2i + 5j)

Simplifying, we get:

proj_w(v) = (-34/29)i + (85/29)j

2. Decomposing vector v into v1 and v2:

v1 is the parallel component of v with respect to w, and we already calculated it as proj_w(v):

v1 = (-34/29)i + (85/29)j

v2 is the orthogonal component of v with respect to w, which can be found by subtracting v1 from v:

v2 = v - v1 = (4i + 5j) - ((-34/29)i + (85/29)j)

Simplifying, we get:

v2 = (142/29)i - (60/29)j

Therefore, the projection of vector w onto v is proj_w(v) = (-34/29)i + (85/29)j, and the decomposition of vector v into v1 and v2 is v1 = (-34/29)i + (85/29)j and v2 = (142/29)i - (60/29)j.

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Answer:

1 2/5

Step-by-step explanation:

The correct option among the given choices is $4,918.16.

To calculate the future value, we can use the formula for compound interest:

FV = P * (1 + r/n)^(n*t)

Where:

FV is the future value

P is the principal amount (initial investment)

r is the interest rate (in decimal form)

n is the number of compounding periods per year

t is the number of years

In this case, the principal amount is $300, the interest rate is 12 percent (0.12), the compounding is semiannual (n = 2), and the time period is 24 years. Plugging these values into the formula, we get:

FV = $300 * \((1 + 0.12/2)^(2*24)\)

  ≈ $300 * \(1.06^{48}\)

  ≈ $300 * 4.91816

  ≈ $1,475.45

Therefore, the future value of $300 after 24 years, compounded semiannually at an interest rate of 12 percent, is approximately $4,918.16. Among the given options, the closest match is $4,918.16.

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If the expression be 23 x² + 3x + 8 then the constant exists 8.

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.

Let the expression be 23 x² + 3x + 8

then the constant exists 8.

Therefore, the correct answer is option C. 8.

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\(\boxed{\sf a_n=\dfrac{a_{n-1}}{10}\times 4,n\gt 1}\)

Lets verify

\(\\ \sf\longmapsto a_2=\dfrac{a_1}{10}\times 4\)

\(\\ \sf\longmapsto a_2=\dfrac{500}{10}\times 4=50(4)=200\)

And

\(\\ \sf\longmapsto a_3=\dfrac{a_2}{10}\times 4\)

\(\\ \sf\longmapsto a_3=\dfrac{200}{10}\times 4=20(4)=80\)

And

\(\\ \sf\longmapsto a_4=\dfrac{a_3}{10}\times 4\)

\(\\ \sf\longmapsto a_4=\dfrac{80}{10}\times 4=8(4)=32\)

Hence verified

Lets predict next term

\(\\ \sf\longmapsto a_5=\dfrac{a_4}{10}\times 4\)

\(\\ \sf\longmapsto a_5=\dfrac{32}{10}\times 4=3.2\times 4=12.8\)

Using the logarithm quotient rule, it can be simplified to log1 - logA. Since log1 = 0 for any base, this simplifies further to -logA.

We simplify and solve the given expressions using the mentioned terms. Here are the step-by-step explanations for each expression:

1. logA: This expression represents the logarithm of a number A to a specified base. Without any base provided, it cannot be simplified further.

2. 1logAA: Since the coefficient of the logarithm is 1, this simplifies to logAA, which represents the logarithm of A to the base A. By definition, logAA = 1.

3. logA x Blog (a/b): This expression seems to have formatting issues, so I'll break it down into two separate expressions: - logA x B: This represents the logarithm of the product AB to a specified base. Using the logarithm product rule, it can be simplified to logA + logB. - log (a/b): This represents the logarithm of the quotient a/b to a specified base. Using the logarithm quotient rule, it can be simplified to loga - logb.

4. log A ^ B: This expression represents the logarithm of A raised to the power of B to a specified base. Using the logarithm power rule, it can be simplified to B * logA. 5. log 1/A: This expression represents the logarithm of the reciprocal of A (1/A) to a specified base.

Using the logarithm quotient rule, it can be simplified to log1 - logA. Since log1 = 0 for any base, this simplifies further to -logA.

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Sharon worked 49 hours to earn $749.

To solve this problem, we need to write an equation that models Sharon's earnings based on her base pay and overtime pay. The equation is as follows:

Earnings = (Base pay x Regular hours) + (Overtime pay x Overtime hours)

Since Sharon earns a base pay of $14 per hour and time and a half for overtime, her overtime pay is $14 x 1.5 = $21 per hour. We can plug these values into the equation:

$749 = ($14 x 40) + ($21 x Overtime hours)

Solving for the overtime hours, we can rearrange the equation and isolate the variable on one side:

$749 - $560 = $21 x Overtime hours

$189 = $21 x Overtime hours

Overtime hours = 9

Therefore, Sharon worked 9 hours of overtime in addition to her regular 40 hours, for a total of 49 hours.

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Answer:

Slant height = 8 feet.

Step-by-step explanation:

If the perimeter of the square base = 12 then each side of the base = 12/4

= 3  feet and its area = 3*3 = 9 ft^2

The area of one of the triangular sides = 1/2 * 3 * h where h is slant height.

So total surface area = 57 = 9 + 4 * 1.5h

9 + 6h = 57

6h = 48

h = 8 feet.

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Answer:

\( \frac{2}{27} \)

Step-by-step explanation:

\( \frac{14}{27} \div 7 = \frac{14}{27} \times \frac{1}{7} \)

if we simplify 14 and 7...

\( \frac{2}{27} \times 1\)

which results in 2/27

2/27 or  0.074 is 14/27 divided 7.

14/27 ÷ 7

First, we change whole number into fractions number,

which is 7/1

14/27 ÷ 7/1

14/27 ÷ 7/1

2/27 or 0.074

Therefore, the correct answer is 0.074.

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Given:

Total produce = 80 liters

15% Acid solution and 25% acid solution

Find-:

How many litres of each

Explanation-:

Let

Total 80 litres

eq(2) - 3eq(1) is:

So, the value of "y" is:

So x is 40

Then,

Answer:

1. 28:15

2. 3:13

Step-by-step explanation:

The ratios above have no common factor.

4:24 .

Common factor : 4

18:30

Common factor : 6

12:14

Common factor : 2

Answer:

28:15

3:13

Step-by-step explanation:

The ratios 28:15 and 3:13 are in their simplest form, meaning that they cannot be simplified any further.

Meanwhile, the other 3 ratios are not in their simplest form and can still be simplified if they are divided by either 2 or 4.

Answer:

31.55

Step-by-step explanation:

First the original value minus the decreased value

then the new anwser over the original value times by 100

31.55%

$382 .............. 100%

$261.50 ..............x%

x = 261.50×100/382

= 26150/382

= 68.45%

The respective prices are given below as

The price of the sandwich is 20/3 dollars.

The salad may be purchased for a price of $16/3.

There is a fee of $2 for the drinks.

Let's say that the price of the sandwich is x.

Allow the price of salad to equal y.

Allow the price of drinks to equal z.

The new total for this meal is $46. It includes three sandwiches, three beers, and two salads. Thus;

3x + 3y + 2z = 40 ——- (eq 1)

The price of $29 covers two sandwiches, two drinks, and one salad.

Thus;

2x + 2y + z = 26 ——-(eq 2)

It will cost you $54 for four sandwiches, one drinks, and three salads. Thus;

4x + y + 3z = 38 ———-(eq 3)

The following are the results of concurrently solving the three equations:

x = 20/3

y = 16/3

z = 2

Therefore, the following is how much each item costs:

There is a charge of $20/3 for the sandwich.

The salad may be purchased for a price of $ 16/3.

There is a fee of $2 for the drinks.

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Therefore, the half-life of Thorium-234 is approximately 24.1 days.

Given that the rate constant for the beta decay of thorium-234 is 2.881 x 10-2 day-1.

We are to find the half-life of this nuclide.

A rate constant is a proportionality constant that links the concentration of reactants to the rate of the reaction. It is denoted by k. It is always specific to a reaction and is dependent on temperature.

A half-life is the time taken for half of the radioactive atoms in a sample to decay. It is denoted by t1/2.

To find the half-life, we use the following formula:

ln (2)/ k = t1/2,

where k is the rate constant given and ln is the natural logarithm.

Now, substituting the given values,

ln (2)/ (2.881 x 10-2 day-1) = t1/2t1/2 = ln (2)/ (2.881 x 10-2 day-1)≈ 24.1 days

Therefore, the half-life of Thorium-234 is approximately 24.1 days.

The half-life of thorium-234 is approximately 24.1 days.

The half-life of a nuclide is the time taken for half of the radioactive atoms in a sample to decay. It is denoted by t1/2. It is used to determine the rate at which a substance decays.

The rate constant is a proportionality constant that links the concentration of reactants to the rate of the reaction. It is denoted by k. It is always specific to a reaction and is dependent on temperature.

The formula used to find the half-life of a nuclide is ln (2)/ k = t1/2, where k is the rate constant given and ln is the natural logarithm.

Given the rate constant for the beta decay of thorium-234 is 2.881 x 10-2 day-1, we can use the above formula to find the half-life of the nuclide.

Substituting the given values,

ln (2)/ (2.881 x 10-2 day-1) = t1/2t1/2 = ln (2)/ (2.881 x 10-2 day-1)≈ 24.1 days

Therefore, the half-life of Thorium-234 is approximately 24.1 days.

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Answer:

the answer equals 3×7=96

Answer:

10, 14, 18

Step-by-step explanation:

We know that the nth term is '4n+6', so we just have to plug in whichever number we want for n, where n is the nth term in the sequence. The first term would be 4 * 1 + 6 = 10, the second term would be 4 * 2 + 6 = 14, and finally the third term would be 4 * 3 + 6 = 18. Therefore, your answer should be 10, 14, 18.

So, the equivalent system of equations is: −3x + y = 12, −3x + 3y = 18, −3x + 4y = 30, −3x + 2y = 18.

To create an equivalent system of equations using the sum of the system and the first equation, we can add the first equation to each of the other equations. Here's the resulting system:

Equation 1: −3x + y = 12

Equation 2: −3x + 3y = 18 (sum of Equation 1 and Equation 2)

Equation 3: −3x + 4y = 30 (sum of Equation 1 and Equation 3)

Equation 4: −3x + 2y = 18 (sum of Equation 1 and Equation 4)

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An equivalent system of equations can be created by adding the first equation to the sum of the system, resulting in: -3xy + (-2x + 4y) = 18.

To create an equivalent system of equations using the sum of the system and the first equation, we need to combine the given system of equations with the first equation.

The given system of equations is:
−3xy = 12
3y = 6

To create an equivalent system of equations, we can add the first equation to the sum of the system:

−3xy + (−3xy + 3y) = 12 + 6

Simplifying this equation:

−6xy + 3y = 18

Therefore, the equivalent system of equations using the sum of the system and the first equation is:

−3xy = 12
3y = 6
−6xy + 3y = 18

In this new system, the first two equations remain the same, while the third equation is the result of adding the first equation to the sum of the system. This equivalent system allows us to solve for the variables x and y.

Remember to always check your answers by substituting the values of x and y back into the original equations to ensure they satisfy all equations in the system.

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a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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We have the following ratio scale:

If we move the DRAWING term to the rght hand side, we get

In our case, the line is 15 inches long, then we have

which gives

Therefore, the answer is 50 inches.

The Kruskal-wallis one-way ANOVA compares the overall difference between two or more independent samples. So, the correct option is option a. kruskal-wallis one-way ANOVA

The answer is option A, the Kruskal-Wallis one-way ANOVA compares the overall difference between two or more independent samples.

The Sign test and Wilcoxon rank test are non-parametric tests used for comparing paired samples, while the Mann-Whitney U test is used for comparing two independent samples.

This test is used to compare the overall difference between two or more independent samples when the assumptions of a regular one-way ANOVA are not met.

The Kruskal-Wallis test is applicable when the data violate the assumptions of normality and/or equal variances required by parametric ANOVA tests.

Instead of comparing means, it compares the ranks of the data values within each group to assess if there are significant differences between the groups.

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