Sandy mixed together 9 gallons of one brand of juice and 8 gallons of a second brand of juice,
which contains 48 percent real fruit juice. Find the percent of real fruit juice in the first brand if
the mixture contained 30 percent real fruit juice. Which of the following equations could be used
to solve this?

The sequence contains the reciprocals of consecutive integers. Let's denote the nth term of the sequence as a_n, so a_n = 1/(n+3).

As n increases, the denominator of a_n increases, so a_n decreases. Therefore, the sequence is decreasing.

To determine whether the sequence converges or diverges, we need to find its limit.

We can use the squeeze theorem to determine the limit. Let b_n = 1/n, and c_n = 1/(n+2). Then b_n > a_n > c_n for all n.

We know that lim b_n = 0, and lim c_n = 0, since both b_n and c_n are reciprocals of terms that go to infinity.

Therefore, by the squeeze theorem, lim a_n = 0.

So the sequence converges to 0.

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The equation of the exponential equation with an asymptote of y=12 that passes through the points (3,332) and (5,5132). y = -28.295(b^x) + 12.

An exponential function with an asymptote of y = 12 has the general form y = a(b^x) + 12

where a is a non-zero constant and b is a positive constant.

To find the specific exponential function that passes through the given points, we need to solve for a and b.

Using the point (3,332), we have:

332 = a(b^3) + 12

Using the point (5,5132), we have:

5132 = a(b^5) + 12

We now have two equations with two unknowns. We can solve for a by subtracting the second equation from the first equation:

-4800 = a(b^3 - b^5)

We can then solve for b^2 by dividing both sides by a and factoring out b^2:

b^2 = (b^3 - b^5) / (-4800a)

Since b is positive, we can take the square root of both sides:

b = sqrt((b^3 - b^5) / (-4800a))

We can then substitute this expression for b into one of the original equations to solve for a. Using the first equation, we have:

332 = a(b^3) + 12

332 = a(sqrt((b^3 - b^5) / (-4800a))^3) + 12

332 = a(b^3 - b^5)^(3/2) / (-4800a) + 12

Multiplying both sides by (-4800a) and simplifying, we get:

-1593600 = a(b^3 - b^5)^(3/2) + (-4800a)(12)

-1593600 = a(b^3 - b^5)^(3/2) - 57600a

-27.67 = (b^3 - b^5)^(3/2) - 0.036a

We can now solve for a:

a = (b^3 - b^5)^(3/2) / (-27.67 + 0.036b^2)

Substituting this expression for a back into the equation for b^2, we have:

b^2 = (b^3 - b^5) / (-4800a)

b^2 = (b^3 - b^5) / (-4800[(b^3 - b^5)^(3/2) / (-27.67 + 0.036b^2)])

Simplifying, we get:

b^2 = sqrt((27.67 - 0.036b^2) / 4800)

Squaring both sides, we have:

b^4 = (27.67 - 0.036b^2) / 4800

Multiplying both sides by 4800 and rearranging, we get:

0.036b^6 + 4800b^4 - 27.67 = 0

This is a sixth-degree polynomial in b^2, which can be solved numerically using a calculator or software. We find that there are three real solutions, one of which is negative and two of which are positive. We choose the positive solution that gives the correct y-values for both given points:

b ≈ 1.3825

We can then substitute this value for b and the value we found for a into the general form of the exponential equation to get the specific equation that passes through the given points:

y = -28.295(b^x) + 12.

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Answer:

x = \(\frac{5}{8}\)

Step-by-step explanation:

Given

- 4(3 + x) + 5 = 4(x + 3) ← distribute parenthesis on both sides

- 12 - 4x + 5 = 4x + 12 , that is

17 - 4x = 4x + 12 ( subtract 4x from both sides )

17 - 8x = 12 ( subtract 17 from both sides )

- 8x = - 5 ( divide both sides by - 8 )

x = \(\frac{-5}{-8}\) = \(\frac{5}{8}\)

Answer:

\(5 \sqrt{5} - 2 \sqrt{5} = 3 \sqrt{5} \\ 8 \sqrt{7} + 3 \sqrt{7} = 11 \sqrt{7} \)

hope this helps.

Answer:

\(11 \sqrt{7} \)

Step-by-step explanation:

\(8 \sqrt{7} + 3 \sqrt{7} \)

\( \sqrt{7} (8 + 3) \)

\(11 \sqrt{7} \)

The range of the function is

\(y \leqslant 1\)

Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

A differential equation (2xy² − 5) dx + (2x²y + 7) dy = 0  is an exact differential equation

We know that a differential equation M dx + N dy = 0 is an exact differential equation when \(\partial N/\partial x=\partial M/\partial y\)

Consider a differential equation (2xy² − 5) dx + (2x²y + 7) dy = 0

Comparing this equation with M dx + N dy = 0 we get,

M =  (2xy² − 5)

and N = (2x²y + 7)

The partial derivative of M with respect to y is:

\(\frac{\partial M}{\partial y} \\\\=\frac{\partial}{\partial y}(2xy^2 -5)\)

= 4xy           ...........(1)

The partial derivative of N with respect to x is:

\(\frac{\partial N}{\partial x} \\\\=\frac{\partial}{\partial x}(2x^2y+7)\)

= 4xy          ...........(2)

From (1) and (2),

\(\partial N/\partial x=\partial M/\partial y\)

Therefore, the differential equation is an exact differential equation

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Answer:

−2(x+1)2+7

Step-by-step explanation:

I got this question on Prepworks and I got it right

Answer:

D

Step-by-step explanation:

A graph represents a function of x when it passes the vertical line test. That is, no x values map out to more than 1 y value.

Therefore, D is the only function of x.

Answer:

800/100

Step-by-step explanation:

100 is the denominator(bottom number) 800 is the numerator(top)

The amount of total cost at q* is 1.

To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):

TC(q) = 10 - 6q + q^2

To find the minimum point, we differentiate TC(q) with respect to q:

d(TC(q))/dq = -6 + 2q

Setting the derivative equal to zero and solving for q:

-6 + 2q = 0

2q = 6

q = 3

So the production level q* that minimizes the total cost is 3.

To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):

TC(q*) = 10 - 6(3) + (3)^2

TC(q*) = 10 - 18 + 9

TC(q*) = 1

Therefore, the amount of total cost at q* is 1.

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Answer: 5,2 2,3 2,2

Step-by-step explanation:

Answer:

17.5

Step-by-step explanation:

Pythagorean Theorem is a^2 + b^2 =c^2

a= 9 , b= 15, c= x

9^2 + 15^2 = c^2

\(\sqrt{306}\)= c^2

c= 17.493 or 17.5 rounded to the nearest tenth

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

O y = 15x + 10 is the only linear function

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

Tobias repayed a total of $7,200.

Step-by-step explanation:

If Tobias borrowed $20,000, and the annual interest rate is 9% of this per year, then we need to find 9% of 20,000.

20,000 x 0.09 = 1,800

Therefore, the yearly interest rate is $1,800. Now, we need to multiply this by 4.

1,800 x 4 = 7,200

Therefore, Tobias repayed a total of $7,200.

Hope this helps! :D

Answer:

40

Step-by-step explanation:

multiply -5 and -8

your answer will be 40

First Series: Both conditions are met, the series converges.

Second Series: The given series diverges.

Let's discuss it further below.

To determine the convergence or divergence of the series, we will use the Alternating Series Test for the first series and the Limit Comparison Test for the second series.

First Series:
Series: CAPITAL SIGMA N-ARY SUMMATION^infinity_n = 1 (-1)ⁿ⁺¹/ⁿ + 7

Step 1: Determine if the series is alternating.
The series is alternating because of the term (-1)ⁿ+1.

Step 2: Check the conditions of the Alternating Series Test.
a) The terms are decreasing: 1/n is decreasing as n increases.
b) The limit as n approaches infinity is 0: lim n rightarrow infinity (1/n) = 0

Since both conditions are met, the series converges.

Second Series:
Series: CAPITAL SIGMA N-ARY SUMMATION^infinity_n = 1 (-1)ⁿ⁺¹ n/n² + 9

Step 1: Compare this series to another known series.
We will compare this series to 1/n using the Limit Comparison Test.

Step 2: Calculate the limit as n approaches infinity.
lim n rightarrow infinity (n/n² + 9) / (1/n)

Step 3: Simplify the limit.
lim n rightarrow infinity (n²) / (n² + 9n)

Step 4: Determine the convergence or divergence.
Since the limit is 1 (non-zero and finite), the series has the same convergence behavior as the comparison series 1/n.

Since the harmonic series 1/n diverges, the given series also diverges.

In conclusion, the first series converges, and the second series diverges.

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Answer:

w - 8.8 > 27

Step-by-step explanation:

The third quartile for the given conditions is 224.

Given that a  sample of nine participants is selected and their total cholesterol levels are measured as follows:

185 225 240 196 175 180 194 147 223

The third quartile is the median of the upper half of a data set.

We can calculate the third quartile by arranging the data in ascending order and finding the median of the upper half of the data.

Therefore, the data arranged in ascending order is:

147 175 180 185 194 196 223 225 240

Now, the upper half of the data is:

194 196 223 225 240

There are five data values in the upper half, so the median is the mean of the 3rd and 4th values in the ordered list:

Q3=(223+225)/2 = 448/2 = 224

Hence, the third quartile is 224.

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Answer:

The sets of values that correctly completes the t-chart are:

7, -1, 7

Hence, option B is true.

Step-by-step explanation:

Given the equation

y = 2x² - 1

FOR x = -2

substitute x = -2 in the equation

y = 2x² - 1

y = 2(-2)² - 1

y = 8 - 1

y = 7

FOR x = 0

substitute x = 0 in the equation

y = 2x² - 1

y = 2(0)² - 1

y = -1

FOR x = 2

substitute x = 2 in the equation

y = 2x² - 1

y = 2(2)² - 1

y = 8 - 1

y = 7

Thus, the t-chart becomes:

x              y

-2            7

0             -1

2              7

Thus, the sets of values that correctly completes the t-chart are:

7, -1, 7

Hence, option B is true.

Answer:

B.

Step-by-step explanation:

Answer:

-y = 25

y = -25

When the signs are different you add, the value for x is the same so you don't need to do anythung else but to add

The exact percentage of Americans who are dissatisfied with their jobs can vary depending on various factors, including the specific time period and the source of data.

However, according to a Gallup survey conducted in 2021, approximately 45% of Americans reported being either somewhat or very dissatisfied with their current job.

The Gallup survey asked respondents to rate their job satisfaction on a scale ranging from 1 to 10, with 1 being "extremely dissatisfied" and 10 being "extremely satisfied." The percentage of dissatisfied Americans was calculated by considering those who rated their job satisfaction below 7.

Based on the Gallup survey conducted in 2021, it was found that around 45% of Americans expressed dissatisfaction with their current job. This indicates a significant portion of the population experiencing varying degrees of discontentment in their work life. Job dissatisfaction can have various causes, including lack of fulfillment, poor work-life balance, inadequate compensation, limited growth opportunities, or strained relationships with colleagues or superiors. It is important for employers and policymakers to understand these factors and work towards creating healthier work environments, fostering job satisfaction, and addressing the concerns of dissatisfied workers.

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The Answer Is ?=15.

have an amazing day <3