In a list of numbers, an odd-sum triple is a group of three numbers in a row that add to an odd number. For instance, if we write the numbers from 1 to 6 in this order,
642135
then there are exactly two odd-sum triples: (4, 2, 1) and (1, 3, 5).
What is the greatest number of odd-sum triples that can be made by writing the numbers from 1 to 1000 in some order?

the solution w = -36 is correct

The given equation is w/4 + 16 = 7.The main objective here is to solve for the variable w. Let us see the step-by-step process to solve for w:

Step 1: Simplify the left side of the equation by subtracting 16 from both sides. w/4 + 16 = 7 ⇒ w/4 = -9The justification for subtracting 16 from both sides is the additive inverse property of equality, which states that if a = b, then a - c = b - c for any real number c.

Step 2: Multiply both sides of the equation by 4 to isolate w. w/4 = -9 ⇒ (4)(w/4) = (4)(-9) ⇒ w = -36The justification for multiplying both sides of the equation by 4 is the multiplication property of equality, which states that if a = b, then ac = bc for any real number c.

Step 3: Check the solution. Substitute -36 for w in the original equation to make sure it satisfies the equation. w/4 + 16 = 7 ⇒ (-36)/4 + 16 = 7 ⇒ -9 + 16 = 7 ⇒ 7 = 7Since 7 = 7 is a true statement, . The justification for this step is that it ensures that the solution obtained in the previous step is valid.

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The initial value solution of the given ODE is y = -2secx + 5/2, where y(π/2) = 3. To find the general solution of the ordinary differential equation (ODE), we'll begin by separating the variables and integrating both sides.

Given the ODE: (tanx)dy = (2y - 5)dx

We can rewrite it as: dy/(2y - 5) = dx/tanx

Integrating both sides, we have:

∫(1/(2y - 5))dy = ∫(1/tanx)dx

Applying the integral on each side, we get:

(1/2)ln|2y - 5| = ln|secx| + C

where C is the constant of integration.

Now, we can simplify the equation further by exponentiating both sides:

e^((1/2)ln|2y - 5|) = e^(ln|secx| + C)

Simplifying the right-hand side using properties of logarithms, we have:

2y - 5 = e^(ln|secx|) * e^C

Since e^C is just a constant, we can rewrite it as a new constant, let's say A:

2y - 5 = A * secx

Now, we can solve for y:

2y = A * secx + 5

y = (A/2) * secx + 5/2

This is the general solution to the given ODE. However, we are also given the initial condition y(π/2) = 3. We can use this condition to find the specific solution.

Plugging in x = π/2 and y = 3 into the equation, we get:

3 = (A/2) * sec(π/2) + 5/2

3 = (A/2) * 1 + 5/2

3 = A/2 + 5/2

A/2 = -2

A = -4

Substituting A = -4 back into the general solution, we have:

y = (-4/2) * secx + 5/2

y = -2secx + 5/2

Therefore, the initial value solution of the given ODE is y = -2secx + 5/2, where y(π/2) = 3.

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The answer of the given question based on the triangle is, option (A) one of the three different points that are equidistant from the three sides of the triangle.

A point of intersection is a point where two or more lines, curves, or surfaces meet or cross each other. In geometry, the point of intersection can be used to find important properties of the objects involved, such as angles, distances, and coordinates.

George is trying to find point that is equidistant from  three sides of the triangle.

The point of intersection of the lines passing through the arcs drawn from the vertices of the triangle using a compass is called the circumcenter of the triangle. The circumcenter is equidistant from three vertices of  triangle, which means that it lies on  perpendicular bisectors of  three sides of  triangle.

In this case, the perpendicular bisectors of JL and YZ are shown as lines JK and WX respectively. The circumcenter of triangle JKL is the point where these two lines intersect. This point is equidistant from the sides KL, LJ, and JK of the triangle.

Therefore, the answer is (A) one of the three different points that are equidistant from the three sides of the triangle.

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The answer is B. George is trying to find one of the three different points that are equidistant from the three vertices of the triangle.

The intersection of two or more lines, curves, or surfaces is known as a point of intersection.

George is trying to find one of the three different points that are equidistant from the three vertices of the triangle JKL.

The intersection of the arcs drawn from the vertices of the triangle will be equidistant from those vertices. This point is called the circumcenter of the triangle, and it is the center of the circumcircle that passes through all three vertices of the triangle.

Since George is drawing lines through the arcs and finding their point of intersection, he is finding the circumcenter of the triangle. The circumcenter is one of the three different points that are equidistant from the three vertices of the triangle.

Therefore, the answer is B. George is trying to find one of the three different points that are equidistant from the three vertices of the triangle.

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Answer:

Let the number be x

when it is 8less than 4times the x the inequality equation we get is:

4x-8<56 (since it says it's less than 56)

4x<56+8

4x<64

x<64÷4

x<16

the possible values are all numbers less than 16

Frequency means how often a number or something appears.

so,

2

4

3

5

Answer:

113.142857 m²

Step-by-step explanation:

As per the provide information in the given question, we have :

We are asked to find the area of the ground.

Since, it is in the shape of circle, so we'll apply here the formula to find the area of the circular ground.

We know that,

>> Area of circle = πr

>> Area of the ground = \( \sf \dfrac{22}{7} \) × 6 m × 6 m

>> Area of the ground = \( \sf \dfrac{22}{7} \) × 36 m²

>> Area of the ground = \( \sf \dfrac{792}{7} \) m²

>> Area of the ground = 113.142857 m²

\( \therefore\) Therefore, area of the ground is 113.142857 m².

Answer:

 50 people

Step-by-step explanation:

Solution

25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel

1/4 * 200 = 50

50 people want the hotel.

Answer: 30.0 feet

Step-by-step explanation:

Answer:

30.0 ft

Step-by-step explanation:

Answer:

This relation is a function.

Step-by-step explanation:

This relation is a function because a there should be no repeating x-coordinates in the relation for it to be a function and that is exactly what happens in this relation.

Answer:

It is a function.

Step-by-step explanation:

no two different outputs, y, have the same input, x, meaning it passes the vertical line test.

sorry for the lousy explanation

Answer:

A.

Step-by-step explanation:

You can read the y-intercept as -2.

We have

y = mx - 2

The slope is 1/2. m = 1/2.

y = 1/2 x - 2

The answer is D. R2, also known as the coefficient of determination, shows the percentage of the total variation in the dependent variable, Y, that is explained by the explanatory variable.

Of the four answer choices provided, only one is true of R2. Answer D is the correct statement regarding R2. It indicates that R2 shows the percentage of the total variation in the dependent variable, Y, that is explained by the explanatory variable. This statement is commonly used to evaluate the strength of a linear relationship between two variables. It is important to note that a high R2 value does not necessarily mean that the explanatory variable causes the dependent variable, but it does suggest a strong correlation between the two. This answer is provided in one paragraph consisting of three sentences.

In other words, R2 measures the proportion of the variance in the dependent variable that can be predicted from the independent variable(s). A higher R2 value indicates a better fit of the data, while a lower value suggests that the model may not explain much of the variation in the dependent variable.

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Answer:10 ft apart

Step-by-step explanation:

The required Perimeter and area of the shape is 27.42 units and 64.26 sq units.

The circumference of a shape is its perimeter. How is a perimeter calculated? The border can be found by including the lengths of each side of a shape.

We have given a shape which made up of two circle and rectangle

diameter of circle = 12 - 6 = 6

then radius = 3 units

Perimeter = 3+3+3+3+3+3+π(3)

= 18 + 3.14(3)

= 18 + 9.42

= 27.42 units

and

Area = area of rectangle + area of two half circles

= 12(3) + π(3)²

= 36 + 28.26

= 64.26 sq units.

Thus, required Perimeter and area of the shape is 27.42 units and 64.26 sq units.

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The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

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Answer:

28 = 2² x 7

Step-by-step explanation:

Factors of 28: 1, 2, 4, 7, 14, 28.

Prime factorization: 28 = 2 x 2 x 7, which can also be written 28 = 2² x 7.

Answer:

Nope.  It would take 32 and 4/13 minutes, which is longer than 30 min.

Step-by-step explanation:

The distance is 35 miles and the speed 65 miles/hour

Dividie the distance by the speed to obtian the time required,

(35 miles)/(65 miles/hour) = 0.538 hours

No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour.  2 and 4/13 minutes more than 30 minutes.

The required answer for the expected value of X is given by : E(X) = 0.1 + 0.2 + 1.5 + 5E(X) = 1.8

The expected value is a statistical concept that quantifies a random variable's long-term mean and is denoted by E(X), where X is the random variable.

It's a crucial concept in probability theory and is used to evaluate investment outcomes, the probability of default, and many other financial metrics.

The formula for calculating expected value is: E(X) = ∑[xi × P(xi)], where xi is the possible value of the random variable X, and P(xi) is the probability of that outcome.

Here is the answer to your question:Given the outcomes of the biased 4-sided die with numbers 1, 2, 5, and 10, we can determine the expected value of the random variable X.

The expected value of X is given by:E(X) = 1 × 0.1 + 2 × 0.1 + 5 × 0.3 + 10 × 0.5

E(X) = 0.1 + 0.2 + 1.5 + 5E(X) = 1.8

Therefore, the expected value of X is 1.8.

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The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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Answer:

$244.51

Step-by-step explanation:

Credit card payment =$5390

After paying $2300 from savings account,

Remaining payment left     = 5390-2300 = $3090

APR = 16.5% or 0.165

Time (t) = 14 months = 14/12 years

Using credit card payment calculator,

Monthly payment = $244.15

Hence, minimum monthly payment to be made to pay off the whole debt in 14 months = $244.15

Answer:

Never

Step-by-step explanation:

If p is true and ~ q is false, then p -> ~ q is ____ false

This translates to:

true -> true

So it will never be false.

Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.

What is quotient?

In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

0. 48 ÷ 0. 8

=0.06

The solution for Long Division of \($\frac{4.8}{8}$\) is 0.6

The solution for Long Division of \($\frac{0.48}{0.08}$\) is 6.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Get the probability of calls within a minute

STEP 2: Write the formula for getting the probability that there are at least two calls in a given minute.

STEP 3: Write the formula for P(X=r)

STEP 4: Find P(X=0)

STEP 5: Find P(X=1)

STEP 6: Find P(X>=2)

Hence, the probability that there are at least two calls in a given minute is 0.0902

The value of f(-5) = -130

A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.

A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:

Ax3 + bx2 + cx +d = 0

For the given question the cubic equation will be:

2x3 + bx2 + cx - 5 = 0

Given

Leading coefficient (a) = 2

Constant (T) = -5

f(1) = 0

f(2) = 9

Therefore the equation formed will be:

2x3 + bx2 + cx - 5 = 0

Now f(1) = 0

2(1)3 + b(1)2 + c(1) - 5 = 0

2 + b + c -5 = 0

b + c = 3  

b = 3-c -----(1)

On solving f(2) = 3

2(2)3 + b(2)2 + c(2) - 5 =3

16 + 4b + 2c – 5 =3

4b +2c = 3 – 11

4b + 2c = -8  ----(2)

Now substitute the b value in equation (2)

4(3-c) + 2c = -8  

12 – 4c +2c = -8

-2c = -20

C =10

Now substitute the c value in equation (1)

b= 3 – c

b = 3 -10

b = -7

Now substitute the b and c values in the cubic equation

2x3 - 7x2 + 10x - 5 = 0

Now calculate f(-5)

2(-5)3 - 7(-5)2 + 10(-5) - 5

= -250 + 175 – 50 -5

= -130

Therefore the value of f(-5) = -130

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Answer:

0.456

Step-by-step explanation:

divide the mass by 1000

Answer:

4 miles

Step-by-step explanation:

4 miles because if if if 58 of mile which is just a half mile basically and she does 7 laps

7 x 0.58=4.06 which is 4 miles

Have a good day :}

Answer:

10.75

-5/4

2 7/24

Step-by-step explanation:

1.)

__+-3.5=7.25

Let missing number = x

x - 3.5 = 7.25

x = 7.25 +3.5

x = 10.75

2.)

-3/4-__=1/2

Let missing number = x

-3/4 - x = 1/2

-3/4 - 1/2 = x

(-3 - 2) / 4 = x

-5/4 = x

3.)

-2 3/8-(-4 2/3) = x

-2 3/8 + 4 2/3 = x

-19/8 + 14/3 = x

(-57 + 112) / 24 = x

55 / 24 = x

2 7/24

The future value of depositing $1,000 every year for 20 years, with payments made at the beginning of each period, at an interest rate of 7% compounded yearly, is approximately $43,865.18.

To calculate the future value of a series of deposits, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value

P is the periodic payment

r is the interest rate per period

n is the number of periods

In this case, the periodic payment is $1,000, the interest rate is 7% (or 0.07), and the number of periods is 20.

Plugging these values into the formula, we get:

FV = 1000 * [(1 + 0.07)^20 - 1] / 0.07

  = 1000 * [1.07^20 - 1] / 0.07

  ≈ 1000 * [2.6532976 - 1] / 0.07

  ≈ 1000 * 1.6532976 / 0.07

  ≈ 43,865.18

Therefore, the future value of this series after 20 years would be approximately $43,865.18.

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Step-by-step explanation:

sum of the triangle's angles is 180°

In the ratio we note the numbers by x

5x + 7x + 3x = 180

15x= 180

x= 12

so smallest angle will be 12*3=36° (because smallest was 3x)

others will be 12*5=60°

12*7=84°