Ms. Smith can go 400 miles on 16 gallons of gas. In Consider the number of miles per gallon. Write an equation to represent the relationship.

Answer:

Let's first convert 1/6 mile into minutes by multiplying the distance by the number of minutes per mile:

1/6 mile * (1 minute/1/6 mile) = 6 minutes/mile

Next, let's convert the 7/9 minutes into miles:

7/9 minutes * (1/6 mile/minute) = 7/9 * 1/6 mile = 7/54 miles

Now that we have the distance and time in the same units, we can calculate Ed's speed as:

Speed = Distance / Time = 7/54 miles / 7/9 minutes = 7/54 miles / (7/9 * 1 minute) = 7/54 miles / (7/9) minutes = 7/54 miles / (7/9) = 54/7 miles/minute

So, Ed's speed is 54/7 miles per minute.

Step-by-step explanation:

If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.

Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.

Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).

For quaternion scalars and matrices:

λ = 2     A = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)

2A = 2\(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)

     = \(\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right]\)

     = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\) × 2 = A2

In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.

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For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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The reliability of the given system is 0.4033.

To calculate the reliability of a system, we need to multiply the reliability values of all the components in the system. In this case, we have a system composed of three components with the following reliability values:

Component 1: 0.90

Component 2: 0.90 0.90 0.85

Component 3: 0.85 0.85 0.92

To find the overall system reliability, we multiply these values together:

System reliability = Component 1 reliability x Component 2 reliability x Component 3 reliability

System reliability = 0.90 x (0.90 x 0.90 x 0.85) x (0.85 x 0.85 *x 0.92)

System reliability ≈ 0.90 x 0.6831 x 0.6528 ≈ 0.4033

Therefore, the reliability of the given system is 0.4033.

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The ratio 10 : 15 signifies that every 2 battleships are equivalently powerful as that of 3 destroyers.

Given is that the ratio of battleships to destroyers in the navy is 10 : 15.

It is given that the ratio of battleships to destroyers in the navy is 10 : 15.

We can write the ratio as fraction as follows -

x = 10/15

Further reducing -

x = 10/15 = (5 x 2)/(5 x 3) = 2/3

x = 2/3

This means that, for every 2 battleships, there are 3 destroyers.

Therefore, the ratio 10 : 15 signifies that for every 2 battleships, there are 3 destroyers.

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Both methods give similar intervals that do not overlap with 0.5, the expected proportion under the null hypothesis of no difference between green and white flowers, indicating a significant deviation from the null hypothesis.

To calculate a confidence interval for the proportion of pea plants with green flowers in Mendel's experiment, we can use the following methods:

Normal approximation method:

This method assumes that the distribution of the sample proportion is approximately normal when the sample size is large enough (n ≥ 30) and the proportion is not too close to 0 or 1.

The formula for the confidence interval is: \(\bar p+ za/2 \times \sqrt{(\bar p(1-\bar p/n)}\), where  is the sample proportion, zα/2 is the critical value from the standard normal distribution corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and n is the sample size.

Substituting the values from Mendel's experiment, we get: 0.249 ± 1.96 × √(0.249×0.751/8000) = (0.227, 0.271) at 95% confidence level.

Clopper-Pearson method:

This method provides a conservative confidence interval that guarantees the true proportion is within the interval with at least the desired level of confidence.

The formula for the confidence interval is: , where B is the inverse cumulative distribution function of the beta distribution with parameters \(n(1-\bar p)+1 and n\bar p+1\), and α is the significance level (e.g., 0.05 for 95% confidence).

Substituting the values from Mendel's experiment, we get: [0.232, 0.267] at 95% confidence level.

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Answer:34

Step-by-step explanation:r4rg

Answer:

The slope of the line with the given coordinates is OL 6 0 - 1 -6 6 6 is undefined. This is because the line is vertical. Vertical lines have an undefined slope.

Parallel lines have the same slope. Therefore, the slope of a line parallel to a vertical line is also undefined.

Let me know if this helps, or if it is wrong.

Step-by-step explanation:

To prove ABC = XYZ using AAS, two angles and one side of each triangle must be congruent. In addition to this, it is necessary to show that the included angle between these two sides is also congruent.

Therefore, the additional piece of information needed to show that ABC = XYZ by AAS is the information that the included angle between the congruent sides is congruent. This means that the angle formed by the two congruent sides of ABC is equal to the angle formed by the two congruent sides of XYZ. Once all three of these conditions are met, we can conclude that the two triangles are congruent by AAS. This is because AAS states that if two angles and one side of one triangle are congruent to the corresponding two angles and one side of another triangle, then the two triangles are congruent.

Therefore, the included angle must also be congruent to prove congruence by AAS.

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The tax rate given as a percentage, can be used to find out the amount

to be paid as tax.

Correct response:

The given parameters are;

Susan Wong's taxable income last year = $52,915

The income tax rate = 2%

Required:

Susan Wong's tax last year

Solution:

The tax rate is given as a percentage of the taxable income.

The amount payable as tax = The tax rate × The taxable income

Therefore;

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Answer:

Pick either point (-6, 24) or (7,-15) and plug the x and y values into the above equation along with the value of m to get b.

Step-by-step explanation:

Answer:

vertex = (- 1, - 7 )

Step-by-step explanation:

Given a parabola in standard form, f(x) = ax² + bx + c (a ≠ 0 )

Then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

f(x) = - x² - 2x - 8 ← is in standard form

with a = - 1 and b = - 2, then

\(x_{vertex}\) = - \(\frac{-2}{-2}\) = - 1

Substitute x = - 1 into f(x) for corresponding y- coordinate

f(- 1) = - (- 1)² - 2(- 1) - 8 = - 1 + 2 - 8 = - 7

vertex = (- 1, - 7 )

This form of the equation is useful because it shows that any periodic function of time can be represented as a sum of sine and cosine functions with different amplitudes and phases.

We can show that acos(wt) + bsin(wt) can be written in the form Rsin(wt + φ) where R and φ are constants and R is the amplitude of the wave.

Using the trigonometric identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b), we can write:

acos(wt) + bsin(wt) = R(sin(wt+φ)),

where R = √(a^2+b^2) and φ = tan⁻¹(b/a).

To see how this works, we can use the values of a = 3 and b = 4 as an example:

acos(wt) + bsin(wt) = 3cos(wt) + 4sin(wt)

R = √(a^2+b^2) = √(3^2 + 4^2) = 5

φ = tan⁻¹(b/a) = tan⁻¹(4/3)

So we can rewrite the equation as:

acos(wt) + bsin(wt) = 5sin(wt + tan⁻¹(4/3))

This form of the equation is useful because it shows that any periodic function of time can be represented as a sum of sine and cosine functions with different amplitudes and phases. It is also helpful in analyzing the properties of waves, such as their amplitude and frequency.

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This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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The function h(x) =  6x² - 60x + 147 is a quadratic function, and the axis of symmetry of the function is x = 5

The equation of the function is given as:

h(x) =  6x² - 60x + 147

Differentiate the function

h'(x) = 12x - 60

Set the function to 0

12x - 60 = 0

Add 60 to both sides

12x = 60

Divide both sides by 12

x = 5

Hence, the axis of symmetry of the function is x = 5

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Answer:

X = 5 is correct

Step-by-step explanation:

just took the test on edge and got 100%

The correct answer is C. (1, 5) is the ordered pair which is the solution to the system of equations.

A group of two or more equations with the same variables is referred to as a system of equations. The set of values for the variables that make all of the equations in a system of equations true is known as the solution.

The solution to the systems of equations is x = 1 and y = 5.

To solve this system of equations, we can begin by subtracting the two equations to get y - y = -x + 6 - (x + 4).

Simplifying, we get -2x = 2.

Then, dividing both sides of the equation by -2, we get x = -1.

We can now substitute the value of x into either one of the original equations to find the value of y.

If we substitute x = -1 into the first equation, we get y = -1 + 4, which simplifies to y = 3.

Therefore, the solution for this system of equations is x = -1 and y = 3.

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Answer:

C

Step-by-step explanation:

the angle in a semicircle = 90° , that is the 3rd angle in the triangle.

the sum of the 3 angles in a triangle = 180° , then

p + 90° + 42° = 180°

p + 132° = 180° ( subtract 142° from both sides )

p = 48°

Answer:

d. 2x³y + 12x²y² + 18xy³

Step-by-step explanation:

Volume = l x b x h

= 2xy × x + 3y × x + 3y

= 2xy × (x + 3y)²

= 2xy × (x² + 6xy + 9y²)

= 2x³y + 12x²y² + 18xy³

Answer:

136 miles

Step-by-step explanation:

subtract $119.59 with how much he rented the truck for, which is $18.95 which makes his money at $100.64, then divide by how much each mile costed which was 74 cents

which gives you 136 so 136 miles.

Hope this helps :)

To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

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Answer:

the answer is d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Root 2 is irrational due to a very complicated theory and proof.

Proof : Let us assume that √2 is a rational number. So it can be expressed in the form p/q where p, q are co-prime integers and q≠0. √2 = p/q. ...

Solving. √2 = p/q. On squaring both the sides we get, =>2 = (p/q)2

It isn't an integer, whole number, or rational number because root 2 doesn't fit into the definitions. The answer is D.

Additional information:

Integer : An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Rational: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.

Whole number: Whole numbers are a set of numbers including all positive integers and 0. Whole numbers are a part of real numbers that do not include fractions, decimals, or negative numbers.

Hope this helps :)

Have a spectacular day!

See attached

(If this is incorrect, please add in parentheses so I can make sure I have the order correct. Thank you.)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

3)6 , 4)5 , 5)11 , 6)5 , 7)-14 , 8)8

Step-by-step explanation:

With a sample size of 10 and a population variance of 4,

a) To calculate the probability that the variance of a random sample exceeds a certain value, you can use the chi-square distribution.

In this case, with a sample size of 10 and a population variance of 4, you can calculate the probability using the cumulative distribution function (CDF) of the chi-square distribution with degrees of freedom equal to 10 minus 1. Here's an example of the code you can use in R:

```

# Set the parameters

sample_size <- 10

population_variance <- 4

test_value <- 6.526

# Calculate the probability

probability <- 1 - pchisq(test_value, df = sample_size - 1)

# Print the result

probability

```

b) To find the probability P(Z < 2) for two independent random samples with different sizes, you can use the standard normal distribution. The probability P(Z < 2) can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. Here's an example of the code in R:

```

# Set the parameter

z_value <- 2

# Calculate the probability

probability <- pnorm(z_value)

# Print the result

probability

```

By running these code snippets in R, you should obtain the desired probabilities for each scenario.

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The coordinate of point G after a rotation of 180° is (4,2).

The complete question is added as an attachment

Rotation is a given a rigid motion or transformation which refers to movement of a figure around a center of rotation.

In this question it is asked to find the coordinates of the new vertices after the 180 degrees rotation, which is define or represented by the rule:

(x, y) = (-x, -y)

From the figure, we have

G = (4,2)

So, we have

G' = (-4,-2)

Hence, the image is (-4,-2)

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Answer:

D. G'(4,2)

Step-by-step explanation:

The probability that at least two of the balls have the same number is 27.40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes

No. of ways to succeed = 90P8

No. of possible outcomes = 90^8

No. of ways to succeed =

nPr = n! / (n-r)!

90P8 = 90! / (90-8)!

90P8 = 90! / (82)!

90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!

90P8 = 90*89*88*87*86*85*84*83

90P8 = 3.13x10^15

P(no 2 have same number) = 3.13x10^15 / 90^8

P(no 2 have same number) = 0.73

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(at least 2 have same number) = 1 - 0.73

P(at least 2 have same number) = 0.2740 = 27.40%

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The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed in a mathematical expression. An order of operations worksheet is a practice tool for students to test their understanding of the order of operations, and helps them develop their ability to solve mathematical expressions accurately and consistently.

Order of operations ensures that mathematical expressions are solved consistently and accurately. It typically consists of a series of mathematical expressions that the student must solve, following the order of operations. The order of operations is often remembered by the acronym "PEMDAS", which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). The main purpose of an order of operations worksheet is to help students develop their understanding of the order of operations, so they can solve mathematical expressions accurately and consistently.

It's important to note that the order of operations is a fundamental concept in mathematics and is used in many other areas of mathematics, including algebra and calculus. Therefore, it's crucial that students master the order of operations early on in their mathematical studies. An order of operations worksheet can be a valuable tool for helping students do just that.

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