a 20 pound platter of cookies costs $77. the platter is a mix of peanut butter that costs $4 per pound, sugar that costs $3 per pound, and chocolate chip that’s costs $4.50 per pound. there are two more pounds of sugar cookies than peanut butter. how many pounds of sugar cookies are on the platter?

Answer:

a = (w - 3b + 4)/6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

w = 3(2a + b) - 4

Step 2: Solve for a

Therefore , the solution of the given problem of polynomials comes out to be 1 -  x² / (x⁴ -2)x² and (x⁶ - 4) x⁵ / x⁵ + 1 .

A polynomial is a mathematical expression that solely uses additions, subtractions, multiplication and division, and powers of positive integer variables. It is composed of coefficients and uncertainty. A single undetermined x polynomial is indicated by the expression x2 4x + 7. In mathematics, a polynomial is a mathematical equation made up of variables (sometimes called indeterminates) plus coefficients that can be added, subtracted, duplicated, and raised through negative integers powers of non-variables. A polynomial is a statement in mathematics involving variables and coefficients.

Here,

Given :

=>x⁶ - 4 / x⁻⁵ +1

=>  x⁶ - 4  / (x⁵ + 1 / x⁵)

=> (x⁶ - 4) x⁵ / x⁵ + 1

and

=> x⁻² - 1 / x⁴⁻2

=> (1- x²/x²) / x⁴ -2

=>   1 -  x² / (x⁴ -2)x²

Therefore , the solution of the given problem of polynomials comes out to be 1 -  x² / (x⁴ -2)x² and (x⁶ - 4) x⁵ / x⁵ + 1 .

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technologies have transformed modern management and individual behavior and decision-making in numerous ways.

Technologies have significantly impacted modern management and individual behavior and decision-making in various ways. One key aspect is the increased accessibility to data and information, enabling managers to make more informed decisions. Advanced analytics and data visualization tools allow for better analysis of complex data sets, leading to improved strategic planning and resource allocation.
Another important aspect is the enhancement of communication and collaboration among teams. Technologies such as video conferencing and project management software have facilitated a seamless flow of information across geographical boundaries. This has fostered a more inclusive and agile work environment, making it easier for managers to coordinate tasks and motivate their team members.
Additionally, automation technologies have streamlined many routine tasks, freeing up managers to focus on more strategic responsibilities. This has led to improved efficiency and productivity, allowing organizations to respond more effectively to dynamic market conditions. Moreover, artificial intelligence and machine learning can provide personalized support to individual employees, enhancing their decision-making abilities.
On the other hand, the widespread adoption of these technologies can also pose challenges. Issues related to privacy and data security have become increasingly significant, and managers must be proactive in addressing these concerns to protect their organization and employees. Furthermore, the rapid pace of technological change can lead to information overload and increased stress levels, potentially hindering individual decision-making.
While these advancements offer many benefits such as improved data analysis, enhanced communication, and increased efficiency, they also present challenges that must be addressed. It is crucial for managers to strike a balance between leveraging technology and managing potential risks to maximize the benefits for their organizations and employees.

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a. The series ∑n=1 to ∞ (n² + 2n) / n diverges.

b. The series ∑n=1 to ∞ (n³ + 2n) / n converges.

c. The series ∑n=1 to ∞ (n³ + n + 1100)  converges.

d. The series ∑n=1 to ∞ (n+1) / 3100 diverges.

e. The series ∑n=2 to ∞ (n⁵ - 3n - 14) / (n² + 5n - 2) converges.

a. The series ∑n=1 to ∞ (n² + 2n) / n diverges.

This can be justified using the divergence test. As n approaches infinity, the term simplifies to n + 2, which does not converge to zero.

Therefore, the series diverges.

b. The series ∑n=1 to ∞ (n³ + 2n) / n converges.

By simplifying the term (n^3 + 2n) / n, we get, which is a polynomial function.

The highest power in the polynomial is and the series converges for polynomial functions of degree 2 or higher.

Therefore, the series converges.

c. The series ∑n=1 to ∞ (n³ + n + 1100) converges. This can be justified by noting that each term in the series is a constant multiple of n³, and the series of n³ converges.

Additionally, the constant term and the linear term do not affect the convergence of the series.

Therefore, the series converges.

d. The series ∑n=1 to ∞ (n+1) / 3100 diverges. This can be justified by observing that the terms (n+1) / 3100 do not approach zero as n approaches infinity.

Therefore, the series diverges.

e. The series ∑n=2 to ∞ (n⁵ - 3n - 14) / (n² + 5n - 2) converges.

This can be justified by using the limit comparison test or the ratio test. By applying the ratio test, the series simplifies to ∑n=2 to ∞ = ∑n=2 to ∞ n.

Since, the series of n converges, the given series also converges.

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20cm^2 assuming that each box is one cm

The notation used for a vector pointing into the point is X.

A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.

Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.

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Answer:

<U=70

Step-by-step explanation:

Straight line=180 degrees

180-120

=60

So, we have 2 angles.

60 and 50

180=60+50+x

180=110+x

70=x

So, U=70

Hope this helps! :)

Answer:

y = - 4

Step-by-step explanation:

x = - 1 is the equation of a vertical line parallel to the y- axis

The equation of a line perpendicular to it will therefore be a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (8, - 4 ) with y- coordinate - 4 , then

y = - 4 ← equation of perpendicular line

The length should be x ≥ 3 inch and 4x ≥ 12 square inches.

What is linear inequality?

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠), can take the place of the equal sign "=" in this expression. Polynomial inequality, rational inequality, and absolute value inequality are the various kinds of mathematical inequalities.

Given a rectangle, length  = 4 inches

area is at least 12 square inches

inequality equation for area

A ≥ 12

area  = l x b

where l = length = 4 inches and b = breadth = x

A ≥ 12

4x ≥ 12

x ≥ 3 inches

Hence the breadth should be x ≥ 3 inches and equation of area is

4x ≥ 12 square inches.

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Answer:

48

Step-by-step explanation:

I do not have one sorry!

The value of the missing length in the triangle is b. 100

from the question, we have the following parameters that can be used in our computation:

The triangle

The height is calculated using the Pythagoras theorem as

h²= 60² - 36²

So, we have

h²= 2304

Evaluate

h = 48

Next, we have

(x -36) * 36 = 48 * 48

When evaluated, we have

x -36 = 64

So, we have

x = 64 + 36

Evaluate

x = 100

Hence, the value of x is 100

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Answer:

\(3^{n}+3^{n-1}\)

Step-by-step explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be \(x^n + yn\)

Because the sequence multiplies by 3 each time, The base number in that equation would be \(3^n +yn\).

So \(3^n\) of the equation would be:
\(3, 9, 27\).

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: \(3^{n-1}\).

Combine these 2 equations together and you get:

\(3^{n}+3^{n-1}\).

Answer:

1). Algebraic expression - a letter or symbol used to represent an unknown.

2). Coefficient - a numerical value.

3). Constant - the constant preceding the variables in a product.

4). Expression - a mathematical expression containing one or more variables.

5). Variable - a mathematical phrase that cannot be determined true or false.

Answer:

a) 3

Step-by-step explanation:

3+10= 13

hope this helped :)

Answer:

A. 3

Step-by-step explanation:

? + 10 = 13

? = 13 - 10

? = 3

Answer:

x = 12°

<B = 48°

Step-by-step explanation:

As alternate angles are equal,

< A = < B

Given that,

< A = 5x - 12

<B = 2x + 24

So,

5x - 12 = 2x + 24

Now solve for x.

5x - 2x - 12 = 24

3x - 12 = 24

3x = 24 + 12

3x = 36

Divide both sides by 3.

x = 12°

Now let us find the measure of angle B.

< B = 2x + 24

< B = 2 × 12 + 24

< B = 24 + 24

<B = 48°

Answer:C) specialization.

Step-by-step explanation:

From the t-test conducted, since the value is greater than the critical values, we fail to reject the null hypothesis.

To determine if there is convincing evidence that the true mean temperature of the system is different from 120 degrees Fahrenheit, we can perform a hypothesis test.

The null hypothesis (H₀) states that the true mean temperature (μ) is equal to 120 degrees Fahrenheit. The alternative hypothesis (Ha) states that the true mean temperature is different from 120 degrees Fahrenheit.

H0: μ = 120

Ha: μ ≠ 120

We will use a t-test to compare the sample mean temperature to the hypothesized mean of 120 degrees Fahrenheit. The significance level (α) is given as 0.05.

Given the sample data:

120.1 124.2 122.4 124.4 120.8 121.4

121.8 119.6 120.2 121.5 118.7 122.0

We can calculate the sample mean (x) and the sample standard deviation (s).

x = (120.1 + 124.2 + 122.4 + 124.4 + 120.8 + 121.4 + 121.8 + 119.6 + 120.2 + 121.5 + 118.7 + 122.0) / 12 = 121.25

s = √[((120.1-121.25)² + (124.2-121.25)² + (122.4-121.25)² + (124.4-121.25)² + (120.8-121.25)² + (121.4-121.25)² + (121.8-121.25)² + (119.6-121.25)² + (120.2-121.25)² + (121.5-121.25)² + (118.7-121.25)² + (122.0-121.25)²) / (12-1)]

Calculating the value of s, we find s ≈ 1.968.

Next, we calculate the t-value using the formula:

t = (x - μ) / (s / √n)

Where μ is the hypothesized mean, xis the sample mean, s is the sample standard deviation, and n is the sample size.

t = (121.25 - 120) / (1.968 / √12)

Calculating the value of t, we find t ≈ 2.013.

To determine if there is convincing evidence, we compare the calculated t-value to the critical t-value for a two-tailed test with a significance level of 0.05 and degrees of freedom equal to n-1 (12-1 = 11). From the t-distribution table or using statistical software, the critical t-value is approximately ±2.201.

Since |t| = |2.013| < 2.201, we fail to reject the null hypothesis. There is not enough convincing evidence at the 0.05 significance level to conclude that the true mean temperature of the system is different from 120 degrees Fahrenheit.

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The slope of the ideal vector, determined by examining the coefficients of the variables in the regression equation is:

Cleaning Ability: 2.3

Cost: 1.0

Disinfecting Ability: 0.6.

In this case, the regression equation is:

Overall Preference = -2.1 + 2.3 * Cleaning Ability + 1.0 * Cost + 0.6 * Disinfecting Ability

The coefficients of the variables represent the weights or importance assigned to each variable in determining the overall preference. Therefore, the slope of the ideal vector would be the coefficients of the variables in the regression equation.

Based on the given regression equation, the slope of the ideal vector would be:

Cleaning Ability: 2.3

Cost: 1.0

Disinfecting Ability: 0.6

These values indicate the relative importance or impact of each variable on the overall preference for Slippery Soap.

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The alpha level for each hypothesis test made on the same set of data is called B. experimentwise alpha

When numerous suppositions are examined concurrently, the likelihood of committing at least one type I mistake grows.

In order to manage the probability of erroneously rejecting the null hypothesis in all tests, scientists usually modify the alpha level for each test, with the purpose of maintaining an experimentwise alpha that reflects the probability of making a type I error in the entire set of tests.

The Bonferroni procedure is a technique utilized to regulate the experimentwise error rate by adjusting the alpha level for each hypothesis test.

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There are 8 third-order partial derivatives for a function f(x, y). They are:

1. ∂³f/∂x³ - third derivative with respect to x
2. ∂³f/∂x²∂y - mixed derivative with two x's and one y
3. ∂³f/∂x∂y² - mixed derivative with one x and two y's
4. ∂³f/∂y³ - third derivative with respect to y
5. ∂³f/∂x∂y∂x - mixed derivative with x, y, and x
6. ∂³f/∂y∂x∂y - mixed derivative with y, x, and y
7. ∂³f/∂x∂y∂y - mixed derivative with x, y, and y (equivalent to 3)
8. ∂³f/∂y∂x∂x - mixed derivative with y, x, and x (equivalent to 2)

We have 8 third-order partial derivatives because there are two variables (x and y), and we can take the derivative up to three times with respect to either variable or a combination of both. This results in different ways to distribute the three derivative operations among the two variables (x and y), leading to the 8 combinations mentioned above. Note that some of these derivatives are equivalent due to the symmetry of mixed derivatives when the function f(x, y) has continuous second-order partial derivatives.

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y = kx

y = 6 (13)

y = 78

Answer:

Common factor from the two pairs

n2+2n-n-2 or

n(n+2)-1(n+2)

Rewrote in factored form

n(n+2)-1(n+2)or

(n-1)(n+2)

Solution

(n-1)(n+2)

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

\(\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6\)

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

check A and C

Step-by-step explanation:

Answer:

Right angle, suppemantary angle, complemantary angle.

Step-by-step explanation:

Ive dont this lesson befoe

Answer:

C

0.8+0.6=1.4

Step-by-step explanation:

eight tenths plus sixty hundredths equals blank

eight tenths = 0.8

sixty hundredths = 0.6

0.8+0.6=1.4

the answer is c

"0.8+0.6=1.4"

Answer:

See below for explanation.

Step-by-step explanation:

Each (x, y) point on the unit circle is equal to (cos θ, sin θ).

To find cot θ, where θ is the angle corresponding to the point (x, y) on the unit circle, we can use the formula:

\(\boxed{\cot \theta=\dfrac{\cos \theta}{\sin \theta}=\dfrac{x}{y}}\)

\(\hrulefill\)

If cot θ = 0, then x must be zero. (If y was zero, the value would be undefined). Therefore, we need to find the points on the unit circle where the x-coordinate (cos θ) is zero.

The points on the unit circle where x = 0 are:

The corresponding angles (in radians) at these points are:

    \(\bullet \quad \dfrac{\pi}{2}\;\;\textsf{and}\;\;\dfrac{3\pi}{2}\)

Therefore, the cotangent has the value of zero at π/2 and 3π/2.

\(\hrulefill\)

If we divide a number by the same (but negative) number, we get -1.

Similarly, if we divide a negative number by the same (but positive) number, we get -1.

Therefore, if cot θ = -1, then the x-coordinate and y-coordinate of the points must be the same, but opposite signs.

The points on the unit circle where -x = y and x = -y are:

    \(\bullet \quad \left(-\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)\;\; \textsf{and}\;\;\left(\dfrac{\sqrt{2}}{2},-\dfrac{\sqrt{2}}{2}\right)\)

The corresponding angles (in radians) at these points are:

    \(\bullet \quad \dfrac{3\pi}{4}\;\;\textsf{and}\;\;\dfrac{7\pi}{4}\)

Therefore, the cotangent has the value of -1 at 3π/4 and 7π/4.

The answer is sin(y) = 4/sqrt(16 - 16x^2).

We can use the following identity:

sin(y) = sqrt\((1 - cos^2(y))\)

Since x = cos(y), we can substitute to get:

sin(y) = sqrt\((1 - x^2)\)

We are given that 0 < x < 1/4. This means that \(x^2\) < \(\frac{1}{16}\)Therefore, we can simplify the expression for sin(y) as follows:

sin(y) = sqrt(\((1 - x^2)\) = sqrt(\(1 - \frac{1}{16}\) = sqrt(\(\frac{15}{16}\)) = 4/sqrt(\(16 - 16x^2\))

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The answer is: A. tan P= 3/4, tan Q=5/4

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratio of the lengths of its sides. There are three primary trigonometric ratios, known as sine, cosine, and tangent, and their reciprocal functions, known as cosecant, secant, and cotangent.

The primary trigonometric ratios are defined as follows:

Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.

sin θ = opposite/hypotenuse

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.

cos θ = adjacent/hypotenuse

Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

tan θ = opposite/adjacent

The reciprocal trigonometric ratios are defined as follows:

Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle.

csc θ = 1/sin θ

Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle.

sec θ = 1/cos θ

Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle.

cot θ = 1/tan θ

Trigonometric ratios are widely used in mathematics, science, and engineering to solve problems involving right triangles, as well as to model and analyze periodic phenomena such as sound waves, light waves, and electromagnetic waves.

Since angle R is a right angle, we can use the tangent ratio for angles P and Q as follows:

tan P = RP / RQ = 12 / 16 = 3 / 4

tan Q = PQ / RQ = 20 / 16 = 5 / 4

Therefore, the answer is: A. tan P= 3/4, tan Q=5/4

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The fraction of infants that are expected to have birth weights between 3210 g and 4480 g is 0.893.

The fraction of infants that are expected to have birth weights below 3210 g is 0.011.

The weight below which an infant will be included in the study is approximately 3151 g.

A standard normal distribution, also known as the Gaussian distribution or the z-distribution, is a specific type of probability distribution. It is a continuous probability distribution that is symmetric, bell-shaped, and defined by its mean and standard deviation.

In a standard normal distribution, the mean (μ) is 0, and the standard deviation (σ) is 1. The distribution is often represented by the letter Z, and random variables that follow this distribution are referred to as standard normal random variables.

The probability density function (PDF) of the standard normal distribution is given by the formula:

f(z) = (1 / √(2π)) * e^(-z^2/2)

where e represents the base of the natural logarithm (2.71828) and π is a mathematical constant (3.14159).

The z-score of an infant who weighs 4584 g can be calculated as follows: Since the mean is 3432 g and the standard deviation is 482 g, the z-score is given by;(4584 - 3432) / 482 = 2.39

Therefore, the z-score of an infant who weighs 4584 g is 2.39.

Approximate fraction of infants with birth weights between 3210 g and 4480 g can be calculated as follows: The standard normal distribution will be used to find this fraction. The z-scores for 3210 g and 4480 g can be computed by;(3210 - 3432) / 482 = -2.3 and (4480 - 3432) / 482 = 2.18

The fraction can be found by subtracting the areas below the curve corresponding to the z-score 2.18 from the area corresponding to the z-score -2.3. That is; Approximately 0.893 is the fraction of infants that are expected to have birth weights between 3210 g and 4480 g.

Approximately what fraction of infants would you expect to have birth weights below 3210 g? Since the mean is 3432 g and the standard deviation is 482 g, the z-score is given by;(3210 - 3432) / 482 = -2.3

The area to the left of this z-score can be obtained from a standard normal distribution table or by using technology. This is approximately 0.0107. Therefore, approximately 0.011 is the fraction of infants that are expected to have birth weights below 3210 g.

Below what weight must an infant's birth weight be in order for the infant to be included in the study ?The lowest 17% of birth weights will be included in the study, so the birth weight must be less than or equal to the 17th percentile. The z-score corresponding to the 17th percentile can be found from the standard normal distribution table or by using technology.

It is approximately -0.17. The weight corresponding to this z-score can be calculated as follows;

(-0.17 x 482) + 3432 = 3151 g

Therefore, the weight below which an infant will be included in the study is approximately 3151 g.

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Answer:

m=30

Step-by-step explanation:

Answer: m = 30

Step-by-step explanation: The equation 7m = 210 can be solved for the value of m by isolating m on one side of the equation.

To do this, we can divide both sides of the equation by 7, since dividing by 7 is the inverse operation of multiplying by 7.

So, 7m/7 = 210/7, which simplifies to m = 30.

Therefore, the value of m that makes the equation true is 30.