n is an integer greater than 1

Prove algebraically that 10 + [tex]n^{2}[/tex] - (n-2)[tex]^{2}[/tex] is always an even number.

Your final line must have, "always even" as part of the line.

The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5

The equation of the function is given as

f(x) = 7x²

Also, we have

Vertex = (3, 5)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (3, 5)

Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 3)² + 5

This also means that

f(x) = 7(x - 3)² + 5

The 7 is gotten from f(x) = 7x²

Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5

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The type of probability are we starting will be relative frequency probability or the empirical probability,

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Given that, Shawna made 67 out of 100 free throw attempts during the course of the basketball season. When we state that she has a 0.67 chance of making a free shot during the postseason,

The ratio of the number of times an event occurs to the total number of outcomes that occurred is known as relative frequency.

Thus, the type of probability are we starting will be relative frequency probability or the empirical probability,

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All the inequality given are all non strict inequalities

Inequality           classification

3x - 2 < 1          non strict inequality    

3x - > 1             non strict inequality

3x - 2 > 1          non strict inequality

3x - 2 < 1          non strict inequality

Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.

The signs used in inequality are of 4 types namely

The strict inequality are those inequality that the equation fails when equality sign is used to represent the relationship of the left and right hand side of an equation.. The inequality sign used here is only less than or greater than

The non strict inequality maintains the balance between both sides of the equation whether the equality is used or not

None of the given expression has the "less than or equal to" OR "greater than or equal to" signs hence they are all strict inequality

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When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3

The product of 6 and the square of a number

Consider the number as x

Then the product of 6 and the square of a number = [tex]6x^2[/tex]

The product of 6 and the square of a number is increased by 5 times the number, the result is 4

Then the equation will be

[tex]6x^2[/tex] + 5x = 4

Move 4 to the left hand side of the equation

[tex]6x^2[/tex] + 5x - 4 = 0

We have to solve the quadratic equation

Split the middle terms

[tex]6x^2[/tex] + 8x - 3x -4 = 0

2x(3x+4) -1(3x+4) = 0

(2x-1)(3x+4)= 0

Then the value of x will be

2x- 1 = 0

2x = 1

x = 1/2

Similarly

3x+4 = 0

3x = -4

x = -4/3

Hence, when the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3

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The equation to find the original cost of hat is

44.80 = (x + 35) - (x+35)× 10/3

In the given question we have,

Ms. emlyn buys a hat and gloves with coupon for 30% off her entire purchase.

discount on total purchase = 30%

cost of gloves before discount = $35

let the cost of hat be $x before discount . The bill paid by Ms emlyn after discount but without tax = $44.80

total cost ( hat+gloves) before discount= $(x+35)

Now, after sum up all information we get,

$(x+35) - 30%discount on $(x+35) = $44.80

=> x+35 - (x+35)100/30 = 44.80

=> x+35 - (x+35)10/3= 44.80

which is required equation for original cost of hat.

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Answer:

Step-by-step explanation:

You have two revenue relations and want the price of each adult and child ticket. 150 adult and 100 child tickets sold for $3087.50; 200 adult and 150 child tickets sold for $4287.50.

Each of the revenue relations can be formulated as an equation. If x and y represent the price of each adult and child ticket, respectively, then ...

  150x +100y = 3087.50

  200x +150y = 4287.50

The solution can be found many ways. A graphing calculator (first attachment) shows the solution to be ...

The calculator function that reduces a matrix to row-echelon form can be used on the augmented matrix of coefficients. That, too, gives the solution about as quickly as you can enter the coefficients. This is shown in the second attachment.

Subtracting twice the second equation from 3 times the first will eliminate the y-variable:

  3(150x +100y) -2(200x +150y) = 3(3087.50) -2(4287.50)

  50x = 687.50

  x = 13.75 . . . . . . divide by 50

From the second equation, ...

  y = (4287.50 -200(13.75))/150 = 1537.50/150

  y = 10.25

A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given sequence, 20 - n²

The 20 - n² represents the nth term of the sequence.

Thus a(n) = 20 - n²

For the third term n = 3

a(3) = 20 - (3)²

a(3) = 20 - 9 = 11

Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".

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Answer:

Another Professional Player

Answer:

A and D

Step-by-step explanation:

8(6) means 8x6 so that's 48

and 12(4) is the same as 4(12) so that should be simple enough

The experiment will end after 4th time.

hence, after 4th  trial experiment will stop.

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The p-value for this z test statistic is equal to 0.0287.

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The z test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

In this scenario, the z test statistic for a one-tailed hypothesis test (lower tail) is equal to -1.9. Therefore, by using a t-distribution and z-score calculator for a normal distribution, the p-value for this test is given by:

P-value = P(t > -1.9)

P-value = 0.0287.

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The pack of hot dogs that the shopper should buy that would be cheaper is six - pack of hot dogs

If the shopper decided to buy the six-pack of hot dogs for $2.10, their total cost to be able to get 48 hot dogs would be:

= Cost per six pack of hot dogs x ( Number of hot dogs needed / Number of hot dogs in pack)
=2.10 x (48 / 6)

= 2.10 x 8

= $16.80

The cost if the shopper wants the eight pack is:

= 3.12 x (48 / 8)

= $18.72

The shopper should pick the six - pack of hot dogs because it is cheaper.

The rest of the question is:

Which option would be cheaper to the shopper?

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Si X es la cantidad total de alimento en la heladera, (1/10)*X es la cantidad de manzanas, entoces vemos que la fraccion es 1/10.

Digamos que la variable X representa la cantidad total de comida en la heladera.

Sabemos que un tercio del total de los alimentos son solidos, entonces la cantidad de alimentos solidos es:

(1/3)*X

Luego 1/2 de estos son verduras, entonces la cantidad de verduras que tenemos es:

(1/2)*(1/3)*X

Finalmente, 3/5 de las verduras son manzanas, entonces la cantidad de manzanas es:

(3/5)*(1/2)*(1/3)*x = (1/10)*x

Asi hemos encontrado la fraccion.

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The equation of the graph in point slope form is y + 2 = -3(x - 1)

The equation of the graph in point slope form can be represented as follows;

y - y₁ = m(x - x₁)

where

using two point let's find the slope

(0, 1)(-1, 4)

Hence,

m = 4 - 1 / -1 - 0

m = 3 / -1

m = -3

Therefore, the slope of the line is - 3.

Therefore, using one coordinates(1, -2) from the graph, the equation of the graph in point slope form is y + 2 = -3(x - 1)

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Answer:

h = 289 feet

Step-by-step explanation:

Comment

You need two givens to use in the formula to solve for the third.

Formula

v = sqrt(2*g*h)

Givens

V = 136 ft/s

g = 32 ft/s^2

h = ?

Solution

v = sqrt(2*g*h)                  Put the givens into the formula.

136 = sqrt(2* 32 * h)         Square both sides

136^2 = sqrt(2*32*h)^2   Expand

18496 = 64* h                  Divide by 64

18496/64 = 64*h/64  

289 feet = h

So the object must fall 289 feet before it reaches 136 m/s

19.50 cost of pizza

Step-by-step explanation:

$8.00-$1.50 = $6.50 × 3 =19.50

In the given parabola equations, the third equation [tex]y = 2x - 3x^{2}[/tex] has a maximum value.

What is the Maximum parabola?

If a parabola opens up, it has the lowest point, and if it opens down, it has the highest point. For a parabola to have a maximum value, it must be the case that the parabola opens down. Algebraically, this means that the leading coefficient in the equation of a parabola is negative (a < 0).

We have,

                              [tex]y = 0.1x^{2} - 3x\\\\y = 4x^{2} + 24x +23\\\\y = 2x - 3x^{2}\\\\y = x^{2} + 2x + 20[/tex]

For a parabola to have a maximum value, the parabola must open downward. Algebraically, this means that the leading coefficient in a parabola equation is negative (a < 0).

By Simplifying the third equation we get its leading coefficient is negative (a < 0).

                              [tex]y = -3x^{2} + 2x[/tex]

Hence in the given parabola equations, the third equation has a maximum value.

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Answer:

375

Step-by-step explanation:

h + c = 680

c = h - 70

h + h - 70 = 680

2h = 680 + 70

2h = 750

2/2 h = 750/2

h = 375

Answer: 7£

Step-by-step explanation:
1. Firstly, we need to subtract the single sign up fee from the total cost. This would be 141-57 =84 pounds
2. We know that you pay a regular amount every month, so therefore we can divide 84 by 12 as there are 12 months in a year.
3. 84/12 = 7. Thus, the answer is 7 pounds a month.

Answer:

£7

Step-by-step explanation:

Given information:

To find the cost of the monthly payments, find the difference between the total cost and the sign-up fee, then divide the result by 12 (as there are 12 months in one year).

The difference between the total cost and the sign-up fee is:

[tex]\implies 141-57=84[/tex]

Therefore, the cost of each monthly payment is:

[tex]\implies \textsf{Monthly fee}=\dfrac{84}{12}=7[/tex]

As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.

The value of p=0.8 and n=20

The probability that exactly 12 flights are on time = 0.1772

The probability that exactly fewer than 12 flights are on time =  0.1049

The probability that at least 12 flights are on time = 0.8951

The probability that between 10 and 12 flights, are on time = 0.1795

(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.

As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.

(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,

p = 80% = 0.8

As, we made 20 trials and n is the total number of trials then,

the value of n be,

n = 20

(c) Now, if the probability of success on an individual trial is p ,

Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)

The probability that exactly 12 flights are on time, be

P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)

P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)

P(X=12) = 10,07,760×0.0687×0.00000256

P(X=12) = 0.1772

(d) Now, the probability that exactly fewer than 12 flights are on time, be

P(X<12) = 1 - P(X>12)

So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)

So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115

P(X>12) = 0.8951

P(X<12) = 1 - 0.8951

P(X<12) = 0.1049

(e)  Now, the probability that at least 12 flights are on time, be

P(X>12)=0.8951

(f) The probability that between 10 and 12 flights, are on time, be

P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772

P(X=10)+P(X=11)+P(X=12) = 0.1795

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Answer:

its "a" your welocome

Step-by-step explanation:

i did the test

Answer: The volunteers are unaware of which surgery they receive.

Step-by-step explanation:

Answer:

32 books

Step-by-step explanation:

Well if each have 8 classes and 2 books per class then to get the total of books you'd multiply 8x2 and you get 16 for one alone. Since its two people sharing a single locker than add 16 with another 16 and you get 32!

sorry I can't physically show the work but writing down a 8x2 on the side and then adding 16 to that answer should show it off! :]

Answer:

Step-by-step explanation:

A=P(1+r/n)^nt

Let the Beth deposite is x.Here r and n will be 1.

A=x(1+1/1)^5

Similarly
B=2x(1+1/n)^nt

B=2x(1+1/1)^5

There combined interest is:
A+B=x(1+1/1)^5+2x(1+1/1)^5

21=32x+64x

21=96x

x=21/96 is the beth deposite.

2x=2*21/96 is the Reena deposite

Answer:

it is important because this will be helpful for your incomes, tax, bills etc. This also will plan for other things that you might pay like savings.

Step-by-step explanation:

Answer:

9/8 m = 21/8

or

9m/8 = 21/8

Step-by-step explanation:

3m = 7

3/8 × 3m = 3/8 × 7

9/8 m = 21/8

The sum X to the power of two plus X to the power of three be written in simpler form is X² + X³.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Based on the information given, this will be illustrated as X² + X³. In this case, it illustrate the addition of exponents.

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