a ratio of the vertical change to the horizontal change of two points is called:_____.

The measure of angle CEB is 50 degrees

The given parameters are:

Start by calculating the measure of angle EAB.

\(\angle EAB = 90 - \angle DAE\) --- angles at a right-angle

So, we have:

\(\angle EAB = 90 - 65\)

\(\angle EAB = 25\)

The measure of angle CEB is then calculated using:

\(\angle CEB = 2 \times \angle EAB \)

Substitute \(\angle EAB = 25\)

\(\angle CEB = 2 \times 25\)

\(\angle CEB = 50\)

Hence, the measure of angle CEB is 50 degrees

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The exact surface area of the cone having height 3 unit and radius 4 unit,  113.09734 unit²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Given that,

A Cone having,

Radius  r = 4 unit

Height  h = 3 unit

Surface Area = ?

Formula for the Cone,

Surface Area of Cone = πrl  + πr²

where, l = \(\sqrt{h^{2}+r^{2} }\)

Surface Area of Cone = πr(\(\sqrt{h^{2}+r^{2} }\)) + πr²

                                     =  πr(\(\sqrt{h^{2}+r^{2} }\)  + r)

                                     =  4π(\(\sqrt{3^{2}+4^{2} }\)  + 4)

                                     =  4π(5 + 4)

                                     =   20π

                                     ≈   113.09734

Thus, the surface area of cone is  113.09734 unit²

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Answer:

x=4y+3

Step-by-step explanation:

I don't know if this is right or not.  Please tell me if it is.

The equation of the tangent line to the graph of the function f(x)=x 1x−4 at the point (0,−14) is 4x + y +14 = 0.

To find the tangent equation we need slope and intercept for the equation.

To find slope we need to differentiate the given function as the differentiation at a given point gives us the slope :

firstly differentiate the given function :

    f(x)=x(x−4)

         = x^2 - 4x

f'(x) = 2x - 4

f'(x) at (0,-14) = 2(0) - 4  

                     = -4

Hence , the slope is -4

Use the formula to find the equation of the tangent line that passes through a point (x1, y1) with the slope m, that is, y-y1=m(x-x1).

y-y1=m(x-x1) at a point (0,−14)

y - (-14) = -4 (x-0)

y+14 = -4x

therefore, 4x + y +14 = 0 is the required equation of the tangent.

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Answer:

9.2

Step-by-step explanation:

The possible terms of trade any value between 2 tons and 3 tons of tin per 1 ton of copper.

A both countries to gain from trade, the terms of trade should fall between the opportunity costs of the two countries. Based on the information given:

Opportunity cost of 1 ton of copper in the United States = 2 tons of tin

Opportunity cost of 1 ton of copper in Mexico = 3 tons of tin

To find a possible range for the terms of trade, the range between the two opportunity costs. The terms of trade should be more favourable to the country with the higher opportunity cost (Mexico in this case) to incentivize trade.

Possible terms of trade:

Between 2 tons and 3 tons of tin per 1 ton of copper

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Step-by-step explanation:

When you multiply or divide both sides of an inequality by a negative, you swap the inequality. You had less than or equal? Now it'll be greater than or equal.

Answer:

flip the sign

Step-by-step explanation:

You just flip the sign...

for example: \(-x < 2\implies x > -2\)

But why is this happening? So let's just analyze the initial inequality we started with: \(-x < 2\)

As you can see here, the x values are negated, or in other words they become negative. So even though -5 is less than 2, it becomes -(-5) which cancels the negative and it becomes 5, this of course makes the inequality false.

The opposite occurs with positive values, the positive value becomes negative, thus any positive value will satisfy this inequality, since it becomes a negative number.

For example 10 is not less than 2, but the negative sign will make it -10, thus making the inequality true.

Even though negative values will cancel out, there are still some negative values that satisfy this equation. Since -1 becomes 1, it satisfies this equation, but once it becomes less than or equal to -2, it becomes false. This is because it becomes a positive value. Thus the equation really just means x must be greater than -2.

I could've used something more abstract, but I wanted to give a specific example so it might be a bit easier to understand.

Answer: the 4

Step-by-step explanation:

Answer: Its B

Step-by-step explanation:

T he value of g(x) of the given g'(x) = (30x² - 40x) × \(7^{(2x^{3} - 4x^{2} )\) with initial condition g(0) = 5 using integrals  is equal to  5 × (\(7^{(2x^{3} - 4x^{2} )\) / ln(7)).

To find g(x), integrate g'(x) with respect to x and apply the initial condition g(0) = 5.

g'(x) = (30x² - 40x) × \(7^{(2x^{3} - 4x^{2} )\)

Integrating g'(x) with respect to x,

∫ g'(x) dx = ∫ [(30x² - 40x) × \(7^{(2x^{3} - 4x^{2} )\)] dx

To integrate this expression,

Use u-substitution.

Let u = 2x³ - 4x². Therefore, du/dx = 6x² - 8x, and rearranging, we have dx = du / (6x² - 8x).

Substituting u and dx into the integral,

∫ [(30x² - 40x) × \(7^{(2x^{3} - 4x^{2} )\)] dx

= ∫ [(30x² - 40x) × \(7^u\)] (du / (6x² - 8x))

Now split the integrand into two separate fractions,

∫ [(30x² - 40x) × \(7^u\)] (du / (6x² - 8x)) = ∫ [30x² × \(7^u\) / (6x² - 8x)] du - ∫ [40x × \(7^u\) / (6x² - 8x)] du

Simplifying the integrals, we have,

∫ [30x² × \(7^u\) / (6x² - 8x)] du = 5∫ \(7^u\) du

∫ [40x × \(7^u\) / (6x² - 8x)] du = -5∫ \(7^u\) du

Integrating \(7^u\) with respect to u, we get,

5∫ \(7^u\) du = 5 × (\(7^u\) / ln(7)) + C1

-5∫ \(7^u\) du = -5 × (\(7^u\) / ln(7)) + C2

where C1 and C2 are constants of integration.

Now, let's substitute back u = 2x³ - 4x²,

g(x) = 5 × (\(7^{(2x^{3} - 4x^{2} )\) / ln(7)) + C1 - 5 × (\(7^{(2x^{3} - 4x^{2} )\) / ln(7)) + C2

Simplifying further,

g(x) = 5 ×(\(7^{(2x^{3} - 4x^{2} )\) / ln(7)) - 5 × (\(7^{(2x^{3} - 4x^{2} )\) / ln(7)) + C

Since the initial condition g(0) = 5, substitute x = 0 and solve for C,

5 = 5 × (\(7^{(2(0)^{3}\) - 4(0)²) / ln(7)) - 5 × (\(7^{(2(0)^{3}\)- 4(0)²) / ln(7)) + C

⇒5 = 5 × (7⁰ / ln(7)) - 5 × (7⁰ / ln(7)) + C

⇒5 = 5/ln(7) - 5/ln(7) + C

⇒5 = C

Substituting C back into the equation,

g(x) = 5 × (\(7^{(2x^{3} - 4x^{2} )\)/ ln(7)) - 5 × (\(7^{(2x^{3} - 4x^{2} )\) / ln(7)) + 5

Simplifying further,

g(x) = 5 ×(\(7^{(2x^{3} - 4x^{2} )\)/ ln(7))

Therefore, using integrals the value of g(x)  = 5 × (\(7^{(2x^{3} - 4x^{2} )\) / ln(7)).

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The above question is incomplete, the complete question is:

Find  g(x) if g'(x) = (30x² - 40x ) × 7^(2x³ -4x²) and g(0) = 5. g(x) = ___.

The experimental probability of not spinning a 5 from the given bar chart above would be = 0.19

To calculate the probability, the formula that should be used would be given below as follows:

Probability = possible outcome/sample space

where:

possible outcome= 19

Sample space= 20+18+22+21+19 = 100

The probability= 19/100 = 0.19

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It will take Isabella 12 days to sell 96 hats at her store.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To solve this problem, we need to determine the rate at which Isabella sells hats.

Since she sells 24 hats every 3 days, we can say that her rate is 8 hats per day.

To find the number of days it will take Isabella to sell 96 hats, we can divide the number of hats she needs to sell by her rate.

This gives us:

96 hats / 8 hats/day =  12 days

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Answer:

38

Step-by-step explanation:

:) hope this helps

To communicate information about the public in broadly understandable terms, researchers and pollsters often rely on aggregated statistical data. By compiling and analyzing large sets of information, they can identify patterns and trends that can be presented in a way that is easy for people to understand.

For example, they may use graphs, charts, or other visual aids to convey complex information in a clear and concise manner. This can be particularly important when trying to share findings with the general public or with policymakers who may not have a background in statistics or research methodology. By using aggregated statistical data, researchers and pollsters can help ensure that important information is communicated effectively and accurately.

This allows them to present complex information in a more accessible and easily digestible format for a wider audience.

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As described in number system the of positive integers is 13

what is number system ?

A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or other symbols to represent the numbers in a given set in a standardised way. In different numeral systems, the same set of symbols may represent various numbers.

Solution:

we want the integers b such that

2013 = 3 ( modb)

=> b is a factor of 2010

since 2010 has 2 * 3 * 5* 67 it has

(1+1)(1+1)(1+1)(1+1) = 16 factors

since b cannot equal to 1, 2, or 3, as these cannot have 3 in there base representation, our answer is 16 - 3 =13.

therefore the number of positive integers is 13

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a) The scale factor of the enlargement from shape P to shape Q is 3.

b) The scale factor of the enlargement from shape R to shape T is 2.

In Mathematics and Geometry, the scale factor of a geometric figure such as a star can be calculated by dividing the dimension of the image by the dimension of the pre-image:

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

Part a.

By substituting the given dimensions into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

Scale factor P to Q = 6/2

Scale factor P to Q = 3.

Part b.

Scale factor = Dimension of image/Dimension of pre-image

Scale factor R to T = 4/2

Scale factor R to T = 2.

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The parametric equations for the position of a plane rising 6 feet for every 35 feet it travels horizontally, with a speed of 336 feet per second, starting at a height of 280 feet above the ground and at a horizontal distance of 0, are x(t) = 35t and y(t) = 6t + 280 - (336/35)t^2.

The plane's motion can be described by the horizontal distance it travels and the height it reaches at any given time t. Let's set the horizontal distance at t=0 to be 0, so the horizontal distance at any time t is simply the product of the plane's speed and time, i.e., x(t) = 336t/1.

To find the height at any given time t, we need to consider the vertical motion of the plane. We know that the plane rises 6 feet for every 35 feet it travels horizontally, which means the vertical distance the plane travels is proportional to the horizontal distance it travels. Therefore, the vertical distance y(t) is given by y(t) = (6/35)x(t) + 280, where the constant 280 represents the initial height of the plane.

However, we also need to take into account the effect of gravity on the plane's motion. Since the plane is traveling in the direction of its velocity, the effect of gravity will cause the plane to slow down. The distance the plane falls due to gravity is given by (1/2)gt^2, where g is the acceleration due to gravity (approximately 32 feet per second squared). Since the plane is traveling in the direction of its velocity, the effect of gravity will reduce the height of the plane at a rate proportional to the square of the time t. Therefore, the final parametric equations for the position of the plane are x(t) = 35t and y(t) = 6t + 280 - (336/35)t^2, where the last term represents the effect of gravity on the height of the plane. These equations describe the position of the plane at any given time t, starting at a horizontal distance of 0 and a height of 280 feet above the ground.

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The approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.

To calculate the approximate enthalpy change, δhrxn, for the combustion of methane, we can use Hess's Law and the enthalpies of formation.

The balanced equation for the combustion of methane is:

CH4 + 2O2 → CO2 + 2H2O

To calculate the enthalpy change, we need to find the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

The enthalpy of formation for methane (CH4) is -74.81 kJ/mol. The enthalpy of formation for carbon dioxide (CO2) is -393.5 kJ/mol, and the enthalpy of formation for water (H2O) is -285.8 kJ/mol.

Using these values, we can calculate the enthalpy change:

ΔHrxn = (2 * -393.5 kJ/mol) + (2 * -285.8 kJ/mol) - (-74.81 kJ/mol)

     = -787 kJ/mol - 571.6 kJ/mol + 74.81 kJ/mol

     = -1283.79 kJ/mol

Therefore, the approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.Please note that the values used for enthalpies of formation are approximate and may vary slightly depending on the source. Additionally, this calculation assumes standard conditions.

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Answer:

A. The Pythagorean Theorem can be used  to determine the side lengths of any right  triangle

Step-by-step explanation:

The Pythagorean Theorem is supposed to be used to identify the SIDE lengths of ANY RIGHT TRIANGLE.

I also had this question today as well, and I got it correct :)

The statement i.e. true about the Pythagorean Theorem is option A.

A. The Pythagorean Theorem can be used  to determine the side lengths of any right  triangle

The following information should be considered;

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Answer

Option 1 is correct.

The graph could easily be the graph of a linear function.

Explanation

The points (2, 5) and (8, 5) can be seen to lie on the same line of y = 5

So, we can conclude that the graph could be a simple linear function, or a curve that passes this point twice.

So, option A is the only correct option here.

Hope this Helps!!!

Answer: 1 / 8806

Step-by-step explanation: not no noticeable way of it being a mixed number.

The student answered 21 questions correctly on a test.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Since the student made an 85% on a test with 25 questions.

To determine the number of questions the student answered correctly, we need to multiply the number of questions by the percentage of questions answered correctly, which is 85%.

= 25 questions × 0.85

Apply the multiplication operation, and we get

= 21.25

Rounding to the nearest whole number,

= 21 questions

Thus, the student answered 21 questions correctly.

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The value of "a" that makes the matrix not invertible is a = 1. For any other value of "a", the matrix is invertible.

To determine the values of "a" that make the given matrix not invertible, we can perform row reduction on the matrix and examine the resulting row-echelon form or reduced row-echelon form.

Specifically, we are looking for cases where the matrix contains a row of zeros or has a row where all entries are zero.

Let's denote the provided matrix as A:

A = [a, 1, 1; 1, a, 1; 1, 1, a]

To perform row reduction, we can use elementary row operations to transform the matrix into row-echelon form or reduced row-echelon form.

Let's start with row reduction:

1. Swap rows R1 and R2 (if necessary) to make the first entry in the first column non-zero:

  R1 <-> R2 (only necessary if a = 1)

2. Subtract R1 from R2 and R3:

  R2 - R1 -> R2

  R3 - R1 -> R3

The resulting matrix after these operations is:

[1, a, 1; 0, a - 1, 0; 0, 0, a - 1]

Now, let's analyze the possible values of "a" based on this row-echelon form:

1. Case 1: If a - 1 = 0, then a = 1:

  In this case, the matrix becomes:

  [1, 1, 1; 0, 0, 0; 0, 0, 0]

  We have a row of zeros, and the matrix is not invertible.

2. Case 2: If a - 1 ≠ 0, then a ≠ 1:

  In this case, the matrix becomes:

  [1, a, 1; 0, a - 1, 0; 0, 0, a - 1]

  We do not have any rows of zeros, and the matrix is invertible.

Hence we can conclude that:

- If a = 1, the matrix is not invertible.

- For any other value of "a", the matrix is invertible.

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Answer:

z/5 = 6

z=30

Step-by-step explanation:

you need 6 so 30 divided by 5 equals 6 so 6-7=-1

(a) Daniel is charged $900 in interest for the 2-year loan

(b) David must repay a total of $5900 to the bank over the 2-year period.

(a) To calculate the interest charged on the loan, we can use the simple interest formula:

I = P * r * t

where I is the interest charged, P is the principal amount (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.

In this case, P = 5000, r = 0.09 (since the annual interest rate is 9%), and t = 2 (since the loan is for 2 years). Plugging these values into the formula, we get:

I = 5000 * 0.09 * 2

I = 900

Therefore, David is being charged an interest amount of $900 for the loan that he borrowed for a period of 2 years.

(b) To calculate the total amount that David must repay to the bank, we need to add the interest charged to the principal amount:

Total amount = Principal + Interest

Total amount = 5000 + 900

Total amount = 5900

Therefore, over the 2-year period, David needs to return a total amount of $5900 to the bank, which includes the principal amount that he borrowed and the interest charged on it.

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A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.

α = 0.05

μ = 2

If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.

This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.

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Answer:

D.  45/8

Step-by-step explanation:

The value of function g (7) is,

⇒ g(7) = 45/8

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Function is,

⇒ g(x) = 7/8x - 1/2

Now, Plug x = 7 in above equation,

⇒ g(x) = 7/8x - 1/2

⇒ g(7) = 7/8 (7) - 1/2

⇒ g(7) = 49/8 - 1/2

⇒ g(7) = 49/8 - 4/8

⇒ g(7) = 45/8

Thus, The value of function g (7) is,

⇒ g(7) = 45/8

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This statement best illustrates money used as a medium of exchange. In this scenario, the individual goes to the store and exchanges $68 for a pair of jeans. Money serves as a medium of exchange when it is used to facilitate transactions between buyers and sellers. In this case, the buyer wants a pair of jeans, and the seller wants to sell them for $68. Without money, they would have to engage in bartering, which can be cumbersome and inefficient. Money makes the transaction smoother and allows both parties to get what they want. Overall, this example demonstrates how money is an essential tool for facilitating transactions in our modern economy.
Hi! Your question is about the function of money as illustrated by the example of paying $68 for a pair of jeans. This statement best illustrates money used as a medium of exchange.

In this scenario, money is being used as a medium of exchange because it is facilitating the transaction between you and the store. Instead of using barter or trading goods and services directly, you use money to acquire the pair of jeans. This makes transactions more efficient and convenient since it eliminates the need for a double coincidence of wants, which is when two parties each have something the other wants. As a medium of exchange, money serves as a universally accepted means to buy and sell goods and services, like your jeans purchase at the store.

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If on  Monday Tom work for 11 extra hours the total amount of money that tom made on Monday is £885.

As per the given data, the extra money he earns can be calculated as,

= [(11 - 7) × 15] × 13 + (7 × 15)]

= (4 × 15 × 13) + 105

= 780 + 105

= £885

Therefore, the amount of money  is £885.

Time and work are concerned with how long it takes a person or a group of people to finish a task and how well each of them completes it.

Indirect proportion is related to time and work. In both directions, when one quantity rises, the other falls, and vice versa. It takes less time to finish the same amount of work when people work more hours.

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