subtract 8 1/6 - 5 1/8

The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.

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Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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Answer:

\(Raisins : Pretzels = 1 : 2\)

\(Almonds: Raisins = 3 : 1\)

Step-by-step explanation:

Given

\(Raisins = 2\)

\(Pretzels = 4\)

\(Almonds = 6\)

Solving (a):

Ratio of Raisins to Pretzels

\(Raisins : Pretzels = 2 : 4\)

Divide 2 and 4 by 2

\(Raisins : Pretzels = 2/2 : 4/2\)

\(Raisins : Pretzels = 1 : 2\)

Solving (b):

Ratio of Almonds to Raisins

\(Almonds: Raisins = 6 : 2\)

Divide 2 and 6 by 2

\(Almonds: Raisins = 6/2 : 2/2\)

\(Almonds: Raisins = 3 : 1\)

Answer:

raisins: pretzels=1:2

Almonds: raisins=3:1

Answer:

y = 0.0807x - 3.4286

Step-by-step explanation:

Given the data above :

X :

1400

1700

1500

Y:

108

133

120

Using a linear regression calculator, the regression equation obtained is :

y = 0.0807x - 3.4286

Slope = 0.0807

Intercept = - 3.4286

x = predictor variable

y = predicted variable

Answer:

Exact form: 2.5185185185185

Simplified form: 2.52

Fraction form: 63/25

Step-by-step explanation:

As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.

Confidence interval,

in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.

Given,

in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.

Here we need to find the given statement is true or false.

While we looking into the given question, we have identified that the value of

Confidence interval = 95%

Sample size = 20

Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).

Therefore, the statement is in correct.

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In addition to being novel, arbitrary matrices with complicated members are seen to hold potential. It is based on a theorem of Schur, who claims that any complex matrix.

A matrix with any number of elements is said to be arbitrary. The following would be a random 2x2 matrix: [a,b] [c,d] where a, b, c, and d are all components of a set (usually the real numbers.)

"Arbitrary" is defined as "undetermined; not assigned a definite value." For instance, the statement x+x=2x is accurate for any value of xR, whereas the statement x+x=2 is only accurate for one particular value, x=1.

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Answer:

If the original recipe requires 2/3 cup of flour and 3 ¾ teaspoons of salt, we can determine the amount of salt needed for one cup of flour using a proportion.

2/3 cup flour : 3 ¾ teaspoons salt

1 cup flour : x teaspoons salt

We can cross-multiply to get:

(2/3) * x = (3 ¾) * 1

2x/3 = 15/4

Multiplying both sides by 3/2:

x = (9/2) teaspoons of salt

Therefore, Lexi needs 9/2 or 4.5 teaspoons of salt when making corn bread with 1 cup of flour to maintain the ratio.

Answer:

C. 40π cm²

Explanation:

• The central angle of the sector = 225 degrees

• The radius of the sector = 8cm

For a sector of radius r and central angle θ, we calculate the area using the formula below:

Substituting the given values, we have:

The area of the sector is 40π cm².

The cutting plane method involves adding new constraints to identify the convex hull of the feasible region in integer linear optimization problems. It is less efficient than the branch and bound method but can still be effective for certain problems.

The approach to solving integer linear optimization problems that tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points is known as the cutting plane method.

The cutting plane method involves iteratively adding new constraints to the optimization problem in an attempt to identify the convex hull of the feasible region. These constraints are chosen in such a way that they do not exclude any feasible integer points, and they are added until the convex hull is identified. Once the convex hull is identified, the optimization problem can be solved using standard linear programming techniques.

This method is often used to solve integer linear optimization problems that are too large or complex to be solved using other methods, such as the branch and bound method. It is generally less efficient than the branch and bound method, but it can still be effective for certain types of problems.

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

$360

Step-by-step explanation:

If the company charges $30 for $500 in one month.

The interest they will be changing for a year = 30*12 = $360 interest.

It's just simple, multipling the the interest value by 12 to get it's annual interest value.

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

The choice that is equivalent to the given product when x>0 is (C) x/2.

The result of multiplying two terms with two different signs will be negative, while the product of two factors with the same signs will be positive.

(xa * xb) = x(m + n) if x is a variable and a and b are positive integers.

To simplify the given product, we can combine the square roots and simplify the coefficients:

\($\begin{aligned} \sqrt{\frac{3x}{2}}\times\sqrt{\frac{x}{6}} &= \sqrt{\frac{3x}{2}\cdot\frac{x}{6}} \ &= \sqrt{\frac{3x^2}{12}} \ &= \sqrt{\frac{x^2}{4}} \ &= \frac{x}{2} \end{aligned}\)

Therefore, the choice that is equivalent to the given product when x>0 is (C) x/2.

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Answer: 34,650 permutations

Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

Step-by-step explanation:

12+ 3x= -24 -3x

Collect like terms

12 +24= - 3x -3x

36 = - 6x

Divide both sides by -6

Therefore, x = -6

Answer:

Im pretty sure its d

Step-by-step explanation:

im not sure but i’m sorry if its wrong

Answer:

D. 180

Step-by-step explanation: multiply

For part (a), we need to find the derivative of the supply equation with respect to the number of units, x.

The supply equation is given by:

S(x) = 30 + 90p * In(4x + 5)

To find the derivative of S(x) with respect to x, we can use the chain rule:

\(\frac{dS(x)}{dx} =\frac{dS(x)}{dp}*\frac{dp}{dx}\)

Since the derivative of S(x) with respect to p is 90 * In(4x + 5), we can substitute this into the equation above:

\(\frac{dS}{dx}=(90*ln(4x+5))*(\frac{dp}{dx} )\)

This gives us the expression for the rate of change of supply price with respect to the number of units supplied.

For part (b), we need to find the rate of change of supply price when the number of units is 30. Substituting x = 30 into the equation above gives us:

\(\frac{Ds(30)}{dx} = (90*ln(4*30+5))*\frac{dp}{dx}\)

For part (c), we need to approximate the price increase associated with the number of units supplied changing from 30 to 31. To do this, we can use the equation from part (a) to find the rate of change of supply price with respect to the number of units supplied and then multiply this rate by the change in the number of units (from 30 to 31).

The approximate price increase is given by:

\(\frac{dS(x)}{dx} *(x2-x1)=\frac{dS(x)}{dx}*(31-30)\)

Substituting the appropriate values into this equation will give us the approximate price increase associated with the number of units changing from 30 to 31.

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Step-by-step explanation:

initial velocity= 27

final velocity= 0

time = 3 sec

now

a= 0-27/3

a=-9 m/s^2

Therefore ,the true bearing of the plane and its speed is ∝=-71.9° and 324.31 mph

A thing with both magnitude and direction is called a vector. A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector. From the vector's tail to its head is the direction of motion. According to the definition of a resultant vector, a single vector is one that has the same result as several other vectors taken together.

Here,

To find the true bearing of the plane and its speed.

We find the vector component,

Since  N75°W is same as 95°+90°=165°

Thus,

f(x)=300cos100 +50cos165 = -100.39

f(y)=300sin100 +50sin165= 308.38

next we find resultant

R=\(\sqrt{f(x)^{2}+f(y)^{2} }\)

R=\(\sqrt{(-100.39)^{2}+(308.38)^{2} }\)

R=\(\sqrt{105178.35}\)

R=324.31 mph

The bearing of the plane=> ∝=\(tan^{-1}\)(308.38/-100.39)

So  ∝=-71.96°

Therefore ,the true bearing of the plane and its speed is ∝=-71.96° and 324.31 mph

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Answer:

x = 7.5

Step-by-step explanation:

Since the midsegment and the third segment of the triangle are parallel to each other, therefore,

\( \frac{8 + 10}{8} = \frac{6 + x}{6} \)

\( \frac{18}{8} = \frac{6 + x}{6} \)

\( \frac{9}{4} = \frac{6 + x}{6} \)

Cross multiply

\( 9*6 = 4(6 + x) \)

\( 54 = 24 + 4x \)

Subtract 24 from each side

54 - 24 = 4x

30 = 4x

Divide both sides by 4

30/4 = x

7.5 = x

x = 7.5

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The set builder notation of the solution inequality represented on the number line is; {x: 3< x <=5}.

It follows from the task content that at point positive 3, there's an open circle which signifies that the number 3 is less than the solution.

And since the number line is shaded from positive 3 to 5, it follows that the maximum value in the solution set is 5.

The representation is therefore; {x: 3< x <=5}.

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On the number line, the solution inequality is represented by the notation x: 3=5, which is the set builder notation of the inequality.

This is further explained below.

Given the information provided in the job, it is logical to conclude that at point positive 3, there will be an open circle. This will indicate that the number 3 will be lower than the answer.

And since the shading on the number line goes from positive 3 to 5, it follows that the highest value that can be found in the set of solutions is 5.

As a result, the representation is written as:

"x: 3 x = 5."

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$3,244.21 can be withdrawn each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

where:

PV is the present value of the annuity

PMT is the payment amount per period

r is the interest rate per period

n is the total number of periods

In this case, we want to withdraw a fixed amount each month for 25 years, which represents 12 ×25 = 300 periods.

The interest rate per period is 7% / 12 = 0.5833%.

Let's assume that you want to withdraw a fixed amount each month, and you want the withdrawals to last for 25 years. To calculate the amount you can withdraw each month,

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

500,000 = PMT × [1 - (1 + 0.005833)⁻³⁰⁰] / 0.005833

Solving for PMT, we get:

PMT = PV × r / [1 - (1 + r)⁻ⁿ]

PMT = 500,000 × 0.005833 / [1 - (1 + 0.005833)⁻³⁰⁰]

PMT = $3,244.21

Therefore, you can withdraw $3,244.21 each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

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The four winning numbers are 24, 32, 27 and 37 respectively

It is important to note the following;

From the information given;

a. First number =  square root of 576

This is represented as

First number = √576

First number = 24

b. Second number =  multiple of 8 between 30 and 39

Second number = 32

c. Third number =  cube of 3

This is represented as;

Third number =  3³

Third number =  37

d. largest prime number less than 40

Fourth number = 37

Hence, the numbers are 24, 32, 27 and 37

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Answer:

5.235 (Simplifies as $5.24)

Step-by-step explanation:

1 gal = 20 miles

1.5 gal = 30 miles

1 gal = $3.49

1.5 gal = $5.235

If (x+1) is a factor p(x)= x²+x+2 then the value of x is -1.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

Now the given polynomial is,

p(x) = x² + x + 2

Now it is also given that,

(x+1) is a factor p(x)= x²+x+2

This mean (x+1) should satisfy p(x)= x² + x + 2

Thus equating (x+1) by zero since it satisfies p(x) we get,

(x+1) = 0

Subtracting 1 both the side we get,

(x+1) - 1 = 0 - 1

Solving we get,

x = -1

this is the required value of x.

Thus, If (x+1) is a factor p(x)= x²+x+2 then the value of x is -1.

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