An equation of the line that passes through point (-2,0) and whose slope is 5/2​

a. The system of equations are:

3x + 5y = 22

12x + 2y = 25

2. Cost for each pound of almond (x) = $1.5

Cost for each pound of jelly beans (y) = $3.5

From the information given above, we can create the system of equations that will be used in solving the problem as shown below.

a. The system of equations that represents the situation is:

3x + 5y = 22 ----> equation 1

12x + 2y = 25 ----> equation 2

b. Multiply equation 1 by 2, and equation 2 by 5:

6x + 10y = 44 ----> equation 3

60x + 10y = 125 ----> equation 4

Subtract equation 4 from equation 3

-54x = -81

-54x/-54 = -81/-54

x = 1.5

Cost for each pound of almond (x) = $1.5

Substitute x = 1.5 into equation 1

3x + 5y = 22 ----> equation 1

3(1.5) + 5y = 22

4.5 + 5y = 22

5y = 22 - 4.5

5y = 17.5

5y/5 = 17.5/5

y = 3.5

Cost for each pound of jelly beans (y) = $3.5

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The book value of the building in 2014 was $3.96 million. The book value of the building in 2028 will be $2.28 million.

a) The book value of the building in 2014 can be calculated as follows:

Book Value = Original Cost - (Depreciation Rate * Years Depreciated)

Depreciation Rate = Original Cost / Number of Years

Depreciation Rate = 6 million / 50 years = $120,000 per year

Years Depreciated = 2014 - 1997 = 17 years

Book Value = 6 million - (120,000 * 17) = 6 million - 2.04 million = $3.96 million

So, the book value of the building in 2014 was $3.96 million.

b) The book value of the building in 2028 can be calculated in a similar manner:

Years Depreciated = 2028 - 1997 = 31 years

Book Value = 6 million - (120,000 * 31) = 6 million - 3.72 million = $2.28 million.

So, the book value of the building in 2028 will be $2.28 million.

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the distinct equivalence classes [0], [1], [2], and [3] form a partition of ℤ.

What is Equivalence relation?

An equivalence relation is a relation between elements of a set that satisfies three properties: reflexivity, symmetry, and transitivity.

a) To prove that R is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer m, we need to show that m R m, i.e., 4 |\((m^2 - m^2).\) Since the difference of squares is 0, which is divisible by 4, the relation is reflexive.

Symmetry: For any integers m and n, if m R n, then we need to show that n R m. If 4 | \((m^2 - n^2)\), then \((m^2 - n^2)\) is divisible by 4. Taking the negative of both sides, we have\((-n^2 + m^2) = (m^2 - n^2)\), which is also divisible by 4. Therefore, n R m, and the relation is symmetric.

Transitivity: For any integers m, n, and p, if m R n and n R p, then we need to show that m R p. Suppose 4 |\((m^2 - n^2)\)and 4 \(| (n^2 - p^2)\). This means \((m^2 - n^2) and (n^2 - p^2)\)are both divisible by 4. Adding these two divisibility statements, we get (m^2 - p^2) is also divisible by 4, which implies m R p. Hence, the relation is transitive.

Since the relation R satisfies reflexivity, symmetry, and transitivity, it is an equivalence relation.

b) The distinct equivalence classes of the relation R can be described by the set of all integers that are congruent modulo 4. In other words, each equivalence class contains integers that have the same remainder when divided by 4.

The distinct equivalence classes can be denoted as follows:

[0] = {..., -8, -4, 0, 4, 8, ...}

[1] = {..., -7, -3, 1, 5, 9, ...}

[2] = {..., -6, -2, 2, 6, 10, ...}

[3] = {..., -5, -1, 3, 7, 11, ...}

Each equivalence class consists of integers that satisfy the condition 4 | (m^2 - n^2), and within each class, any two integers have their squares yielding the same remainder when divided by 4.

c) The distinct equivalence classes [0], [1], [2], and [3] form a partition of ℤ. A partition of a set is a collection of non-empty, pairwise disjoint subsets whose union is the entire set.

In this case, the equivalence classes [0], [1], [2], and [3] are non-empty and pairwise disjoint because no integer can simultaneously belong to two different equivalence classes. Also, the union of all the equivalence classes covers the entire set of integers, as each integer belongs to exactly one of the equivalence classes.

Therefore, the distinct equivalence classes [0], [1], [2], and [3] form a partition of ℤ.

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She needs to locate the squares of the integers between 7.1 and 7.2 in order to estimate √51.

Finding an integer's square root is the inverse of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root of a number can be discovered by looking for a number that, when squared, produces the original value. It follows that a× a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number.

In the question given to us,

look at the table, we know

(7.1)² = 50.41 and (7.2)² = 51.84

So, (7.1) < √51 < 7.2 { estimate }

They should therefore determine the squares of the numbers between 7.1 and 7.2.

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The complete question is :

Meredith is trying to estimate √51 She uses this table of values:

What should she do next to find √51 to the nearest hundredth?

A. She should find the average of 7. 1 and 7. 2.

B. She should find the squares of numbers between 7. 2 and 7. 3.

C. She should find the squares of numbers between 7. 1 and 7. 2.

D. She should estimate that √51 is 7. 20.

The court's action of taking judicial notice that it is impossible to travel from New York to Tampa without crossing a state line has the effect of establishing a fact without requiring formal proof during the trial.

Judicial notice is a legal doctrine that allows a court to accept certain facts as true without requiring formal evidence or proof. In this case, the court has taken judicial notice of the fact that it is impossible to travel from New York to Tampa without crossing a state line. By doing so, the court treats this fact as common knowledge that does not need to be proven during the trial. This means that the prosecutor does not have to provide specific evidence or arguments to establish the element of crossing state lines, as it is considered an indisputable fact in this particular case. The court's action simplifies the proceedings by accepting this fact without requiring further substantiation.

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The study conducted by the researcher suffers from several limitations, including the absence of a control group, small sample size, participant bias, and experimenter bias. Furthermore, the sample selection is inadequate, as all the participants are students of one course in a single university.

Moreover, the study fails to account for extraneous variables that might affect the results. Therefore,  that textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. T he study is flawed, and more research is needed to assess the effect of textbooks on learning.

The study conducted by the researcher suffers from several limitations. First, there is no control group, which makes it difficult to determine whether the results are due to the absence or presence of the textbook. Second, the sample size is small, which reduces the generalizability of the findings.

Third, there is participant bias, as some students might have bought the textbook even though it was optional, while others might not have bought it even though it was required. Fourth, there is experimenter bias, as the professor who scored the essays knew which section had the textbook and which did not.

Fifth, the sample selection is inadequate, as all the participants are students of one course in a single university. Moreover, the study fails to account for extraneous variables that might affect the results, such as the students' prior knowledge, motivation, and study habits.

Therefore, the  textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. The study is flawed, and more research is needed to assess the effect of textbooks on learning.

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Divide the number sold by the percentage:

72 / 0.12 = 600

Total crop was 600 apples.

Answer:

600

Step-by-step explanation:

let the total number of apples be x

12/100×x=72

x=72×100/12

x=600

therefore total number of apples in the crop is 600

The sketch of the function y = \(x^{2}\) - x - 3 for -3 <= x <= 3 reveals a parabolic curve that opens upwards. The turning point of the parabola, also known as the vertex, can be identified as (-0.5, -3.25).

To sketch the graph of y = \(x^{2}\) - x - 3, we consider the given domain of -3 <= x <= 3. The function represents a parabola that opens upwards. By calculating the coordinates of the turning point, we can locate the vertex of the parabola.

To find the x-coordinate of the turning point, we use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1. Substituting these values, we have x = -(-1)/2(1) = -0.5.

To find the y-coordinate of the turning point, we substitute the x-coordinate (-0.5) into the equation y = \(x^{2}\) - x - 3. Evaluating this expression, we get y = \(-0.5^{2}\) - (-0.5) - 3 = -3.25.

Therefore, the turning point of the parabola is approximately (-0.5, -3.25).

From the sketch, we can estimate the approximate solutions to the equation \(x^{2}\)- x - 3 = 0 by identifying the x-values where the graph intersects the x-axis. These solutions are approximately x ≈ -2.5 and x ≈ 1.5.

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The limits of integration for z are -8 to 8

To simplify the integration process, we can parameterize the surface S. Let's introduce new variables y and z as parameters to represent points on the surface. Since the surface is defined by the equations y² + z² = 64 and x + y = 10, we can express y and z in terms of these parameters.

Let's solve the equation y² + z² = 64 for y:

y = √(64 - z²)

Now, substitute the expression for y into the equation x + y = 10:

x + √(64 - z²) = 10

Solving for x gives us:

x = 10 - √(64 - z²)

So, we have parameterized the surface S as follows:

x = 10 - √(64 - z²)

y = √(64 - z²)

z = z

To calculate the surface integral, we need to determine the surface area element dS. The surface area element is given by the cross product of the partial derivatives of the parameterized surface with respect to the parameters y and z.

Let's calculate the partial derivatives:

∂r/∂y = [-1, 1, 0]

∂r/∂z = [√(64 - z²) / 2z, -z / √(64 - z²), 1]

Now, take the cross product:

dS = ∂r/∂y x ∂r/∂z

= [(-z / √(64 - z²)), (√(64 - z²) / 2z), 1]

Now that we have the parameterization of the surface S and the surface area element dS, we can set up the integral as follows:

∫∫S xz dS

Since the integral is over the surface S, we need to determine the limits of integration for the parameters y and z. Looking at the given equations, we know that z varies from -8 to 8 because of the equation y² + z² = 64. As for y, it varies based on the value of z to satisfy x + y = 10.

Thus, the limits of integration for z are -8 to 8, and for y, it is from -√(64 - z²) to √(64 - z²).

The integral now becomes:

∫∫S xz dS = ∫[-8, 8] ∫[-√(64 - z²), √(64 - z²)] (10 - √(64 - z²))z dA

Here, dA represents the area element in the yz-plane, which is dydz..

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Answer:

9(20−(3)(8))−42

=9(20−24)−42

=(9)(−4)−42

=−36−42

=−36−16

=−52

The answer is

In step 2, the addition property of equality was applied.

In step 4, the division property of equality was applied.

Proof that the answer is correct.

Answer:

addition

division

Step-by-step explanation:

The straight line distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

The sheehan lake (point A) is at 2000 m .

The small lake ( point B) is at 3700 m .

Distance between the two lake can be calculated by finding the difference between lakes .

To find the distance between sheehan lake and small lake = point B - point A .

Distance =  3700 - 2000

Distance = 1700 m .

The distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

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The question is incomplete the complete question is :

On solving the provided question we can say that - the removable discontinuity of f(x) located is -5

Discontinuous functions in graphs are those that have no connections to one another. Discontinuities come in three different flavors: removable, jump, and infinite.. If the left limit and the right limit of a function, f(x), are both different, then the function has a first-kind discontinuity at x = a. a characteristic that cannot be mathematically continuous. Continuous functions allow you to sketch without having to lift your pen. In such a case, the function is said to as discontinuous.

here,

f(x) = \(\frac{x+5}{x^2+3x-10}\)

\(x^2+3x-10\)

x(x+5) - 2(x+5)

(x+5 )(x-2 )

x = 2, -5

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Answer:

40 divided by 200 is x.

x = 5

Hope this helped!

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

6 - n = 6 - (-#) = 6 + n

3 (6n) = greatest value

Answer:

(x-1)(x-1)

Step-by-step explanation:

Step-by-step explanation:

3 supervisors = 60 employees

=> 264 supervisors = 60 * (264/3) = 5,280 employees. (C)

The probability of guessing at least 4 out of 10 correctly is approximately 0.3770.

In this scenario, each question has five choices, so the probability of guessing a question correctly is 1/5, and the probability of guessing incorrectly is 4/5. Since the student is guessing on each question, we can model this as a binomial distribution problem.

To find the probability of guessing at least 4 out of 10 correctly, we need to calculate the probability of guessing 4, 5, 6, 7, 8, 9, or 10 questions correctly and sum up these probabilities.

Using the binomial probability formula, the probability of guessing exactly k questions correctly out of n questions is given by the formula P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of questions, k is the number of correct guesses, and p is the probability of guessing a question correctly.

In this case, n = 10, k ranges from 4 to 10, and p = 1/5. We can calculate the probability for each value of k and then sum them up to find the overall probability of guessing at least 4 out of 10 correctly.

Calculating these probabilities and summing them up, we find that the probability of guessing at least 4 out of 10 correctly is approximately 0.3770, or 37.70%.

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Answer:

5,000,000 in standard form is 5 × \(10^{6}\)
800,000 in standard form is 8 × \(10^{5}\)

50,000 in standard form is 5 × \(10^{4}\)

300 in standard form is 3 ×\(10^{2}\)

Hope it helps and have a great day! =D

~sunshine~

To test the claim that the mean weight of tortilla chip bags from Factory A is the same as the mean weight from Factory B, we can conduct a two-sample t-test.

The null hypothesis, denoted as H0, assumes that the means are equal: μA = μB. The alternative hypothesis, denoted as Ha, assumes that the means are not equal: μA ≠ μB.

We calculate the test statistic, which follows a t-distribution under the null hypothesis, using the formula:

t = (xA - xB) / sqrt((sA^2 / nA) + (sB^2 / nB))

where xA and xB are the sample means, sA and sB are the sample standard deviations, and nA and nB are the sample sizes.

Plugging in the values:

t = (11.09 - 11.03) / sqrt((0.04^2 / 120) + (0.09^2 / 90))

Calculating this expression, we find the value of t. We then compare this value to the critical value of the t-distribution at a significance level of 0.05, with degrees of freedom equal to (nA - 1) + (nB - 1).

If the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean weight of tortilla chip bags from Factory A is different from the mean weight of bags from Factory B. Otherwise, if the calculated t-value falls within the critical region, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim of a difference in means.

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Since both sides are equal, we have shown that ∑(i=1 to 6) (dx_i + e) = d(∑\((i=1 to 6) x_i\)) + 6e. This represents the summation of the terms \((5x_3 + i)\) for i = 1 to 6.

To show that ∑(i=1 to 6) \((dx_i + e)\)= d(∑(i=1  \(x_i\)) + 6e, we can expand both sides and compare.

Left-hand side:

∑\((i=1 to 6) (dx_i + e) = (dx_1 + e) + (dx_2 + e) + (dx_3 + e) + (dx_4 + e) +\)(dx_5 + \(e) + (dx_6 + e)\)

                        = \(dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6 + e + e + e + e\)+ e + e

                        = \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6) + 6e\)

Right-hand side:

d(∑\((i=1 to 6) x_i)\)+ 6e = d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\)+ 6e

Now, let's compare the two sides:

Left-hand side: \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6)\) + 6e

Right-hand side: d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\) + 6e

Since both sides are equal, we have shown that ∑\((i=1 to 6) (dx_i + e)\) = d(∑(i=1 to 6)\(x_i)\) + 6e.

To represent the equation\((5x_3 + 4) + (5x_3 + 5) + (5x_3 + 6) + (5x_3 +\)7) + \((5x_3 + 8) + (5x_3 + 9)\) using a Sigma operator notation, we can write it as:

∑\((i=1 to 6) (5x_3 + i)\)

This represents the summation of the terms \((5x_3 + i)\)for i = 1 to 6.

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The angle of elevation from Michael to the kite is 40 degrees

We have six different trigonometric ratios, they are;

From the information given, we have that;

The opposite side of the angle = 56 feet(that is, the height of the kite)

The adjacent side of the angle = 68 feet(that is the distance)

Using the tangent identity states as;

tan θ = opposite/adjacent

substitute the values, we get;

tan θ = 56/68

divide the values

tan θ = 0. 8235

Find the inverse

θ = 40 degrees

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Answer:

D. 2/10, 3/10, 4/10

Step-by-step explanation:

D. is the correct answer because the fractions have a common denominator of 10, whereas the other answer choices do no.

D. has similar fractions

Good luck to you!

Answer: (3,3)

Step-by-step explanation:

Answer:

\(\dfrac{n^2 - 6}{n^2 - 2}\)

\( n \neq \pm \sqrt{5} \)

\( n \neq \pm \sqrt{2} \)

Step-by-step explanation:

\( \dfrac{n^4 - 11n^2 + 30}{n^4 - 7n^2 + 10} = \)

\( = \dfrac{(n^2 - 5)(n^2 - 6)}{(n^2 - 5)(n^2 - 2)} \)

\(= \dfrac{n^2 - 6}{n^2 - 2}\)

The factor of the denominator that was removed is n^2 - 5.

Restrictions:

\( n \neq \pm \sqrt{5} \)

From the factor remaining in the denominator, we get

\( n \neq \pm \sqrt{2} \)

Answer:

\(\dfrac{n^2 - 6}{n^2 - 2}\)

\( n \neq \pm \sqrt{5} \)

\( n \neq \pm \sqrt{2} \)

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

To determine the amount that 60% or more of all 1 bedroom apartments in Freeburg would rent for, we can use the concept of standard deviations.

Given that the average rent for a 1 bedroom apartment in Freeburg is $295 and the standard deviation is $25, we can determine the rent threshold for 60% or more of all apartments.

To find the threshold, we need to calculate the Z-score corresponding to the desired percentile. The Z-score measures how many standard deviations a data point is from the mean. The Z-score formula is given by (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

To find the Z-score for the 60th percentile, we look up the corresponding value in the Z-table. The Z-table provides the area under the normal distribution curve up to a certain Z-score. In this case, we want to find the Z-score that corresponds to an area of 0.60.

Assuming a normal distribution, a Z-score of approximately 0.253 corresponds to the 60th percentile.

Using the formula (Z-score * standard deviation) + mean, we can calculate the rent threshold: (0.253 * $25) + $295 = $301.325.

Therefore, 60% or more of all 1 bedroom apartments in Freeburg would rent for approximately $301.325 or higher.

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Answer:

2

Step-by-step explanation:

2−(x−10)=5x

Step 1: Simplify both sides of the equation.

2−(x−10)=5x

2+−1(x−10)=5x(Distribute the Negative Sign)

2+−1x+(−1)(−10)=5x

2+−x+10=5x

(−x)+(2+10)=5x(Combine Like Terms)

−x+12=5x

−x+12=5x

Step 2: Subtract 5x from both sides.

−x+12−5x=5x−5x

−6x+12=0

Step 3: Subtract 12 from both sides.

−6x+12−12=0−12

−6x=−12

Step 4: Divide both sides by -6.

−6x−6=−12−6

x=2

Answer:

x=2

Answer:

x = 2

Step-by-step explanation:

2-(x-10) = 5x

distribute the - into the  (  )

2 -x + 10 = 5x

combine like terms

12 - x = 5x

     +x    +x

12 = 6x

divide both sides by 6

x = 2

Hope this helps!!!