Mrs. Merritt, has 75% of her $300 dollar goal, how much money does she have?

Use the limit comparison test to determine the convergence or divergence.

[infinity]n=2 Σ \(\frac{1}{n^{7/8-1}}\)  =  lim (n→∞) \(1/n^{7/8-1}\)/ (1/n²)

To establish a comparison, we need to find a value of p such that our series is larger than the p-series for all n greater than some value N. We can do this by simplifying the expression \(1/n^{7/8-1}\) to 1/nᵃ, where a = 7/8 - 1 = -1/8.

Now, we want to find a p-series with p > 0 that is smaller than our series. One such series is the p-series Σ 1/n², since p = 2 > 0.

We can then apply the limit comparison test, which states that if the limit of the ratio of the two series is a finite positive number, then both series either converge or diverge. Specifically, we have:

lim (n→∞) \(1/n^{7/8-1}\)/ (1/n²)

= lim (n→∞) \(n^{(2-7/8+1)}\)

= lim (n→∞) \(n^{1/8}\)

In summary, we can use the limit comparison test to compare the series Σ \(1/n^{7/8-1}\) to the p-series Σ 1/n², and find that both series converge. The key concept in this method is the idea of comparing series using limits and established results.

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Answer:

7 1/2 m

Step-by-step explanation:

C = πd

in this problem, d = 15 which means that r = 15/2 or 7 1/2

The estimated mean volume of the diet cola cans is between 11.97 and 12.05 ounces with 95% confidence for the particular hour.

This means that if the supervisor were to repeat this process many times, in 95% of the cases, the true mean volume of the diet cola cans would fall within the interval of 11.97 to 12.05 ounces.

The sample size of 10 cans selected at random is sufficient for this confidence interval to be accurate. This information can be used by the company to ensure that their cans are consistently filled to the advertised volume, and by consumers to have confidence in the volume of the product they are purchasing.

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The inequality to represent how much Jessica can spend on a T-shirt =

$59 + $x ≤ $75

By utilizing the "equal to" symbol in mathematics, equations are not necessarily balanced on both sides. Occasionally it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. A relationship between two numbers or other mathematical expressions that yields an unfair comparison is referred to as an inequality in mathematics.

Given, Jessica spent the following amount out of $75 =

Bracelet = $8

Sunglasses = $15

Beach towel = $12

Hat = $10

Sandals = $14

So, the total amount spent = 8 + 15 + 12 + 10 + 14 = $59

Let Jessica spends x dollars on T-shirt.

Certain algebraic mathematical expressions are referred to as inequalities.

Now, using inequalities we can represent the amount Jessica can spend on a T-shirt:

= $59 + $x ≤ $75

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The maximum point of a function found by solving f'(x) = 0

1.Y(x) = 900, if x ≤ 30

2.900 - 40(x - 30), if x > 30

3.T(x) = x × Y(x)

4.dT/dx = 900, if x < 30

5.2100x - 40x² if x > 30

6.The derivative dT/dx equals zero at x = 52.5, but it is not valid in the given context.

7.The maximum yield occurs at x = 30 trees per acre, with a maximum yield of 27,000 peaches per acre.

8.T(x) is differentiable at x = 30.

To find the function that describes the per-tree yield, Y, in terms of x, use the given information:

If there are 30 or fewer trees planted per acre (x ≤ 30), the per-tree yield is 900 peaches per tree.

If there are more than 30 trees planted per acre (x > 30), the per-tree yield decreases by 40 peaches for every extra tree planted beyond 30.

The function Y(x) as follows:

Y(x) = 900, if x ≤ 30

Y(x) = 900 - 40(x - 30), if x > 30

find the total yield per acre, T, that results from planting x trees per acre. The total yield is simply the per-tree yield (Y) multiplied by the number of trees per acre (x):

T(x) = x × Y(x)

differentiate T with respect to x (dT/dx) to find where the maximum yield occurs.

dT/dx = d/dx (x × Y(x))

dT/dx = d/dx (x × (900 - 40(x - 30)))

To find if this derivative ever equals zero, it to zero and solve for x:

0 = 900 - 40(x - 30)

40(x - 30) = 900

x - 30 = 22.5

x = 52.5

So, the derivative dT/dx equals zero at x = 52.5. However, we need to check whether this value is valid for our function. Recall that if x > 30, the per-tree yield decreases by 40 peaches for every extra tree planted beyond 30. Therefore, planting 52.5 trees per acre would result in a negative per-tree yield, which is not physically meaningful in this context. Thus, the maximum yield occurs at the critical point within the valid domain, which is x = 30.

Now, let's find the maximum value of the yield at x = 30:

T(30) = 30 ×Y(30) = 30 × 900 = 27,000 peaches per acre

The optimal value of x that maximizes the yield is 30 trees per acre, and the maximum yield is 27,000 peaches per acre.

Finally, let's determine if T(x) is differentiable when x equals 30. Since T(x) is a piecewise function, we need to check if the left and right-hand derivatives at x = 30 are the same.

Left-hand derivative (x < 30):

dT/dx = d/dx (x × 900) = 900

Right-hand derivative (x > 30):

dT/dx = d/dx (x × (900 - 40(x - 30))) = d/dx (x × (900 - 40x + 1200)) = d/dx (2100x - 40x²)

Now, evaluate the right-hand derivative at x = 30:

dT/dx = 2100(30) - 40(30)² = 63,000 - 36,000 = 27,000

Since the left-hand derivative and the right-hand derivative at x = 30 are equal (both are 27,000), T(x) is differentiable at x = 30.

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Answer:

D)  12 1/2 miles

Step-by-step explanation:

you can create a proportion for inches over miles equals inches over miles

(3/4 ÷ 15/2) = (5/4 ÷ m)

cross-multiply to get:

3/4m = 75/8

cross-multiply again:

24x = 300

x = 12 1/2

Answer:

f=48

Step-by-step explanation:

Its correct good luck!

The polar equation is given

To determine the radius and center of the polar equation,

The polar equation of a circle centered on an axis , would take the forms.

Negative x-axis.

Then the center is diameter divide by 2.

The diameter is 10.

Hence the circle, diameter of 10, center at (-5,0).

The correct option is C.

Answer:

15

Step-by-step explanation:

50 + 45 is 95 1h - 10min is 15

Answer:

2:05

Step-by-step explanation:

11:20 then 12:30 then 1:15 finnaly 2:05

The distance between the coordinates is 2+√19.

According to the question, the given problem can be solved by using the standard distance formula.

Now, the coordinate values are:

p(a, 2a); q(4, 3) and Distance = 10 units

Therefore, from the given parameters we can write:

x1 = a; y1 = 2a; x2 = 4; y2 = 3

Now,

Distance^2 = (x1 - x2)^2 + (y1 - y2)^2

Substituting the given values, we get:

Distance^2 = (4 - a)^2 + (3 - 2a)^2 = 16 +a^2 - 8a + 9 +4a^2 - 12a

100 = 25 + 5a^2 - 20a

5a^2 - 20a - 75 = 0

a^2 - 4a - 15 = 0

a = 2+√19

Hence, the distance between the coordinates is 2+√19.

What is distance?

Distance can be defined as the resultant displacement between the two endpoints. It can measured in different units like meters, centimeters, kilometers, etc. And the respective values can be calculated by using the standard formula.

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It seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

To compute the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane, we can use the surface integral.

The surface integral of a vector field F⃗ over a surface S is given by the formula:

∬S F⃗ · dS = ∬S F⃗ · (n⃗ dS)

where F⃗ is the vector field, dS is the differential area vector, and n⃗ is the unit normal vector to the surface.

In this case, the surface S is given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0. We can parameterize this surface as:

r(x, z) = xi⃗ + yj⃗ + zk⃗ = xi⃗ + (x^2+z^2)j⃗ + zk⃗

To find the normal vector n⃗ to the surface, we can take the cross product of the partial derivatives of r(x, z) with respect to x and z:

n⃗ = ∂r/∂x × ∂r/∂z

= (1i⃗ + 2xj⃗) × (0i⃗ + 2zj⃗)

= -2xz i⃗ + 2zj⃗ + 2xk⃗

Now, we can calculate the flux:

∬S F⃗ · (n⃗ dS) = ∬S (3(x+z)i⃗ + 2j⃗ + 3zk⃗) · (-2xz i⃗ + 2zj⃗ + 2xk⃗) dS

= ∬S (-6x^2z - 4xz + 6xz^2 + 6xz) dS

= ∬S (-6x^2z + 2xz + 6xz^2) dS

To evaluate this integral, we need to determine the limits of integration for x, y, and z.

Since the surface is defined by 0≤y≤16, x≥0, z≥0, we have:

0 ≤ y = x^2 + z^2 ≤ 16

Simplifying the inequality, we get:

0 ≤ x^2 + z^2 ≤ 16

From this, we can see that x and z both range from 0 to 4.

Now, we can evaluate the flux:

∬S (-6x^2z + 2xz + 6xz^2) dS = ∫∫ (-6x^2z + 2xz + 6xz^2) dA

where dA is the differential area.

Integrating over the limits 0 ≤ x ≤ 4 and 0 ≤ z ≤ 4, we can calculate the flux.

However, it seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

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Answer:

Over time, the function is DECREASING. Cho ran at a faster rate during segment K.

Step-by-step explanation:

The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

To solve the given initial-value problem, we start by rearranging the equation:
3 11 16 × -(: * *:)* X' = 1 1 3
-(: * *:)* X' = (1/16)  (1/11)  (1/3)
Integrating both sides with respect to t:
-(: * *:)* X = (1/16) t + C1, where C1 is the constant of integration.
Multiplying both sides by the inverse of the matrix -(: * *:) gives:
X = (-1/8) t + C1/8 + C2, where C2 is another constant of integration.
To find the values of C1 and C2, we use the initial condition X(0) = (0) - (5):
X(0) = (-1/8) (0) + C1/8 + C2 = -5
C1/8 + C2 = -5
Since X'(t) = (-3/8), we have X'(0) = (-3/8). Using the equation X'(t) = (-3/8) and the initial condition X(0) = (0) - (5), we can solve for C1:
X'(t) = (-1/8) => (-3/8) = (-1/8) + C1/8 => C1 = -2
Substituting C1 = -2 into C1/8 + C2 = -5 gives:
(-2)/8 + C2 = -5 => C2 = -39/8
Therefore, the solution to the initial-value problem is:
X = (-1/8) t - 1/4 - (39/8)

The solution to the given initial-value problem is X = (-1/8) t - 1/4 - (39/8). The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

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Therefore, the division of \((x^3 + 6x^2 + 12x + 8)/(x^2 - 12x + 32) by (x^3 + 8)/(x^2 - 64)\) is equal to \((x+2)^2(x+8)/((x-4)(x+1)(x^2-x+1)).\)
What is division ?

In mathematics, division is an arithmetic operation that involves distributing a quantity into equal parts or groups. Division is the inverse operation of multiplication.

In division, we have a dividend, a divisor, and a quotient. The dividend is the number that is being divided, the divisor is the number by which the dividend is being divided, and the quotient is the result of the division.

For example, in the division problem 12 ÷ 3 = 4, the number 12 is the dividend, the number 3 is the divisor, and the number 4 is the quotient. This means that 12 is being divided into 3 equal parts, each of which is 4.

According to the question:
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.

So, we can rewrite the expression as

\([(x^3 + 6x^2 + 12x + 8)/(x^2 - 12x + 32)] * [(x^2 - 64)/(x^3 + 8)]\)

Now, we can factor the polynomials in the numerator and denominator:

\([(x+2)(x+2)(x+2)/(x-4)(x-8)] * [(x-8)(x+8)/((x+2)(x+1)(x^2-x+1))]\)

Next, we can cancel out any common factors in the numerator and denominator:

\([(x+2)(x+2)/(x-4)] * [(x+8)/((x+1)(x^2-x+1))]\)

Finally, we can multiply out the numerator and simplify:

\([(x^2 + 4x + 4)/(x-4)] * [(x+8)/((x+1)(x^2-x+1))]\)

\(= [(x+2)^2/(x-4)] * [(x+8)/((x+1)(x^2-x+1))]\)

\(= (x+2)^2(x+8)/((x-4)(x+1)(x^2-x+1))\)

Therefore, the division of \((x^3 + 6x^2 + 12x + 8)/(x^2 - 12x + 32) by (x^3 + 8)/(x^2 - 64)\) is equal to \((x+2)^2(x+8)/((x-4)(x+1)(x^2-x+1)).\)

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The value of quadratic equation is,

⇒ y = x² + 10x + 22

Let the value of quadratic equation is,

⇒ y = ax² + bx + c

Now, Let the points from tables as;

⇒ (- 6, 2) (- 5, - 1) (- 4, - 2)

Substitute all the values in equation as;

⇒ y = ax² + bx + c

⇒ 2 = a(- 6)² + b(-6) + c

⇒ 2 = 36a - 6b + c

⇒ - 1 = a (- 5)² + b (- 5) + c

⇒ - 1 = 25a - 5b + c

⇒ - 2 = a (- 4)² + b (- 4) + c

⇒ - 2 = 16a - 4b + c

Solve expression for the values of a, b and c as;

a = 1

b = 10

c = 22

Thus, the value of quadratic equation is,

⇒ y = x² + 10x + 22

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Answer:

D. 16 years old

Step-by-step explanation:

Step 1: Let T be Tien's age and J as Jordan's age (today),

\(T=\frac{1}{4}J\)

Step 2: Let T be Tien's age and J as Jordan's age (in 2 years),

\(T+2=\frac{1}{3} (J+2)\)

\(T=\frac{1}{3}(J+2)-2\)

Step 3: As their age differences will always be similar we can have the two equations above equal to find Jordan's age,

\(\frac{1}{4} J=\frac{1}{3}(J+2)-2\\\frac{1}{4}J-\frac{1}{3}J=\frac{2}{3} -2 \\-\frac{1}{12}J= -\frac{4}{3} \\\\J=16\)

Thus, the part of the trinomial that's equal to the product of p and q is the constant

term!

B: The Constant Term

Step-by-step explanation:

When the value of the variable = 2 the value of  W = 3.When the value of one quantity increases with respect to decrease in other or vice-versa, then they are said to be inversely proportional. It means that the two quantities behave opposite in nature. For example, speed and time are in inverse proportion with each other. As you increase the speed, the time is reduced.

In the problem it's given that "y varies inversely as x," and "when x = 6, then y = 4."

We need to find y when x = 7, we can use the formula for inverse variation:

y = k/x  where k is the constant of variation.

To find the value of k, we can plug in the given values of x and y:

4 = k/6

Solving for k:

k = 24

Now, we can plug in k and the value of x = 7 to find y:

y = 24/7

Answer: y = 24/7

Function for the inverse variation between W and square of 2 can be written as follows,

W = k/(2)^2 = k/4

It is given that when 12 = 3, W = 3,

So k/4 = 3

k = 12

Now, we need to find W when variable = 2,

Thus,

W = k/4

W = 12/4

W = 3

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Hope it a right answer for you

Answer:

Removing the number 7 wont change the median nor the range

Answer:

Not enough tables.

Step-by-step explanation:

Circumference is 2*pi*r

The diameter is 2 times the radius or 2r, if the table diameter is 180cm. All we need to do is multiply by pi (3.14159) to get the circumference.

180*pi = 556.48cm

If each guest needs 70cm then we divide the circumference by 70

556.48/70 = 8.08 but we cant have a portion of a person so we can fit 8 people per table.

18 tables with 8 at a table is 8 x 18 = 144

If 145 guests are attending then there aren't enough tables, you are 1 table short.

The expression as given does not have a meaningful interpretation.

The expression "(a•b) x (c•d)" is not meaningful because the dot product "•" operation is defined for vectors, whereas the cross product "x" operation is defined between two vectors. The dot product of "a" and "b" would result in a scalar value, as would the dot product of "c" and "d". However, taking the cross product of scalar values is not a valid mathematical operation. The cross product is only defined between two vectors and results in a new vector that is perpendicular to both input vectors. Therefore, the given expression lacks a meaningful interpretation due to the incompatible combination of dot product and cross product operations.

Therefore, the expression as given does not have a meaningful interpretation.

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Given question is incomplete, the complete question is below

State whether the expression is meaningful. If not, explain why. If so, state whether it is a vector or scalar.

(a•b) x (c•d)

∑xn=11−x

when x

is in the radius of convergence

∑(−x)n=11+x∑(−x2)n=∑(−1)nx2n=11+x2∑(−1)n(2–√x)2n=∑(−1)n(2n)x2n11+2x2x∑(−1)n(2n)x2n=x1+2x2∑(−1)n(2n)x2n+1=x1+2x2

The series convenes by the root test if:

limn→∞|an−−√nx|<1

|an−−√n|=|2n2n+1x|<1

|x|<2√2

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Answer:

Manny should keep the old car since he gets to spend less on it in three years compared to getting the fuel-efficient car.

Step-by-step explanation:

Step 1:

Number of miles Manny commutes per week = 160

Cost per gallon of gasoline. = $2.9

Mileage of old car = 20 miles per gallon

Maintenance cost per year of old car = $760

Cost of new car = $7000

Maintenance cost per month of new car = $10

Mileage of new car = 31 miles per gallon

Step 2:

There are 52 weeks in a year. Total distance Manny will commute in 3 years = 160 * 52 * 3 = 24960 miles

Maintenance cost of old car in 3 years = $760 * 3 = $2280

Maintenance cost of new car in 3 years = $10/month * 12 months * 3 = $360

Gasoline usage of old car in 3 years = 24960 miles/20 miles per gallon = 1248 gallons

Cost of gasoline = 1248 * $2.9 = $3619.2

Gasoline usage of new car in 3 years = 24960 miles/31 miles per gallon

Cost of gasoline = $2.9 * 24960 miles/31 miles per gallon = $2334.97 or approximately $2335

Step 3:

Total expenditure on old car for 3 years = $2280 + $3619.2 = $5899.2

Total expenditure on new car for 3 years = $7000 + $360 + $2335 = $9695

From the calculations above, Manny will spend $5899.2 on the old car compared to $9695 on the new car in three years.

Therefore, Manny should keep the old car since he gets to spend less on it in three years compared to getting the fuel-efficient car.

The given function is

First, we make x = 0.

Second, we make g(x) = 0.

Third, we graph the points (0, 4) and (-16, 0).

At last, we draw the line through the points to get the line.

The limit of the fraction as x approaches 3 is 4.

We can use algebraic manipulation to simplify the fraction.

StartFraction x squared minus 12 Over x squared minus 3 x EndFraction

= StartFraction x squared minus 12 Over x squared minus 3 x EndFraction x squared

= StartFraction x squared minus 12 x squared Over x squared times x squared minus 3 x EndFraction

= StartFraction x squared times x squared minus 12 x squared Over x squared times x squared minus 3 x EndFraction

= StartFraction x to the fourth minus 12 x squared Over x squared times x squared minus 3 x EndFraction

Now we can plug in x = 3 to get the limit:

= StartFraction 3 to the fourth minus 12 x 3 squared Over 3 squared times 3 squared minus 3 x EndFraction

= StartFraction 81 - 36 Over 27 - 9 EndFraction

= StartFraction 45 Over 18 EndFraction

= 4

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