How many integers n satisfy both of the inequalities 4n + 3 < 25 and -7n + 5 < 24?

Given that, 567 teams participate in a football tournament, If each team plays against every other team only once, number of matches played in total is 160461.

To determine the total number of matches played, we apply Combination.

ⁿCr = n! / r!( n-r )!

Given that;

We substitute

[tex]^nC_r = \frac{n!}{r!(n-r)!} \\\\^nC_r = \frac{567!}{2!(567-2)!} \\\\^nC_r = \frac{567!}{2!(565)!}\\\\^nC_r = \frac{567 * 566 * 565!}{2!(565)!} \\\\Cancel-common - factor: 565!\\\\^nC_r = \frac{567 * 566 }{2!} \\\\^nC_r = \frac{567 * 566 }{2*1}\\\\^nC_r = \frac{ 320922 }{2} \\\\^nC_r = 160461[/tex]

Given that, 567 teams participate in a football tournament, If each team plays against every other team only once, number of matches played in total is 160461.

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Answer:

67.

Step-by-step explanation:

n - m = 66

The 66 includes the number m+1   up to and including n (buy not m).

So the number of integers is 66 +1 = 67

Answer:

Dude their answers are the same

Step-by-step explanation:

Adding a negative is the same as subtracting

Answer:

Yes, they're both correct

Step-by-step explanation:

They are both correct because both equations are equal. You could rewrite 7x + (-3) as 7x + 1(-3) and when you "distribute" the positive 1 the equation becomes 7x-3 which is the same thing as 7x-3. When you're subtracting 1 you're also technically adding negative 1

The total amount after 2 years is $2180

The given parameters are:

Principal, P =$2000

Rate, r =4.5%

The interest in 2 years is calculated as:

I = PRT

So, we have:

I = 2000 * 4.5% * 2

Evaluate

I = 180

Hence, the interest after 2 years is $180

This is calculated as:

Amount = P + I

So, we have:

Amount = $2000 + $180

Evaluate

Amount = $2180

Hence, the total amount after 2 years is $2180

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The integer form is + 40.

The integer form is - 25

An integer is a whole number from the set of negative, non-negative, and positive numbers.

Therefore, integers can be written without fractional components.

Hence, integers may include negative or positive numbers . Examples are -1, 2, 5, -8, 9 and many more.

A deposit of 40 dollars means gain. Therefore, the integer form is + 40.

A loss of 25 pounds mean loss. Therefore, the integer form is - 25

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The fraction π/4 comes from the the ratio of the area of the circle to the area of the square from a cross section.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

Volume of cone = (π/4) * volume of pyramid it fits inside

Ratio of area of cone to area of square = πr²/(2r)²  = πr²/4r² = π/4

The fraction π/4 comes from the the ratio of the area of the circle to the area of the square from a cross section.

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(B.) It is the ratio of the area of the circle to the area of the square from a cross section.

The value of x in the proportion is x = 39/8

The proportion is given as:

3/8 =x/13

Cross multiply

8 * x = 3 * 13

Evaluate

8x = 39

Divide by 8

x = 39/8

Hence, the value of x in the proportion is x = 39/8

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The GDP and the years illustrated will be:

It should be noted that the gross domestic product simply means the monetary value of the overall economic activity in a country.

The gross domestic product and their corresponding years have been given.

The business cycle that was illustrated showed that there was a gradual expansion before getting to the peak where recession sets in

Also, the short run Philips curve is illustrated as there's a trade off between inflation and unemployment.

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Answer:

y = 2x + 3

Step-by-step explanation:

Hello!

Solve for y by isolating the variable.

The solution is y = 2x + 3.

To Calculate :-

Solution :-

⇒ -20x + 10y = 30

☆ Transposing (-20x) to R.H.S. sign would be changed to positive.

⇒ 10y = 30 + 20x

⇒ y = 30 + 20x / 10

⇒ y = 10 (3 + 2x) / 10

☆ Cancelling 10,

⇒ y = 3 + 2x / 1

⇒ y = 2x + 3

Answer:

20

Step-by-step explanation:

To find x, note that:

Therefore,

(2x + 20)° = 60°

Removing bracket.

2x + 20 = 60

collecting like term.

2x = 60 - 20

2x = 40

dividing bothsides by 2

2x/2 = 40/2

x = 20

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

How do I solve for X?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Angles [tex]\bf{60^\circ}[/tex] and [tex]\bf{2x+20}[/tex] are vertical angles. They are congruent, or equal.

Thus,

[tex]\bf{2x+20=60}[/tex] | subtract 20

[tex]\bf{2x=40}[/tex] | divide the equation by 2

[tex]\bf{x=20}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

          [tex]\bf{=x=20}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

Putting different values in the variable could give the total money spend.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Marcy had $10.00 to spend at the state fair. She spent all of it on the ride tickets.

The rides cost either $0.50, $1.00, or $1.25 each.

The equation form;

0.50x + 1.00y + 1.25z = 10

Putting different values in the variable could give the total money spend.

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Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does the problem want:

 ⇒use the substitution method

      ⇒ to solve the problem

Let's substitute y's value from the second equation to our first equation

  [tex]2x-y=8\\y=x-3\\\\\rm \hookrightarrow 2x-(x-3)=8\\\rm \hookrightarrow 2x-x+3=8\\\rm \hookrightarrow x=8-3=5[/tex]

Now substitute the x's value into the first equation

[tex]y=x-3\\x=5\\\\\rm \hookrightarrow y=(5) - 3 =2[/tex]

The solution is (5,2)

Answer: (5,2) or (B)

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Answer:

X=-8

Step-by-step explanation:

A number x is multiplied by 4, added to 3, and then divided by x+2, leaving us with 7/2. Or, as an equation:

[tex] \frac{4x + 3}{x + 2} = \frac{7}{2} [/tex]

Now, let's cross multiply:

[tex]2(4x + 3) = 7(x + 2)[/tex]

[tex]8x + 6 = 7x + 14[/tex]

And solve:

[tex]x + 6 = 14[/tex]

[tex]x = - 8[/tex]

Answer:

24/5

Step-by-step explanation:

[tex]\frac{6}{1}*\frac{4}{5} = \frac{24}{5}[/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Multiply, and simplify your answer, and write it as a mixed number,

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Write the first fraction as 6/1 and multiply it times 4/5.

[tex]\bf{\dfrac{6}{1}\times\dfrac{4}{5}=\dfrac{6\times4}{1\times5}}=\dfrac{24}{5}}[/tex] | Have you noticed that we multiply the numerators together, and we do the exact same thing with the denominators?

[tex]\bf{4\dfrac{4}{5}}[/tex]

[tex]\cline{1-3}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=4\dfrac{4}{5}}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

Answer:

The correct answer: a line

When proving the properties of logarithms when exponents must be used, the property that is used in all of these is D. [tex]log_{b} (b^y) = y[/tex]

When proving any property of logarithms that have to do with exponents, one property that should always be used is  [tex]log_{b} (b^y) = y[/tex].

Expressing y as a product of [tex]log_{b} (b^y)[/tex] is the most basic property of using exponents on logs because it has both product, quotient, and power rules of logarithms.

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Answer:

p = 9

Explanation:

There is no remainder when a polynomial is completely divided by divisor.

Here:

Set to zero:

Insert into equation.

f(6) = 0

(6)³ - 13(6)² + 6p(6) - 72 = 0

216 - 468 + 36p - 72 = 0

-324 + 36p = 0

36p = 324

p = 324/36

p = 9

Answer:

Step-by-step explanation:

Attached is graphed piecewise function.

Take note, if the inequality is a less than or equal to or (more than or equal to), the dots will be solid, otherwise it will be hollow.

Since this is a piecewise function, here is one question you might want to ask yourself:

Does the limit exist when x approaches 4?

The parallel lines cuts the sides in equal proportion to give NP = 0.8

The given diagram consists of a line parallel to one of the sides of the triangle.

According to the triangle proportionality theorem, the parallel line, NQ, proportionally divides the sides MR and MP, such that:

NQ || PR

By triangle proportionality theorem;

[tex]\mathbf{ \frac{ MN }{ NP} } = \frac{ MQ }{ QR } [/tex]

Which gives;

[tex] \mathbf{ \frac{ 5 }{ NP} } = \frac{ 8}{ 2 } [/tex]

2×5 = 8 × NP

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The inventory account expected to have by December 31 is more than $5800. Option C

The formula for end inventory is given as ;

Ending inventory = Beginning inventory + net purchases –sales

Beginning inventory = $5800

Net purchases = $65000

Sales = $112000

Put into the formula

Ending inventory = $ [tex]5800 + 65000 - 112000[/tex]

Add first,

Ending inventory = $ [tex]70800 - 112000[/tex]

Ending inventory = $ -41, 200

Thus, the inventory account expected to have by December 31 is more than $5800. Option C

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Answer:

23

Step-by-step explanation:

the answer is the y intercept of the equation

Answer:

23m, at t=2s

Step-by-step explanation:

Putting the physics part aside, you can rewrite the height function as

[tex]h(t)= 23 - 5(t-2)^2[/tex]. Now you have a fixed value, 23, and you're subtracting to it a quantity that, being a square, is at least zero. The maximum value of that sum you have when you're not subtracting anything, that is 23. That happens when [tex]5(t-2)^2 = 0 \rightarrow t=2[/tex]

Alternatively, if you know how to determine the velocity from that kind of motion, you can find out the speed, and the highest altitude you reach when the speed is zero, which leads to a bunch of calculation for the same result.

The chi-squared test statistic will be 3.11. The test statistic is contrasted with a predicted value based on the Chi-square distribution.

Finding the squared difference between the actual and anticipated data values, then dividing that difference by the expected data values, constitutes the test statistic.

The formula for the chi-squared test statistic is;

[tex]\sum \frac{(O_i-E_i)^2}{E_i } \\\\[/tex]

Where,

[tex]\rm O_i[/tex] is the observed value

[tex]\rm E_i[/tex] is the expected value

The chi-square test statics is;

[tex]\rm( \frac{18-18}{18} )^2 +( \frac{14-18}{18} )^2 + (\frac{24-18}{18} )^2+( \frac{16-18}{18} )^2 \\\\ 0+ \frac{16}{18}+ \frac{36}{18} +\frac{4}{18}\\\\ \frac{56}{18} \\\\ 3.11[/tex]

Hence, the chi-squared test statistic will be 3.11.

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Answer:

hope they do help. in case of any questions feel free to ask.

Answer: 23

Step-by-step explanation:

The first term is 0.5 and the common difference is 0.4.

Using the sum of an arithmetic series formula,

[tex]S_{10}=\frac{10}{2}[2(0.5)+(10-1)(0.4)]=\boxed{23}[/tex]

The missing numbers are 13 and 50

Given the numbers;

1, 2, 3, 7, -, 24, -.

Find the numbers by preceding numbers together, thus;

1 + 1 =2

1 + 2 = 3

1 + 2 + 3 = 7

1 + 2 + 3 + 7 = 13

1 + 2 + 3 + 7 + 13 + 24 = 50

Thus, the missing numbers are 13 and 50

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Let, the points be A (8, −4) and B (1, −5). The slope of line AB exists 1/7.

Utilize the slope formula to estimate the slope of a line provided the coordinates of two points on the line.

The slope formula exists [tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex], or the difference in the y values over the difference in the x values. The coordinates of the first point symbolize [tex]$x_{1}[/tex]and [tex]$y_{1}[/tex]. The coordinates of the second points exist [tex]$x_{2} , y_{2} .[/tex]

The slope of the line exists the ratio of the rise to the run, or rise separated by the run.

[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]

The Line, AB contains points A (8, −4) and B (1, −5).

Substitute the value of points in the equation then we get

[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]

m = (-5-(-4))/(1 - 8)

Simplifying the above equation, we get

m = (-5+4)/(1 - 8)

m = (-1)/(-7)

m = 1/7

Therefore, the slope of line AB exists 1/7.

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Answer:

4n - 10

Step-by-step explanation:

Jay: n tickets

Pillar: 3n tickets

Jay + Pillar = n + 3n = 4n tickets

Now, Jay and Pillar together sold 10 more tickets than Amie, which means, in reverse, Amie sold 10 less tickets than Jay and Pillar together, so the expression for the number of tickets sold by amie would be:

4n-10 (4n is the number of tickets Jay and Pillar sold together, 10 is the difference between them and Amie).