A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.



Which equation can be used to determine the amount of cherry juice in each mixture?

Answer:

train A is 475 tons and train B is 40 tons

Step-by-step explanation:

515 minus 475 is 40 since train a is heavier you make the weight of it 475 and train b lighter

Answer:

Step-by-step explanation:

Sum:515 tones

Difference:475 tones

First train's weight:(Sum-Difference)÷2=(515-475)÷2=40÷2=20 tones

Second train's weight:(Sum+Difference)÷2=(515+475)÷2=990÷2=495 tones.

Answer:

If it does not cross the x axis.

Step-by-step explanation:

If the quadratic equation does not cross the x axis (or more specifically, if the quadratic is an upward opening parabola and the vertex is above the x axis, or if the quadratic is a downward opening parabola and the vertex is below the x axis), it will have no real solution

The fundamental theorem of algebra says that quadratics must have 2 solutions, so the solutions must be imaginary.

Answer:

N=15

Step-by-step explanation:

Simplify 1/4 (2n-8)

2n-8/4+1/4n=1/2(n+6)

Factor out the common term 2.

2(n-4)/4+1/3n=1/2(n+6)

Simplify  2(n-4)/4 to n-4/2

n-4/2+n/3=1/2(n+6)

Simplify  1/3n to n/3

n-4/2+n/3=1/2(n+6)

Simplify 1/2(n+6) to n+6/2

n-4/2+n/3=n+6/2

Multiply both sides by 6 (the LCM of 2, 3,).

3(n−4)+2n=3(n+6)

7 Expand.

3n−12+2n=3n+18

Simplify  3n-12+2n to  5n-12

5n−12=3n+18

Add 12 to both sides.

5n=3n+18+12

Simplify  3n+18+12  to  3n+30

5n=3n+30

Subtract 3n from both sides.

5n-3n=30

Simplify  5n-3n to 2n.

2n=30

Divide both sides by 22

n= 30/2

Simplify 30/2 to 15.

n=15

n=15

Brainliest

Answer:

n = 15

Explanation :

1/4(2n-8) + 1/3n = 1/2(n+6)                 Distribute

1/2n -2  + 1/3n = 1/2(n+6)                    Combine like terms

5/6n -2 = 1/2(n+6)                               Distribute

5/6n -2 = 1/2n +3                                 Pass 1/2n  to the other side

5/6n - 1/2n -2 = 3                                Combine like terms

1/3n  -2 = 3                                            Pass -2 to the other side

1/3n = 3+2                                           Combine like terms

1/3n = 5                                                 Divide both sides by 1/3

n = 15                                                     and then you will get your answer .

This limit is less than 1 if and only if |x-1| < 1/6, so the interval of convergence is: (1-1/6, 1+1/6) = (5/6, 7/6)

The Taylor series for f(x) = -14/x centered at x=1 is:

\(f(x) = f(1) + f'(1)(x-1) + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...\)

Taking the derivatives of f(x), we have:

f(x) = -14/x

\(f'(x) = 14/x^2\)

\(f''(x) = -28/x^3\)

\(f'''(x) = 84/x^4\)

Evaluating these at x=1, we get:

f(1) = -14

f'(1) = 14

f''(1) = -28

f'''(1) = 84

Substituting these values into the Taylor series, we get:

\(f(x) = -14 + 14(x-1) - 28(x-1)^2/2! + 84(x-1)^3/3! - ...\)

To determine the interval of convergence, we can use the ratio test:

\(lim_{n- > inf} |a_{n+1}(x-1)/(a_n(x-1))| = lim_{n- > inf} |(84/(n+1))/(14/n)| |x-1| = |6(x-1)|.\)

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The interval of convergence for the Taylor series of f(x) = -14/x at x = 1 is (0, 2) in interval notation.

To determine the interval of convergence for the Taylor series of f(x) = -14/x at x = 1, we first find the Taylor series representation. Since f(x) is a rational function, we can rewrite it as f(x) = -14(1/x) and then use the geometric series formula:

f(x) = -14Σ((-1)^n * (x - 1)^n), where Σ is the summation symbol and n runs from 0 to infinity.

To find the interval of convergence, we use the ratio test. The ratio test involves taking the limit as n approaches infinity of the absolute value of the ratio of consecutive terms:

lim (n→∞) |((-1)^(n+1)(x - 1)^(n+1))/((-1)^n(x - 1)^n)|

Simplify the expression:

lim (n→∞) |(x - 1)|

For convergence, this limit must be less than 1:

|(x - 1)| < 1

This inequality gives us the interval of convergence:

-1 < (x - 1) < 1

Add 1 to each part:

0 < x < 2

So, the interval of convergence for the Taylor series of f(x) = -14/x at x = 1 is (0, 2) in interval notation.

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Answer: Hope it helps, have a nice day :)

A: 0.3

A:  3/10

B: 0.6

B: 6/10 (3/5 if simplified)

C: 1.4

C: 1 4/10

D: 1.9

D: 1 9/10

Step-by-step explanation:

The first letter is decimal and the second is fractions- just likes yours

The difference after the subtraction is: 2a³ +  10a² - 5a - 4

A polynomial is an expression which has one or more of its variables with a power of at least 2 degrees. It can be expressed in form of a term.

Therefore, a polynomial equation is a means of expressing an expression with terms and on variable with a degree of 2 or more.

To find the difference by subtracting the polynomials, we have:

4a³ + 6a² - 11a - 3 - (2a³ - 4a² - 6a + 1) = 4a³ + 6a² - 11a - 3 - 2a³ + 4a² + 6a - 1

collecting like terms,

4a³ - 2a³ +  6a² + 4a²  - 11a + 6a - 3 - 1 = 2a³ +  10a² - 5a - 4

Therefore, the difference by subtracting the two polynomials is:

2a³ +  10a² - 5a - 4

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The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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Answer:

Step-by-step explanation:

no because 6 , 7 and 10 doesn't add up to 180 so it is not

A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.

To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:

a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.

In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.

The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.

The sum of 36 kilometers and 49 kilometers is 85 kilometers.

The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.

Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.

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Answer:

64%

Step-by-step explanation:

If  9 out of 25 people are left-handed

That means 25-9 = 16 people are right handed

or 16/25 are right handed

Multiply the top and bottom by 4 to get it out of 100

64/100

Percent means out of 100

64% are right handed

The weight of a beagle that is 1 standard deviation below average is 22 pounds, the weight of a beagle that is 1 standard deviation above average is 28 pounds, and approximately 68% of the data falls within the range of 22 to 28 pounds.

If the weights of beagles are approximately normally distributed with a mean weight of 25 pounds and a standard deviation of 3 pounds, we can use the empirical rule to determine the weight of a beagle that is 1 standard deviation below average and 1 standard deviation above average.

According to the empirical rule, approximately 68% of the data falls within 1 standard deviation of the mean. Therefore, the weight of a beagle that is 1 standard deviation below average would be:
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25 - (1 x 3) = 22 pounds

Similarly, the weight of a beagle that is 1 standard deviation above average would be:

25 + (1 x 3) = 28 pounds

Thus, we can expect the weights of approximately 68% of beagles to fall within the range of 22 to 28 pounds.

The normal distribution is a bell-shaped curve that is symmetrical around the mean. In this case, the mean weight of beagles is 25 pounds, which is the highest point on the curve. As we move away from the mean, the probability of encountering a particular weight decreases. One standard deviation away from the mean covers a large proportion of the data, but as we move further away, the proportion decreases rapidly.

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Answer:

2(w - 6)

Step-by-step explanation:

subtract 6 from w and then multiply by 2

The time it takes to type the document increases proportionately to the

number of words in the document.

Reasons:

From the possible figure from a similar question, we have;

The points on the graph are; (0, 0), (1, 60), (2, 120), (3, 180), (4, 240)

The graph is a straight line, therefore, given that the starting point is at the origin, using the points, (0, 0), (1, 60), we have;

The slope of the graph = 60

The y-intercept = 0

The equation that represents the proportional relationship shown on the graph is therefore;

y = 60·x

Where;

y = The number of words

x = The time it takes to type the document

The time it would take Maya to type the document of 2,160 words is given as follows;

2,160 = 60·x

Therefore;

\(\displaystyle Time, \ x = \frac{2,160 \ words}{60 \ words/minute} = \mathbf{36 \ minutes}\)

The time it would take Maya to type the document is x = 36 minutes

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Based on the two-tangent theorem, the value of x is calculated in the circle as: x = 2.

Based on the two-tangent theorem, if two tangents are drawn from a circle to meet each other at any point outside the circle, then the lengths of the tangents are congruent to each other, that is, they are equal.

Therefore, we would create the following equation based on the two-tangent theorem:

20x + 6 = 10x + 26

Combine like terms:

20x - 10x = -6 + 26

10x = 20

Divide both sides by 10:

10x/10 = 20/10

x = 2

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Answer:

D

Step-by-step explanation:

Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect

Answer:

Step-by-step explanation:

This is a combination of 6 out of 15

Correct choice is C

Answer:

C right?

Step-by-step explanation:

Answer:

Step-by-step explanation:

let a be the first term and r be common ratio.

\(a_{3}=ar^2=-45\\a_{5}=ar^4=-405\\divide\\\frac{ar^4}{ar^2} =\frac{-405}{-45} =9\\r^2=9\\r=\pm3\\9a=-45\\a=-5\\a_{7}=ar^{7-1}=ar^6=ar^4 \times r^2=-405 \times 9=-3645\)

The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.

What is an Exponent?

The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.

Calculation of the total number of candies in the store

(36)2 * 30

Using the properties of an exponent, we have

A number with an exponent of 0 always gives 1

(36)2 * 1

(3)6×2 * 1

312 * 1

312

Thus, the total number of candies in the store is 312.

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Answer:

Step-by-step explanation:

yes

The cost of installing a fence around an 80 ft. wide and 120 ft. deep rectangular lot, with the fence priced at $3.25 per linear foot, will be $1,300.

To determine the cost of installing a fence around a rectangular lot, you need to calculate the total length of the fence required and then multiply that by the cost per linear foot. The given dimensions of the lot are 80 feet wide and 120 feet deep.
First, calculate the perimeter of the rectangular lot. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length (or depth) and W is the width. In this case, the perimeter is P = 2(120) + 2(80) = 240 + 160 = 400 feet.
Next, multiply the total length of the fence by the cost per linear foot, which is $3.25. So, the cost of installing the fence is 400 feet × $3.25 per linear foot = $1,300.

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Answer:

3²

Step-by-step explanation:

3³x3³=3^6

3^6÷3^4=3²

The machine discharge more than 7.0 oz or does the difference represent chance variation is 0.0274

What is meant by variation?

In math, variance refers any difference between the individuals in a species or groups of organisms of any species.

Here we have given that a coin-operated soft drink machine was designed to discharge, on average, 7 oz of beverage per cup. in a test of the machine, 10 cupful's of beverage were drawn from the machine and measured. the average and SD of the ten measurements were 7.1 oz and 0.12 oz, respectively. assume that the histogram of beverage discharge from this machine roughly follows a normal curve.

And we need to find machine discharge more than 7.0 oz or does the difference represent chance variation.

By using the Applet, to find the exact p-value we first need to find P(Z≥2.63) where Z is a t9​ random variable.

=> P(Z≥2.63)=0.0137

=> 2×P(Z≥2.63)=0.0274

=> P-value=0.0274

So, the p-value associated with the test is 0.0274

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Compared with the graph of the parent function, an equation which shows only a vertical compression by a scale factor of 1/3 and a shift downward of 4 units is: A. y = 1/3∛x - 4.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (1/3x, 1/3y)

Where:

In this scenario, the only equation that is vertically compressed by a scale factor of 1/3 and translated (shifted) downward by 4 units is given by:

y = 1/3∛x - 4.

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Answer:

The first part is A

and second part is D

Step-by-step explanation:

100% on edge 2023

The correct option is c) between 32 and 37. The box part of the box plot contains all the values between 32 and 37.

A box-and-whisker plot, also known as a box plot, is a visual representation of a set of data that shows the distribution and variability of the data. The box part of the box plot contains the middle 50% of the data, which is also known as the interquartile range (IQR).

In the given example, the box ranges from 32 to 37, which means that 50% of the data falls within this range. The line that divides the box at 36 represents the median, which is the middle value of the data set.

The whiskers, on the other hand, extend from the box to the minimum and maximum values in the data set that are not considered outliers. In this example, the whiskers range from 27 to 40, which means that the minimum and maximum values in the data set are 27 and 40 respectively.

Therefore, the answer to the question is option C, between 32 and 37, as this is the range that the box covers. The other options do not correctly represent the range of values that fall within the box.

Overall, box-and-whisker plots are useful tools for summarizing and comparing data sets, as they provide a clear and concise visual representation of the distribution and variability of the data.

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The required expression in terms of cosine is sin(22) = ±cos(68).

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

Here,
Using the identity \(sin^2(x) + cos^2(x) = 1\), we can write:

\(sin^2(x) = 1 - cos^2(x)\)

Substituting x = 22 degrees, we get:

\(sin^2(22) = 1 - cos^2(22)\)

\(cos^2(22) = 1 - sin^2(22) = cos^2(68)\)

Taking the square root of both sides, we get:

cos(22) = ±cos(68)

Since 22 degrees is in the first quadrant and cos(x) is positive in the first quadrant, we can take the positive value of cos(68) and write the expression in terms of cosine:

\(sin^2(22) = cos^2(68)\)

sin(22) = ±cos(68)

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If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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The value of x is -1/2 if the function f(x) (6x + 4)e^(-6x) has one critical number.

To find the critical number of the function f(x) = (6x + 4)e^(-6x), we need to find the value(s) of x where the derivative of f(x) is equal to zero or undefined.

Let's start by finding the derivative of f(x). We can use the product rule for differentiation:

f'(x) = [(6x + 4) * d(e^(-6x))/dx] + [e^(-6x) * d(6x + 4)/dx]

To differentiate e^(-6x), we use the chain rule, which states that d(e^u)/dx = e^u * du/dx:

d(e^(-6x))/dx = e^(-6x) * d(-6x)/dx = -6e^(-6x)

Differentiating 6x + 4 with respect to x gives us 6.

Substituting these values back into the derivative expression:

f'(x) = [(6x + 4) * (-6e^(-6x))] + [e^(-6x) * 6]

Simplifying:

f'(x) = -36x e^(-6x) - 24e^(-6x) + 6e^(-6x)

Now, let's find the critical number by setting the derivative equal to zero:

-36x e^(-6x) - 24e^(-6x) + 6e^(-6x) = 0

Combining like terms:

-36x e^(-6x) - 18e^(-6x) = 0

Factoring out e^(-6x):

e^(-6x)(-36x - 18) = 0

Now, we have two possibilities:

e^(-6x) = 0 (which is not possible since e^(-6x) is always positive).

-36x - 18 = 0

Solving this equation for x:

-36x = 18

x = 18/(-36)

x = -1/2

Therefore, the critical number of the function f(x) = (6x + 4)e^(-6x) is x = -1/2.

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Answer: i am so confused lol

Step-by-step explanation:

Answer:

Something

Step-by-step explanation:

First you type shift then s, o, m, e, t, h, i, n, and g