Use induction to prove that 2 divides n^2 n whenever n is a positive integer

in essence, how many times does 1/4 go into 6 and 1/2?

[tex]\stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{2}\div \cfrac{1}{4}\implies \cfrac{13}{2}\cdot \cfrac{4}{1}\implies \cfrac{13}{1}\cdot \implies \cfrac{4}{2}\cdot 13\cdot 2\implies 26[/tex]

Answer:

t < 1.5

Step-by-step explanation:

Mon-Thu: 5.5 hours

each of the remaining 3 days: t hours each day

total time: 3t + 5.5

The total time must be less than 10 hours.

3t + 5.5 < 10

3t < 4.5

t < 1.5

Based on the calculations, the most likely value of t is equal to 2.2.

Given the following data:

A null hypothesis ([tex]H_0[/tex]) can be defined the opposite of an alternate hypothesis ([tex]H_a[/tex]) and it asserts that two (2) possibilities are the same.

For the one-tail test, we would reject the null hypothesis ([tex]H_0[/tex]) when the p-value is lesser than the value of [tex]\alpha[/tex];

[tex]H_o: P(Z > |\delta|) < 0.02[/tex]

For the two-tail test, we would fail to reject the null hypothesis ([tex]H_0[/tex]) when the p-value is greater than the value of [tex]\alpha[/tex];

[tex]H_o: 2P(Z > |z|) > 0.02\\\\H_o: P(Z > |z|) > 0.01[/tex]

Next, we would determine the positive value of z-score that satisfies this expression;

[tex]0.01 < P(Z < z) < 0.02\\\\[/tex]

From the z-table, we have:

[tex]P(Z > 2.326)\;and\; P(Z > 2.054)\\\\2.054 < z < 2.326[/tex]

Therefore, t = 2.2.

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answer:ok

there are 3 and one fith apples

he need 4

apples

he adds 5/8

apples to his basket

how many apples doess  he end up with

Step-by-step explanation:you add them together

Answer:

10%

Step-by-step explanation:

I think it's right lol but I could be wrong I forgot a lot of this stuff

but out of all the data it goes from 22-42 so 20 points in total

there is only 2 of the data points behind 24, so it is 2/20 or 10%

Answer:

5 11/13km

Step-by-step explanation:

4 ( 1 6/13)

4× 19/13

= 5 11/13

Answer:

2,8,14,20...… the 49th term is 294.

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

294

Step-by-step explanation:

formula

an=a1 +(n-1)d

n= unknown term

d= difference between each term

8=a1

14=a2

20=a3

a49=8+(49-1)×(6)

a49= 8+ 48 ×(6)

a49= 8+ 288

a49= 294

Answer:

112

Step-by-step explanation:

Sum of interior angles in quadrilaterial = 360

360 - 100 - 104 - 44 = 112

Step-by-step explanation:

Let the 4th angle = x

Now,

x + 100 + 104 + 44 = 360° ( the sum of interior angle of quadrilateral is 360°)

x + 248 = 360°

x = 360° - 248

x = 112

Hence, the fourth angle is 112....

Answer:

B

Step-by-step explanation:

the common ratio r of a geometric sequence is calculated as

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{12}{3}[/tex] = 4

Answer:

B   4

Step-by-step explanation:

Divide any number (other than the first one) in the sequence by the previous number.

12/3 = 4

48/12 = 4

Answer: B   4

1hour=600

2hour=600+600

=1200words

Answer:

8 more pieces

Step-by-step explanation:

First, divide 1042 by 35 to get 29 and 27/35. Since each exhibit needs 35 pieces, and since 35- 27 is 8, the museum needs 8 more pieces.

Hopefully this helps- let me know if you have any questions!

Answer: answer C.

Step-by-step explanation: you have to add and divide

Answer:

Scale: 100 meters per 1 meter

Actual: 316 per unknown meters(our scale)

So order our units:-

_______   _______ =  _______, solve for x;

1/100 = x/316

*316      *316

3.16 = x, 3.16 rounded = 3.20 is the scale.

Step-by-step explanation:

please mark me as brainlest

Answer:

(2) n > 6 (3) -4, -3, -2, -1, 0, and 1.

Step-by-step explanation:

(2) to solve first we subtract 12n from both sides making it 3n > 18 then we divide 3...making it n>6 (remember if you're solving an inequality its not unlike solving an equation)

(3) For this let's separate it into -2<n+3 which solving gets us n > -5

Steps: we subtract 3 from both sides again which makes it -5 < n but usually the variable should go to the left of an equality so n> -5

The other part is n+3 is less than equal to 4. which equals n is less than equal to 1 (I think you get how to solve now :)

once we combine both of the inequalities you'll get -5<n less than equal to 1. Which means the possible values are -4, -3, -2, -1, 0, and 1.

(a). The solution is [tex]n > 6[/tex]

(b). The all possible values of n are [tex]-4,-3,-2,-1,0,1[/tex]

(a). The given inequality is;

                  [tex]15n > 12n+18[/tex]

Now we have to solve inequality,

                    [tex]15n > 12n+18\\\\15n-12n > 18\\\\3n > 18\\\\n > 18/3\\\\n > 6[/tex]

(b).  Inequality is [tex]-2 < n+3\leq 4[/tex]

  Now we have to solve inequality,

                    [tex]-2 < n+3\leq 4\\\\-2-3 < n\leq 4-3\\\\-5 < n\leq 1[/tex]

So that, the all possible values of n are [tex]-4,-3,-2,-1,0,1[/tex]

Learn more about the inequality here:

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Answer:

Step-by-step explanation:

Number the weekdays, and relevant time, then look for the pattern

We get the series:

If you notice, the difference between the terms is:

It indicates the following terms are:

Since z represents the seventh term, the running time on Sunday is 28 minutes.

As we see looking for patterns helped to solve the question.

Correct choice is D

Answer:

D

Step-by-step explanation:

Because its D

since  y = - 3x and y = x - 4

we have

- 3x = x - 4

4x = 4

x = 1

and then y = - 3 * 1 = - 3

(1 ; - 3)

Answer:

(1,-3)

Step-by-step explanation:

y = -3x

y= x-4

Substitute -3x for y in the second equation

-3x = x-4

Subtract x from each side

-3x-x = x-4-x

-4x = -4

Divide each side by -4

-4x/-4 = -4/-4

x=1

Now we can find y

y = x-4

y = 1-4

y= -3

(1,-3)

Answer:

23 square meter from Nthabiseng Selina Tsolo

The straw is placed diagonally in the rectangular prism, therefore, the length of the straw is √109 inches

Diagonal of a rectangular prism = √(l² + w² + h²)

Where,

Therefore,

l = 6 inches

w = 3 inches

h = 8 inches

diagonal = √(6² + 3² + 8²)

diagonal = √36 + 9 + 64

diagonal = √109 inches

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Answer:

1200

Step-by-step explanation:

600 in grams = 600 x 1000

= 6 x 10^5

(6 x 10^5) / 500 = 1200.

Answer:

1200 packets

Step-by-step explanation:

1 kg = 1000 gram

600 kg = 1000 × 600 = 600,000

now,

packets of tea were ( 600000 ÷ 1000) = 1200 packets

Answer:

(x+3)(x+5)

x( x + 5) +3 ( x + 5)

x² + 5x + 3x + 15

x² + 8x + 15

The algebraic expressions out of the given options that are binomials is given by: Option B: x^2y - 3x and Option D: 4xy - 2/5

Polynomials are algebraic expressions having only addition, subtraction, multiplication and exponentiation (non-negative) of variables involved in it.

Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.

Example:

[tex]x^3 + 3x +5[/tex]

is a polynomial consisting 3 terms as

[tex]x^3[/tex], 3x and 5

Checking all the options:

It has only one term, so its not a binomial.

It has two terms, and there is only integer powers of variables and variables are in multiplication in forming terms, so its a polynomial.  And because of two terms and being polynomial, it is binomial.

Because of square root over variable 'y', the variable 'y' got non-integer power 1/2 as square root is also written as exponentiation by 1/2.

Thus, its not a polynomial.

Its a polynomial as there are constants only and variables with multiplication. And because of two terms and being polynomial, it is binomial.

we can write the second term as:

[tex]\dfrac{3}{x} = 3x^{-1}[/tex]

Thus, the variable x has negative power. Thus, its not a polynomial. Or simply, since the variable is in division in simplified form, therefore, its not a polynomial.

Thus, the algebraic expressions out of the given options that are binomials is given by: Option B: x^2y - 3x and Option D: 4xy - 2/5

Learn more about binomials here:

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Answer:

Sammis work is correct

Step-by-step explanation:

when handling equations such as 107d= 1,733.4

you see that d is being multiplied to 107 to equal the total,

so to find the answer to d you would divide 107 by the total to get your value of d

Answer:the last one

Step-by-step explanation:

The amount of juice by Benito is an illustration of volumes

The amount of juice made is 900 milliliters

The question is incomplete, as the figure and the dimensions are not given.

So, I will give a general solution

Assume the following parameters

The amount of juice would be:

V = πr^2h

This gives

V = 3.14 * 4^2 * 18

Evaluate

V = 904.32

Approximate

V = 900

Hence, the amount of juice made is 900 milliliters

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The coefficient of determination is the ratio of the sum of squares regression and the ssy

The sum of squares regression is 27

The given parameters are:

Coefficient of determination, R^2 = 0.12

SSy = 225

The coefficient of determination is calculated as:

R^2 = SSR/SSY

So, we have:

0.12 = SSR/225

Make SSR the subject

SSR = 0.12 * 225

Evaluate the product

SSR = 27

Hece, the sum of squares regression is 27

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The sum of squares regression is 27

The coefficient of determination or R squared method is the proportion of the variance in the dependent variable that is predicted from the independent variable.

The coefficient of determination is calculated by using the following formula;

[tex]\rm R^2 = \dfrac{SSR}{SSY}\\\\ 0.12= \dfrac{SSR}{225}\\\\ SSR = 225 \times 0.12 \\\\ SSR = 27[/tex]

Hence, the sum of squares regression is 27.

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#SPJ3

Answer: 7(n + 1)(n - 1)

Step-by-step explanation:

[tex]7n^2-7[/tex]

[tex]\mathrm{Rewrite\:}7\mathrm{\:as\:}7\cdot \:1[/tex]

[tex]=7n^2-7\cdot \:1[/tex]

[tex]$$ Factor out the common term 7[/tex]

[tex]=7\left(n^2-1\right)[/tex]

[tex]$$ Factor $n^2 - 1[/tex]

[tex]\mathrm{Rewrite\:}1\mathrm{\:as\:}1^2[/tex]

[tex]=n^2-1^2[/tex]

[tex]$$ Apply difference of two squares formula $ x^2 - y^2 = (x+y)(x-y)[/tex]

[tex]n^2-1^2=\left(n+1\right)\left(n-1\right)[/tex]

[tex]\therefore \bf{7\left(n+1\right)\left(n-1\right)}[/tex]

Total Area:- Area of square + area of Semicircle

Total area :- (L×B)+ (½× πr²)

Total area:- (12×12)+(½×π6²)

Total area:- 144+(½× 113)

Total area:- 144+ 56.5

Total area :- 200.5