A salesman sold 75 percent of his first shipment of 800 units. How many of his next shipment of 600 units must he sell in order to have sold 80 percent of all of the units?

Answer: 3 hours and 15min

Step-by-step explanation:

Answer:

3 houurs and 9 minutes

Step-by-step explanation:

The Maclaurin series for 2x₁ x₂ converges on the open interval `(-1,1)` and diverges elsewhere.

The Maclaurin series for the function 2x₁ x₂ is given by `f(x) = ∑_(n=0)^∞ ((2x₁ x₂)^n)/n!`.

We will determine the radius of convergence of this series using the ratio test.

The ratio test states that if `lim_(n->∞) |(a_(n+1))/(a_n)| = L`, then the series is convergent if `L < 1` and divergent if `L > 1`.

If `L = 1`, the test is inconclusive.

Applying this to our Maclaurin series, we have:`|((2x₁ x₂)^(n+1))/((n+1)!)|/|((2x₁ x₂)^n)/n!|``= |2x₁ x₂|/(n+1)`

Taking the limit as n → ∞:`lim_(n->∞) |2x₁ x₂|/(n+1)``= 0`

Therefore, the ratio test is inconclusive and we cannot determine the convergence or divergence of the series. In this case, we need to use an alternative test to determine the radius of convergence. One such test is the root test.

The root test states that if `lim_(n->∞) |a_n|^(1/n) = L`, then the series is convergent if `L < 1` and divergent if `L > 1`.

If `L = 1`, the test is inconclusive.

Applying this to our Maclaurin series, we have:

`|((2x₁ x₂)^n)/n!|^(1/n)``= |2x₁ x₂|^(1/n) n^(-1/n)`

Taking the limit as n → ∞:`lim_(n->∞) |2x₁ x₂|^(1/n) n^(-1/n)``= lim_(n->∞) e^((ln|2x₁ x₂|)/n) n^(-1/n)`

This limit evaluates to 1, so we can conclude that the radius of convergence of the series is `R = 1/lim_(n->∞) |2x₁ x₂|^(1/n) n^(-1/n) = 1`.

Therefore, the Maclaurin series for 2x₁ x₂ converges on the open interval `(-1,1)` and diverges elsewhere.

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The value of X is 6.8, if X squared is approximately equal to 46.

The problem asks us to find the value of X, rounded to the nearest tenth, if X squared is approximately equal to 46. This means that we need to find the square root of approximately 46.

To do this, we can use a calculator. Using the square root function, we get:

√(46) ≈ 6.782329983

This means that X is approximately equal to 6.782329983. However, the question asks us to round our answer to the nearest tenth. The digit in the tenths place is the first digit to the right of the decimal point.

Since the digit in the tenths place is 8 and greater than or equal to 5, we round the digit in the ones place up by 1. Therefore, X is approximately equal to 6.8 (rounded to the nearest tenth).

Hence, X = 6.8.

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--The complete question is, Find the value of X, rounded to the nearest tenth, if X squared is approximately equal to 46. X = ? (round your answer to the nearest tenth) (Hint: Find a decimal that, when multiplied by itself, will be approximately 46.)--

Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + C(n, 2)a^(n-2) b^2 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n

The binomial expansion of (2x - 3y)^5 is:

32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5

The binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

The given expression is (2x-3y)⁵.

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial.

(2x)⁵+⁵c₁(2x)⁴(3y)¹+⁵C₂(2x)³(3y)²+⁵C₃(2x)²(3y)³+⁵C₄(2x)(3y)⁴+⁵C₅(3y)⁵

= 32x⁵+5(16x⁴)(3y)+10.(8x³)(9y²)+10(4x²)(27y³)+5(2x)(81y⁴)+243y⁵

= 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵

Therefore, the binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

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Answer: 7x^2+3y^2-4x

Choose the first option

Step-by-step explanation:

Ok, so let me show you how to do this.

First, distrubute the negative sign

12x^2-11y^2-13x-(5x^2-14y^2-9x)=

12x^2-11y^2-13x-5x^2+14y^2+9x

Now combine like terms

(12x^2-5x^2)=7x^2

(-11y^2+14y^2)=3y^2

(-13x+9x)=-4x

7x^2+3y^2-4x is the answer.

Answer:

97.336 (unit)³

Step-by-step explanation:

V=a³=(4.6)³=97.336 (unit)³

Answer: 3, 4, 5

Step-by-step explanation:

(1) False, those two angles added together would be equal to angle 1, not 4.

(2) False. Angles 2, 3, 5 added together would make 180, not 3, 4, 5.

(3) True, an interior angle and its corresponding exterior angle are supplementary.

(4) True by the exterior angle theorem.

(5) True because the angles in a triangle add to 180 degrees

The geometric sequence's sixth term is -1/3.

The geometric sequence's sixth term must be found here.

Given:

The series is 3125/96, -625/48, 125/24.....

The following is the formula to determine the nth term in a geometric sequence:

aₙ= a × rⁿ⁻¹

where aₙ = nth term of the sequence

a = first term of the sequence

r = common ratio

common ratio(r) = -625/48 ÷ 3125/ 96

                           = -625/48 × 96/3125

                            = -2/5

Now we have to find the 6th term of the series.

= 3125/96(-2/5)⁶⁻¹

= 3125/96(-2/5)⁵

= 3125/96 × (-32/3125)

= -32/96

 = -1/3

Therefore the 6th term is -1/3.

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The angle of elevation of the point T on the top of the pole from the point A on the level ground, obtained using Pythagorean Theorem and the relationship between similar triangles is about 39.3°.

Similar triangles are triangles that have the same shape (the sizes may be different) and in which the ratio of the corresponding sides are equivalent.

The triangles ΔXBA, ΔXAC, and ΔABC are right triangles, such that the angles, ∠ABX in triangle ΔXBA is congruent to triangle ∠CAX in triangle ΔXAC, and ∠ABC in ΔABC.

The 90° angle in the right triangles are congruent (All 90° angle are congruent), therefore;

ΔXBA ~ ΔXAC ~ ΔABC by AA (Angle-Angle), similarity postulate

The length of the hypotenuse in the right triangle, ΔABC, \(\overline{BC}\), can be obtained using Pythagorean Theorem as follows;

\(\overline{BC}\)² = 14² + 25² = 821

\(\overline{BC}\) = √(821)

\(\overline{BC}\)/\(\overline{AC}\) = \(\overline{AB}\)/\(\overline{AX}\)

√(821)/25 = 14/\(\overline{AX}\)

\(\overline{AX}\) = 25 × (14/(√(821)) = 350/(√(821))

Let θ represent the angle of T from A, we get;

tan(θ) = 10/(350/(√(821)))

θ = arctan(10/(350/(√(821)))) ≈ 39.3°

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Answer:

Graph points where the first line passes through (2,0) and (0,-6)

For the second line graph points when the line passes through (0,8) and (16,0)

Step-by-step explanation:

To show that FU{u} is linearly independent, we assume that there exist scalars such that a linear combination of vectors in FU{u} equals the zero vector. By writing out the linear combination and using the fact that u is in the span of F, we can show that the only solution to the equation is when all the scalars are zero. This proves that FU{u} is linearly independent.

Let \(F = {v_1, v_2, ..., v_n}\) be a linearly independent set in vector space V, and let u be a vector in V such that u is in the span of F. We want to show that FU{u} is linearly independent.

Suppose that there exist scalars \(a_1, a_2, ..., a_n\), b such that a linear combination of vectors in FU{u} equals the zero vector:

\(\[a_1v_1 + a_2v_2 + ... + a_nv_n + bu = 0\]\)

Since u is in the span of F, we can write u as a linear combination of vectors in F:

\(\[u = c_1v_1 + c_2v_2 + ... + c_nv_n\]\)

Substituting this expression for u into the previous equation, we have:

\(\[a_1v_1 + a_2v_2 + ... + a_nv_n + b(c_1v_1 + c_2v_2 + ... + c_nv_n) = 0\]\)

Rearranging terms, we get:

\(\[(a_1 + bc_1)v_1 + (a_2 + bc_2)v_2 + ... + (a_n + bc_n)v_n = 0\]\)

Since F is linearly independent, the coefficients in this linear combination must all be zero:

\(\[a_1 + bc_1 = 0\]\)

\(\[a_2 + bc_2 = 0\]\)

\(\[...\]\)

\(\[a_n + bc_n = 0\]\)

We can solve these equations for a_1, a_2, ..., a_n in terms of b:

\(\[a_1 = -bc_1\]\[a_2 = -bc_2\]\[...\]\[a_n = -bc_n\]\)

Substituting these values back into the equation for u, we have:

\(\[u = -bc_1v_1 - bc_2v_2 - ... - bc_nv_n\]\)

Since u can be written as a linear combination of vectors in F with all coefficients equal to -b, we conclude that u is in the span of F, contradicting the assumption that F is linearly independent. Therefore, the only solution to the equation is when all the scalars are zero, which proves that FU{u} is linearly independent.

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The angle measures of the triangles before and after dilation are the same

Given that, we have a triangle that is dilated to form another triangle by a scale factor of n

The dilation transformation is a rigid transformation

This means that it changes the size of a shape after it is applied

However, the shape and the image would be similar shapes and as such would have their angles unchanged

This means that irrespective of the value of the scale factor n, the angle measures would remain the same

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The ratio of cups of mixed nuts to cups of granola is 2:11.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

Given:

Rolled oats= 6 cups

Mixed nuts=2 cups

Sesame seeds=1/2 cup

Cranberries= 1 cup

Dried unsweetened coconuts=1

Honey =1/2 cup

As, the ingredients listed

Total cups of granola= Rolled oats + Mixed nuts + Sesame seeds + Cranberries + Dried unsweetened coconuts + Honey

=6 + 2 + 1/2 + 1 + 1 + 1/2

=11 cups

Hence, the ratio of cups of mixed nuts to cups of granola is 2:11.

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The complete question is

Granola 6 cups rolled oats 2 cups mixed nuts 1 2 cup sesame seeds 1 cup dried cranberries. What is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to . 1 cup dried unsweetened coconut 1 2 cup honey

Answer:

A, all three angles of a triangle equal 180

Answer:

b. x + 40 = 90

Step-by-step explanation:

This is a right triangle, so we already know one of the angles is 90 degrees. The other angles combine to make the other 90 degrees. So, we have to figure out what the other angle is, as the second one is 40 degrees.  To figure that out, use the equation x + 40 = 90. (This is extra, but x is 50, right?)

Based on the calculations, the length, in cm, of an adjacent side of this rectangle is equal to 6.0 centimeters.

Given the following data:

Perimeter of rectangle = 40.0 centimeters.

Length of rectangle = 14.0 centimeters.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Note: The length of an adjacent side refers to the the width of this rectangle.

Substituting the parameters into the formula, we have;

40.0 = 2(14.0 + W)

40.0 = 28.0 + 2W

2W = 40.0 - 28.0

2W = 12.0

W = 12.0/2

Width, W = 6.0 centimeters.

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Answer:

3

Step-by-step explanation:

A simple way to solve this is by substituting, we start with trying 1 for x, 2+6=8, and 1+9=10. Because the two values are different, that means 1 is the incorrect value. We can try 2, 4+6=10, and 2+9=11, once again inequivalent. We finally try 3, and 6+6=12 and 3+9=12 meaning x must be 3

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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The maximum value of f(x, y) over the feasible region is 159, and the minimum value is 13.

f max = 159

f min = 13

To determine the global extreme values of the function f(x,y) = 11x - 5y subject to the given constraints, we need to find the maximum and minimum values of f(x,y) over the feasible region.

First, we can find the corner points of the feasible region by solving the system of inequalities:

y ≥ x - 9

y ≥ -x - 9

y ≤ 6

The intersection points of the lines y = x - 9, y = -x - 9, and y = 6 are:

(-3, -12), (3, -6), (15, 6)

We also need to check the extreme points on the boundary of the feasible region.

Along the line y = x - 9, the maximum and minimum values of f(x,y) occur at the endpoints of the segment: (3, -6) and (15, 6).

f(3,-6) = 11(3) - 5(-6) = 63

f(15,6) = 11(15) - 5(6) = 159

Along the line y = -x - 9, the maximum and minimum values of f(x,y) occur at the endpoints of the segment: (-3, -12) and (3, -6).

f(-3,-12) = 11(-3) - 5(-12) = 47

f(3,-6) = 11(3) - 5(-6) = 63

Finally, we need to check the point where y = 6, which is (x,y) = (3,6).

f(3,6) = 11(3) - 5(6) = 13

To determine the global extreme values of the function f(x,y) = 11x - 5y, we need to analyze the given constraints:

1. y ≥ x - 9

2. y ≥ -x - 9

3. y ≤ 6

These constraints define the region within which we are looking for extreme values.

We can find these values by examining the function at the corner points and along the boundary lines of the region. The corner points are:

A. (0, -9) - Intersection of y = x - 9 and y = -x - 9

B. (3, 6) - Intersection of y = x - 9 and y = 6

C. (-3, 6) - Intersection of y = -x - 9 and y = 6

Now, we evaluate the function at these corner points:

f(A) = 11(0) - 5(-9) = 45

f(B) = 11(3) - 5(6) = 3

f(C) = 11(-3) - 5(6) = -57

Next, we analyze the function along the boundary lines by solving for the gradient of the function:

∇f(x, y) = (11, -5)

Since the gradient is a constant and does not depend on x or y, there are no additional extreme values along the boundary lines.

Now, we compare the function values at the corner points to find the global maximum and minimum:

f_max = 45 (at point A)

f_min = -57 (at point C)

In conclusion:

f max = 45, f min = -57

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Answer:

The formula you provided is for the area of a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides. The formula states that the area (A) of a trapezoid is equal to half the sum of the lengths of its parallel sides (b1 and b2) multiplied by its height (h).

Using this formula and the values you provided, we can calculate the area of the trapezoid:

A = ((8 cm + 6 cm) * 4 cm) / 2 A = (14 cm * 4 cm) / 2 A = 56 cm² / 2 A = 28 cm²

So, according to these calculations, the area of this trapezoid is 28 square centimeters.

Answer:

2.556818 miles

Step-by-step explanation:

x = 20 is not an inequality .

The correct inequality for x = 20 is:

x = 20 (read as "x is equal to 20")

In this case, the inequality is not expressed with an inequality symbol (<, >, ≤, ≥) since we are specifying the exact value of x. When we state x = 20, it means that the value of x is precisely 20.

An inequality, on the other hand, represents a range of values that x can take. For example, x ≤ 20 would indicate that x can be any value less than or equal to 20, while x > 20 would indicate that x can be any value greater than 20.

However, when we state x = 20, it is a statement of equality, indicating that x has a fixed value of 20. There is no inequality involved in this statement.

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The given problem involves a partition of a time interval and the calculation of the Stratonovich integral, mean square of the expression converges to B² as the number of partitions approaches infinity.

To begin, let's consider the expression Dn: 2B(ti-1+t)/2∫B dt, where B is a stochastic process and ti represents the partition points. The subscript i ranges from 1 to n, and n represents the number of partitions. We want to show that as n approaches infinity, the mean square of Dn converges to B².

The Stratonovich integral, represented by the symbol ſ, is defined as the limit of the mean square of a sum of terms as the partition becomes finer and finer. In this case, as n approaches infinity, the partition becomes finer, and we are interested in the mean square behavior of Dn.

To prove the convergence, we need to show that the mean square of Dn minus B² tends to zero as n approaches infinity. This can be done by calculating the mean square difference and then taking the limit as n goes to infinity. The calculations involve properties of the stochastic process B and the partition points ti.

By carefully analyzing the properties of the given partition and applying mathematical techniques, such as the properties of stochastic processes and integration theory, it is possible to show that the mean square of Dn converges to B² as the number of partitions increases. This convergence result is crucial in understanding the behavior of the Stratonovich integral and its relationship with the stochastic process B.

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3 out of every 5 students prefer to play Wii than do their homework, so we can calculate how many students this is by dividing the total number of students (20) by 5 and then multiplying by 3.

Dividing is the process of breaking down a larger whole into smaller parts. In the example of 100 words, it would mean splitting the words into smaller groups or sections, such as 25 words each.

20 / 5 = 4

4 x 3 = 12

Therefore, 12 out of the 20 students in Ms. Richard's homeroom prefer to play Wii than do their homework.

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Answer:

It's false.... correct is a2+2ab+b2

Step-by-step explanation:

This cannot be factored anymore although. when we try to substitute a with 5 and b with 2, the answer in the right hand side of the equation is -9. That's why it's false.

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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To solve the equation -9x + 9 = -7 algebraically, we can use various algebraic techniques to isolate the variable x. By applying the steps of solving linear equations, we can determine the solution to the equation.

To solve the equation -9x + 9 = -7, we can follow these steps:

Begin by subtracting 9 from both sides of the equation to isolate the term with x:

-9x + 9 - 9 = -7 - 9

-9x = -16

Divide both sides of the equation by -9 to solve for x:

(-9x)/(-9) = (-16)/(-9)

x = 16/9

Therefore, the solution to the equation -9x + 9 = -7 is x = 16/9, which is a fraction in reduced form.

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