Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n 1 is odd, (iii) 3n 1 is odd, (iv) 3n is even.

Answer:

Step-by-step explanation:

we call the number X

x/5 is the fifth part of that number

I propose equality:

x + x/5 = 17

we add the fractions on the left side:

6x/5 = 17

We pass 5 to multiply to the other side:

6x = 5 * 17

6x = 85

we clear x

x = 85/6

x = 14.17

test

14.17 + 2.83 = 17

okay

Answer:

14.1666666667

Step-by-step explanation:

We can write the equation as:

x + x/5 = 17

=> 5/5x + 1/5x = 17

=> 6/5x = 17

=> 6x = 17 * 5

=> 6x = 85

=> x = 85/6

=> x = 14.1666666667

Let's check whether our answer is correct

=> 14.1666666667 + 14.1666666667 / 5 = 17

=> 14.1666666667 +  2.83333333333 = 17

=> 17 = 17

So, the answer is 14.1666666667

Answer:

Jeff has 3 watermelons left

Step-by-step explanation:

44-31=13 watermelons

Answer:

13

Step-by-step explanation:

44

-31

13

Answer:

Step-by-step explanation:

Keywords:

System of equations, variables, cost, tickets, adults, children.

For this case we must solve a system of equations with two variables represented by the tickets of students and adults of a school production.

We define the variables according to the given table:

a: Number of tickets sold to adults

c: Amount of tickets sold to children.

We then have the following system of equations:

A + c = 67

10a + 5c =440

From the first equation, we clear the value of the variable c:

C = 67 - a

Answer:

The value that could replace c in the table is:

C = 67 - a

Option C is the answer!

Hope it helped u if yes mark me BRAINLIEST!

Tysm! Plz

Answer: 0.0546 and 0.9829

Step-by-step explanation:

solution:

= P( 1.50< Z <2.25 )

= P(Z <2.25 ) - P(Z <1.50 )

Using z table,

= 0.9878-0.9332

=0.0546

b.

= P( -2.12< Z <3.73 )

= P(Z <3.73) - P(Z <-2.12 )

Using z table,

= 0.9999-0.0170

=0.9829

The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)

The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80

This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%

We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.

The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)

=========================================

In summary, we have these answers

Answer:

15/2 cups: 2 1/2 cups

2 cups: 2/3 cups

2 1/2 cups: 5/6 cups

Step-by-step explanation:

Take and divide each by the smaller number

15/2 cups: 2 1/2 cups

First put in improper fraction form

15/2 : 5/2

Divide each by 5/2

15/2 ÷ 5/2  : 5/2 ÷5/2

15/2 * 2/5  : 1

3 :1   yes

1 cup: 1/4 cups

Divide each by 1/4 ( which is the same as multiplying by 4)

1*4  : 1/4 *1

4 : 1    no

2/3 cups: 1 cup

Divide each by 2/3  ( which is the same as multiplying by 3/2)

2/3 * 3/2  : 1 * 3/2

1 : 3/2   no

3 3/4 cups: 2 cups

Change to improper fraction

( 4*3+3)/4  : 2

15/4    : 2

Divide each side by 2

15/8  : 2/2

15/8   : 1    no

2 cups: 2/3 cups

Divide each side by 2/3 ( which is the same as multiplying by 3/2)

2 * 3/2 : 2/3 *3/2

3  : 1   yes

2 1/2 cups: 5/6 cups

Change to an improper fraction

( 2*2+1)/2 : 5/6

5/2  : 5/6

Divide each side by 5/6( which is the same as multiplying by 6/5)

5/2 * 6/5  : 5/6 * 6/5

3  : 1   yes

The 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.

For checking: 15/2 cups: 2 1/2 cups

= (15/2)/(5/2)       [2(1/2) = 5/2]

= 3

For checking:  1 cup: 1/4 cups

= 1/(1/4)

= 4

For checking: 2/3 cups: 1 cup

=(2/3)/1

= 2/3

For checking: 3 3/4 cups: 2 cups

= (15/4)(2)

= 15/8

For checking: 2 cups: 2/3 cups

= (2)/(2/3)

= 3

For checking: 2 1/2 cups: 5/6 cups

= (5/2)/(5/6)

= 3

Thus, the 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

Learn more about the ratio here:

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Answer:

Butter per portion equals 60 cents .

Step-by-step explanation:

A pound of butter is worth $ 5.60.

5.60 dollars are converted to cents, 1 dollar equals 100 cents, then:

- One pound of butter equals 560 cents.

A portion of onion compote requires 1.7 oz of butter.

Convert 1.7 oz to pounds, so:

- 1.7 oz of butter equals 0.10625 pounds.

If a pound of butter is worth 560 cents, how much will 0.10625 pounds of butter be worth.

- Rule of 3 is used:

- 560 cents        1 pound butter

  X cents            0.10625 pounds of butters

X = 560 * 0.10625

X = 59.5 cents

X = 60 cents per portion

Answer:

C

Step-by-step explanation:

reciprocal of z=1/z

[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]

Answer:

Step-by-step explanation:

12x - 9 = 8x + 7

4x - 9 = 7

4x = 16

x = 4

solution is C

The solution is Option C.

The value of x is given from the equation x = 4

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as CD

Let the second line be represented as XY

Now , CD is the perpendicular bisector of XY

So , the point F is the midpoint of the line segment XY

The measure of line segment XF = 12x - 9

The measure of line segment FY = 8x + 7

From the perpendicular bisector theorem ,

The measure of line segment XF = The measure of line segment FY

Substituting the values in the equation , we get

12x - 9 = 8x + 7

Subtracting 8x on both sides of the equation , we get

4x - 9 = 7

Adding 9 on both sides of the equation , we get

4x = 16

Divide by 4 on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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Answer:

Brainliest!

Step-by-step explanation:

36x^-4y^2/5x^2y^-3z^-2

36y^5z^2/5x^6

make everything positive

The function is always positive.

(0,5) is the y-intercept, since the graphed line never crosses the x axis, there is no x-intercept.

The function is positive and  greater than 4 for all values of x

Not sure what the actual choices are on a couple of the questions. The choices would help answering.

Answer:

36

Step-by-step explanation:

formula of area for square:

A=s^2

s=6

A=6^2

A=36

Answer:

36

Step-by-step explanation:

I got it right

Answer:

B =

[tex]4x - 1 - \frac{4}{2x - 3} [/tex]

Step-by-step explanation:

In this type of questions the answers are required in the

[tex]quotient \: + \frac{remainder}{divisor} [/tex]

form.

First of all, the equations in question must be arranged properly

[tex](8 {x}^{2} - 14x - 1) \div 2x - 3[/tex]

Then you divide.

[tex]2x - 3 \sqrt{8 {x}^{2} - 14x - 1 } [/tex]

Answer

[tex]4x - 1 - \frac{4}{2x - 3} [/tex]

Answer:

D

Step-by-step explanation:

Let the number of rows be x

And the numbers of holes in each be y

xy = 32

x and y must be factors of 32

From options stated

4 is the only factor of 32

Hence option D is correct

Answer:

x = -1 or x = -5

Step-by-step explanation:

−3 * |2x + 6| = −12 / -3

|2x + 6| = 4

because this is an absolute value equation there are 2 solutions:

2x + 6 = 4 or 2x + 6 = -4

2x = -2 or 2x = -10

x = -1 or x = -5

Answer:

x = -1 or x = -5

Step-by-step explanation:

cuz it is

Answer:

The correct answer is:

c. Joe will go running, biking and hunting

Step-by-step explanation:

Parallel construction or parallelism or parallel structure is a style used in writing a sentence, where there is a balance in phrases or clauses within one or more sentences by them having the same grammatical structure. parallelism adds elegance, clarity and symmetry to sentences. It essentially has to so with a repetition of a chosen grammatical form within a sentence.

In our example:

a.  Jim likes to hunt, bike, and throwing darts. (not parallel)

    Jim likes to hunt, bike, and throw darts (parallel)

The verbs, hunt, bike and throw must be in the same form (present continuous) to be parallel

b. Mimie has to study, drive her sister to the store, and enjoy herself in the garden. (not parallel).

The sentence in option b is not parallel because the other actions apart from "study" have a place where they took place; drive her sister to the store, enjoy herself in the garden, however, "study" doesn't have a place where the action occurs.

c. Jane will throw a ball, then she will mow the lawn. (not parallel)

the sentence is not parallel because there is an inconsistency in the pattern of the construct. a parallel version is:

Jane will first throw a ball, then she will mow the lawn, or

jane will throw a ball and mow the lawn.

d. Joe will go running, biking, and hunting. (parallel)

all the verbs are in the present continuous form.

Answer:

Option (D) : (3.5, 8.75)

Answer:

The  p-value is  [tex]p-value = 0.62578[/tex]

Step-by-step explanation:

From the question we are told that    

    The  sample size of male infant is  [tex]n_1 = 12[/tex]

     The  sample size of female infant is [tex]n_2= 9[/tex]

     The sample mean of male infant is  [tex]\= x_1 = 7.70 \ lb[/tex]

      The sample mean of female infant is  [tex]\= x_2 = 7.80 \ lb[/tex]

     The population standard deviation is  [tex]\sigma = 0.5[/tex]

       The significance level is  [tex]\alpha = 0.05[/tex]

The null hypothesis is  [tex]H_o : \mu_ 1 = \mu_2[/tex]

The  alternative hypothesis is  [tex]H_1 : \mu_1 > \mu_2[/tex]

The  test statistics is mathematically represented as

            [tex]t =\frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma }{n_1} } + \frac{\sigma }{n_2} } }[/tex]

=>          [tex]t = \frac{7.70 -7.80}{\sqrt{\frac{0.5 }{12} } + \frac{0.5 }{9} } }[/tex]

=>        [tex]t = -0.3207[/tex]

From the z-table  the p-value is  obtained, the value is  

     [tex]p-value = P(Z > -0.3207) = 0.62578[/tex]

     [tex]p-value = 0.62578[/tex]

Answer:

97290

Step-by-step explanation:

47 different people can win first

47

Now there are only 46 people left

46 different people can win second

46

45 different people can win third

47*46*45

97290

Find the powers [tex]a=\sqrt{2}+\sqrt{3}[/tex]

$a^{2}=5+2 \sqrt{6}$

$a^{3}=11 \sqrt{2}+9 \sqrt{3}$

The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.

Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$

so fits with the other answers.

Answer:

[tex]y^3 -6y-6[/tex]

Answer:

Inequality: 3 + 1.2c

What you'd put on graph: 1 ≥ 13.50

Answer:

495.56 should be p[aid for 40 hours.

Step-by-step explanation:

concept used

In ratio

a:b = c:d

__________________________________________

Given

IS PAID 473.88 FOR 38 1/4 HOURS OF WORK

38 1/4 hour = 38.25 hours

if we get ratio for payment per hour

we have

473.88 / 38.25 or  473.88 : 38.25

___________________________________

now we have to find payment for 40 hours

let that payment be x

thus,  ratio for payment per hour in this case will be

x/40 or x:40

since

x:40 and  473.88 : 38.25 is representative of same program enhancement unit both ratio will be equal

thus

x:40 =  473.88 : 38.25

x/40 =  473.88 / 38.25

=> x = 40*(473.88 / 38.25 ) = 495.56

Thus,  495.56 should be p[aid for 40 hours.

Step-by-step explanation:

Hey, there!!!

According to your question,

case i

force (f) = 60 n

acceleration due to gravity (a)= 10m/s^2

now,

force = mass × acceleration due to gravity

or, 60 = m × 10

or, 10m= 60

or, m= 60/10

Therefore, the mass is 6 kg.

now,

In case ii

mass= 6kg {Because there was no change in mass only change in force}

force= 54 n

now, acceleration due to gravity = ?

we have,

f=m×a

or, 54= 9×a

or, 9a= 54

or, a= 54/9

Therefore, the acceleration due to gravity is 6m/ s^2.

Hope it helps....

Answer:

random

Step-by-step explanation:

Monte Carlo simulation is a technique which is used to analyze the impact of risk and uncertainty in financial projects and forecasting models. It helps to understand the potential outcomes to better understand the decision based on risk level. It analyzes the probability of different outcomes by intervention of random variables.

Answer: Option B, 16/81

Step-by-step explanation:

So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.

We know that every integer number can be "decomposed" into a product of prime numbers.

Then a number N,  that is divisible by 3, can be written as:

N = 3*k

Where k is another integer.

Here we will have a product of 4 numbers, each of them are in between 1 and 6.

Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2

Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.

Then we must have a 1, 2, 4 or 5.

The probability of 4 outcomes out of 6, is:

P = 4/6.

But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:

P = (4/6)^4 = (2/3)^4 = 16/81

Answer:

16

Step-by-step explanation:

Answer:

(-7, -4)  which is your answer D in the list of options

Step-by-step explanation:

The center of the circle should be located half way in between the given points on the plane.

Then the center ahs to be located half way for the x coordinates of both points:

half way between -12 and -2 (notice that there is a difference of 10 units between them), therefore half way would be at 5 units to the right from the furthest point, that is  -12 + 5 = -7

Similarly, for the y coordinate, we see that the difference is between -5 and -3 (a difference of two units) therefore the center point will be located half way  (that is one unit) up from the lowest y coordinate: -5 + 1 = -4

Then the center of the circle is located at (-7, -4)

Answer:

An aluminum bar 4 feet long weighs 24 pounds

Step-by-step explanation:

Answer:

There are 24 avocados in each crate.

Step-by-step explanation:

This is a division problem.

8640/360 = 24

There are 24 avocados in each crate.

Step-by-step explanation:

There is 1 root at x = 1, where the function crosses the x-axis.

There are 2 roots at x = -2, where the function touches the x-axis but does not cross.

So there are 3 real roots total.

The function is:

y = (x − 1) (x − (-2))²

y = (x − 1) (x + 2)²

Answer:

Outliers have great effect on the mean and standard deviation of the data set

Step-by-step explanation:

Mean =(43+37+50+51+58+52+45+45+58+130)/10

Mean= 579/10

Mean = 57.9

Arranging in ascending order

= 37,43,45,45,50,51,52,58,58,130

Median= (50+51)/2

Median= 101/2

Median= 50.5

IQR= (130-37)/2

IQR= 93/2

IQR= 46.5

Standard deviation

=√(((37-57.9)²+(43-57.9)²+(45-57.9)²+(45-57.9)²+(50-57.9)²+(51-57.9)²+(52-57.9)²+(58-57.9)²+(58-57.9)²+(130-57.9)²)/10)

Standard deviation= 25.1

1.5*(46.5)= 69.75

The number more than 69.75 is 130 and it's the outlier

Without outlier

Mean= (43+37+50+51+58+52+45+45+58)/9

Mean = 449/9

Mean = 49.88

Arranging in ascending order

= 37,43,45,45,50,51,52,58,58

Median= 50

IQR= (58-37)/2

IQR=21/2

IQR=10.5

Standard deviation