write the slope intercept form of the equation of the line through the given points with given slope

Word form One hundred three and five hundred three thouandth

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Answer:

$1,038

Step-by-step explanation:

the equation for annual compound interest is y=p(1±r)^t, where p is the principal (starting amount), r is the rate (as a decimal), and t is the number of years (time).

2.5% as a decimal is 0.025

We will add that to 1, because when we earn interest, we are gaining money.

So we will substitute our given numbers into the equation:

y=6500(1.025)^6

solve:

y=$7,5638 (rounded)

That's the total amount he earned (principal + interest). To find out how much interest he earned over those 6 years, subtract our new amount from our starting amount

75638-6500

$1,038

So he made $1,038 in interest

Answer:

-2x-10y-8

Step-by-step explanation:

Rearange terms

-2(x+4+5y)

-2(x+5y+4)

Distribute

Johnny can improve his meal in 6 different ways by choosing two condiments from his four options. Some examples of the different combinations include ketchup and salt, ketchup and pepper, salt and pepper, and so on.

To determine the number of different ways Johnny can improve his meal using condiments, we can use the concept of combinations.

Since Johnny can only make two additions to his meal, we need to find the number of combinations of condiments he can choose from his four options: ketchup, salt, pepper, and shredded cheese.

To calculate the number of combinations, we can use the formula for combinations:
nCr = n! / (r! * (n - r)!)

Where n represents the total number of items and r represents the number of items to be chosen.

In this case, n is 4 (since Johnny has four condiment options) and r is 2 (since Johnny can only make two additions).

Plugging these values into the formula, we get:

4C2 = 4! / (2! * (4 - 2)!)

Simplifying this expression:

4C2 = 4! / (2! * 2!)

The exclamation mark (!) represents the factorial operation, which means multiplying a number by all positive integers less than itself down to 1.

Calculating the factorials:
4! = 4 * 3 * 2 * 1 = 24
2! = 2 * 1 = 2

Substituting these values back into the equation:
4C2 = 24 / (2 * 2)

Simplifying further:
4C2 = 24 / 4

Finally, dividing:
4C2 = 6

Therefore, Johnny can improve his meal in 6 different ways by choosing two condiments from his four options. Some examples of the different combinations include ketchup and salt, ketchup and pepper, salt and pepper, and so on.

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Answer:

Cost of staying hotel with fixed charge of 50 and $6 for each day stay

where d is number of days of stay

M is total money charged by hotel.

Step-by-step explanation:

We have to describe a situation to fit into the given model.

model is M = 50 + 6d

it consist of two part

constant part 50

and variable part 6d which depends on value of d,

Let take M as money

d as days

in hotel,  hotel service charge is fixed at 50

and for each day stay 6$ is charged.

Thus,

total money charged by hotel will be equal to sum of

fixed part 50

$6d for staying d days in the hotel

which can be modeled by given equation

M = 50 + 6d

Answer:

0, 8/5

Step-by-step explanation:

You can use the app photo math you just take a picture of the problem and it gives you the answer and shows the steps:)

Answer:

I think it is 96KM.

Step-by-step explanation:

2cm is 24KM, so

8 divided by 2 equals 4, so

24 times 4 is 96KM.

Answer:

1/2 x base x height

Step-by-step explanation:

hope this helps!

The required return for a stock with a beta of 2.20, a risk-free rate of 2%, and a market risk premium of 6% is 14.39%.  The correct option is c.

To calculate the required return, we can use the Capital Asset Pricing Model (CAPM), which relates the expected return of a stock to its beta, the risk-free rate, and the market risk premium. The formula for CAPM is as follows:

Required Return = Risk-Free Rate + (Beta × Market Risk Premium)

In this case, the risk-free rate is 2% and the market risk premium is 6%. The beta of the stock is given as 2.20. Plugging these values into the formula, we get:

Required Return = 2% + (2.20 × 6%) = 2% + 13.2% = 15.2%

Therefore, the correct answer is option C: 14.39%.

The CAPM is a widely used model in finance to estimate the required return on an investment. It takes into account the risk-free rate, which represents the return on a risk-free investment such as government bonds, and the market risk premium, which represents the additional return investors expect to receive for taking on the risk of investing in the overall market.

The beta of a stock measures its sensitivity to market movements, and multiplying it by the market risk premium gives us an estimate of the stock's additional required return. By summing this additional return with the risk-free rate, we obtain the required return for the stock.

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Check the picture below.

\(\cfrac{x}{10}=\cfrac{24.5}{14}\implies x=\cfrac{(10)(24.5)}{14}\implies x=\cfrac{245}{14}\implies x=17.5\)

The volume of the triangular prism is  270m³

The formula for the volume of a triangular prism is expressed with the equation;

V= 1/2 bhl

Given that the parameters are;

Now, substitute the values

Volume, V = 1/2 × 10 × 9 × 6

Multiply the values, we get;

Volume = 1/2 × 540

Divide the values

Volume = 270m³

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The number of spanning trees of a connected graph can be proven to be the product of the number of spanning trees of each of its blocks.

Here are the steps-

1. Consider a connected graph G with blocks B1, B2, ..., Bk. Each block is a maximal connected subgraph with no cut-vertex.

2. The number of spanning trees of G can be denoted as T(G), and the number of spanning trees of each block Bi can be denoted as T(Bi).

3. To prove the given statement, we need to show that\(T(G) = T(B1) * T(B2) * ... * T(Bk).\)

4. We can start by considering a single block B1. Since B1 is a maximal connected subgraph with no cut-vertex, it is a connected graph on its own.

5. The number of spanning trees of B1, T(B1), can be calculated using any method such as Kirchhoff's theorem or counting the number of spanning trees directly.

6. Now, consider the original graph G. We can remove block B1 from G, which leaves us with a graph G' that consists of the remaining blocks B2, B3, ..., Bk.

7. G' is still a connected graph, but it may have cut-vertices. However, the removal of B1 does not affect the connectivity between the other blocks, as each block is a maximal connected subgraph.

8. The number of spanning trees of G', denoted as T(G'), can be calculated using the same method as step 5.

9. Since G' is the remaining part of G after removing B1, the number of spanning trees of G can be expressed as T(G) = T(B1) * T(G').

10. We can repeat this process for the remaining blocks B2, B3, ..., Bk. For each block Bi, we remove it from G and calculate the number of spanning trees of the remaining graph.

11. By repeating steps 6-10 for all blocks, we can express the number of spanning trees of G as-

\(T(G) = T(B1) * T(G')\)

\(= T(B1) * T(B2) * T(G'')\)

= ...

\(= T(B1) * T(B2) * ... * T(Bk).\)

12. Therefore, we have proved that the number of spanning trees of a connected graph G is the product of the number of spanning trees of each of its blocks.

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Answer:

hope this helped

Step-by-step explanation:

y = mx + b

b, the y-intercept, = 3 because when x is 0, y is 3

find m, slope:

(0,3) (2,2)

2 - 3/2 - 0

-1/2

-0.5 or -/2

y = -1/2x + 3

or

y = -0.5x + 3

Answer:

4 over 1 is the slope. of this table

Answer:

4

Step-by-step explanation:

m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

(0, 6)

(- 1, 2)

m = \(\frac{2-6}{-1-0}\) = 4

y = 4x + 6

The set A {a,b,c}  that is neither symmetric nor antisymmetric is option D)  {(a, b), (b, a),(a, c)} on {a,b,c}

We are looking for a relation on the set A that is neither symmetric nor antisymmetric. Here are the given options:
A. the empty set on {a, b, c}
B. {(a, b), (b, a), (a, a), (a, a)} on {a, b, c}
C. {(a, b), (b, a)} on {a, b, c}
D. {(a, b), (b, a), (a, c)} on {a, b, c}

A relation R on set A is symmetric if for all (x, y) in R, (y, x) is also in R. It is antisymmetric if for all (x, y) in R, (y, x) in R implies x = y.

Let's examine each option:

A. The empty set has no elements(null set), so it is both symmetric and antisymmetric, which does not satisfy the required condition.

B. {(a, b), (b, a), (a, a), (a, a)}: Since (a, b) and (b, a) are in the relation, it is symmetric.

However, (a, a) makes it not antisymmetric, as (a, a) does not imply a = b.

Thus, this option is symmetric and does not satisfy the condition.

C. {(a, b), (b, a)}: This relation is symmetric since (a, b) and (b, a) are both in the relation, but it is not antisymmetric. Therefore, this option does not satisfy the condition.

D. {(a, b), (b, a), (a, c)}: This relation is neither symmetric nor antisymmetric. It is not symmetric because (a, c) is in the relation but (c, a) is not.

It is not antisymmetric because (a, b) and (b, a) are both in the relation but a ≠ b. Thus, this option satisfies the required condition.

Hence the relation on the set A that is neither symmetric nor antisymmetric is D. {(a, b), (b, a), (a, c)} on {a, b, c}.

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Answer:

it depends on whether the outlier is a high outlier or a low outlier

Step-by-step explanation:

The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier

Answer:

y=-7/9x+8/9

Step-by-step explanation:

Answer:

y=7/9x+64/9

Step-by-step explanation:

4+3/-4-5=7/9

y-4=7/9x+28/9

y=7/9x+64/9

x = 5√3 + (-5)t

y = 5 + 5√3t

z = 4 + (-2√3)t

These are the parametric equations for the tangent line to the curve at the point (5√3, 5, 4).

To find the parametric equations for the tangent line to the curve at the specified point, we need to determine the derivatives of the given parametric equations and evaluate them at the point of interest. Then, we can use this information to write the equation of the tangent line.

Let's start by finding the derivatives of the given parametric equations:

dx/dt = -10 sin(t)

dy/dt = 10 cos(t)

dz/dt = -4 sin(2t)

Next, we need to determine the value of the parameter t that corresponds to the point of interest (5√3, 5, 4). We can do this by solving the equations for x, y, and z in terms of t:

10 cos(t) = 5√3

10 sin(t) = 5

2 cos(2t) = 4

Dividing the second equation by the first equation, we get:

tan(t) = 5/5√3 = 1/√3

Since the value of t lies in the first quadrant (x and y are positive), we can determine that t = π/6 (30 degrees).

Now, let's evaluate the derivatives at t = π/6:

dx/dt = -10 sin(π/6) = -10(1/2) = -5

dy/dt = 10 cos(π/6) = 10(√3/2) = 5√3

dz/dt = -4 sin(2π/6) = -4 sin(π/3) = -4(√3/2) = -2√3

So, the direction vector of the tangent line is given by (dx/dt, dy/dt, dz/dt) = (-5, 5√3, -2√3).

Finally, we can write the equation of the tangent line using the point of interest and the direction vector:

x = 5√3 + (-5)t

y = 5 + 5√3t

z = 4 + (-2√3)t

These are the parametric equations for the tangent line to the curve at the point (5√3, 5, 4).

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Answer:

13) cos D = 0.4706

14) cos G = 0.28

15) cos M = 0.6667

Step-by-step explanation:

13) Cos D = 8/17 = 0.4706

14) GI² = 7² + 24²

GI² = 49 + 576 = 625

GI = 25

cos G = 7/25 = 0.28

15) MN² = 3²- (√5)²

MN² = 9 - 5 = 4

MN = 2

cos M = 2/3 = 0.6667

Answer:



These are the inequalities

A: \(W\geq -7\)

B: \(W > -7\)

C: \(W < -7\)

D: \(W\leq -7\)

I assume the "different" one is referring to the wording of the expression. B, C, and D are all similarly worded so I believe A is the "different" one.

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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When 9.40 grams of chromium (III) oxide and 4.25 grams of Si are combined and react together, the chromium (III) oxide (Cr₂O₃) is reduced to form chromium metal (Cr) while the silicon (Si) is oxidized to form silicon dioxide (SiO₂).

The balanced chemical equation for the reaction can be written as:2 Cr₂O₃ + 3 Si ⟶ 4 Cr + 3 SiO₂

The equation above shows that two moles of chromium (III) oxide react with three moles of silicon to form four moles of chromium metal and three moles of silicon dioxide. We can use this stoichiometric ratio to find the mass of chromium metal produced from the given mass of chromium (III) oxide and silicon.

1. Calculate the moles of each reactant. The molar mass of Cr₂O₃ is 152.0 g/mol.

Therefore, the number of moles of chromium (III) oxide (Cr₂O₃) is: 9.40 g ÷ 152.0 g/mol = 0.0618 mol

The molar mass of Si is 28.09 g/mol.

Therefore, the number of moles of silicon (Si) is: 4.25 g ÷ 28.09 g/mol = 0.1515 mol

2. Use the stoichiometry of the balanced chemical equation to find the number of moles of chromium metal formed from the given amount of chromium (III) oxide and silicon.

In the balanced chemical equation above, two moles of Cr₂O₃ react to produce four moles of Cr.

Therefore, the number of moles of Cr produced from 0.0618 moles of Cr₂O₃ is:

0.0618 mol × 4 mol/2 mol = 0.1236 mol

In the balanced chemical equation above, three moles of Si react to produce four moles of Cr.

Therefore, the number of moles of Cr produced from 0.1515 moles of Si is:

0.1515 mol × 4 mol/3 mol

= 0.2020 mol3.

Calculate the mass of chromium metal produced from the number of moles found above.

The molar mass of chromium (Cr) is 52.0 g/mol. Therefore, the mass of chromium metal produced is:

0.1236 mol + 0.2020 mol = 0.3256 mol

52.0 g/mol × 0.3256 mol = 16.94 g

Hence, 16.94 g of chromium metal is produced from the given mass of chromium (III) oxide and silicon.

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The digit in the hundreds place is 4

From the question, we have

(21 × 10¹)+(3×10²) + (9 × 10²)

=210+300+900

=1410

The digit in the hundreds place is 4 and the value is 400.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

x=5

y=-5

Step-by-step explanation:

I don't agree , as represents a value of 2.

Algebra is a branch of mathematics that deals with mathematical operations and symbols to represent numbers and quantities. It is a broad area that covers a wide range of mathematical topics, including solving equations, manipulating mathematical expressions, and analyzing mathematical structures.

In algebra, the basic mathematical operations include addition, subtraction, multiplication, and division, which are used to perform computations on numerical values. Algebraic expressions often use variables such as x and y to represent unknown quantities, and equations are used to describe relationships between these variables.

Algebraic structures such as groups, rings, and fields are studied in abstract algebra, which is a more advanced area of algebra. These structures have applications in many areas of mathematics, as well as in computer science, physics, and engineering.

As we can see ,

3x  is equal to 6 × 1,

3x = 6

x=2≠3

We know that x represent  a value 2 not 3.

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The complete question is:

9514 1404 393

Answer:

Step-by-step explanation:

Reduced ratios are found by removing (dividing out) the greatest common factor (GCF). For several of these, that factor is the smallest number or the difference between the numbers. Knowledge of multiplication tables is helpful.

  9 : 36 = 1 : 4 . . . . common factor of 9

  21 : 27  = 7 : 9 . . . . common factor of 3

  48 : 72 = 2 : 3 . . . . common factor of 24

  60 : 45 = 4 : 3 . . . . common factor of 15

  10 : 70 = 1 : 7 . . . . common factor of 10

_____

Comment on GCF

The greatest common factor can be found from your knowledge of multiplication tables and/or divisibility rules. It can also be found using Euclid's algorithm. For that, you ...

  Divide the larger number by the smaller and keep the remainder.

  If the remainder is 0, the smaller is the GCF.

  If the remainder is not zero, replace the larger number with the remainder and repeat from the first step.

Example:

  27/21 = 1 r 6

  21/6 = 3 r 3

  6/3 = 2 r 0 . . . . 3 is the GCF of 21 and 27

Answer:

391.3

Step-by-step explanation:

13x43=559

559-167.70=391.3

As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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Answer:

x ≥ -5

Step-by-step explanation:

Because this is a close circle, so there will be an equal sign. The line is going to the right of -5, so it will be larger. So, the inequality is x ≥ -5