Divide the following and then check by multiplying.
7)84
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
OA. The quotient does not have a remainder. The quotient is
B. The quotient has a remainder not equal to 0. The quotient is
OC. The quotient is undefined.

By using the formula for the mean:

(x₁ + x₂ + ...)/N

We will see that the mean is 7 minutes.

If we have a set of N elements:

{x₁, x₂, x₃...}

The mean of these values is given by:

(x₁ + x₂ + ...)/N

Here we have a set of 3 points, such that the points are {5, 6, 10} the mean of these points is:

M = (5 + 6 + 10)/3

M = 21/3

m = 7

The mean of the tmes is 7 minutes.

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If Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. The number of gray shirts that Joanie have is: 2.

Let x represent the number of gray shirts

Let Joanie black shirts = 3x + 3

Let Joanie white shirts =  5x - 1

Let Joanie brown shirts =   2x

So,

3x + 3 = 5x - 1

Substract 3 from both side

3x + 3-3 = 5x - 1 -3

3x = 5x -4

Substract 5x from both side

3x-5x = 5x -4 -5x

-2x =  -4

Divide both side by

x = -4/-2

x =2

Therefore, Joanie has 2 gray shirts.

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If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution.

The option (a) is n=3.

If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution. If n=3 is obtained after solving the equation, then the student should chose option (a) as the answer.

The option (b) is "no solution".

While solving an equation, if we obtain an equation which is mathematically false, then the equation will have no solution. So, no solution is chosen when no value is obtained for n and the final equation is mathematically false.

The option (c) is "infinitely many solutions".

While solving an equation, if we obtain an equation which is mathematically correct such as 0=0, 7=7 etc., then the equation will have infinietly many solutions. So, infinitely many solutions is chosen when no value is obtained for n and the final equation is mathematically correct.

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Answer:

B. 6p²+5p-6

Step-by-step explanation:

[tex]\bf \left(2p+3\right)\left(3p-2\right)[/tex]

Let's apply the FOIL method:-

[tex]\bf \left(2p+3\right)\left(3p-2\right)=[/tex]

[tex]\bf 2p\times \:3p+2p\left(-2\right)+3\times\:3p+3\left(-2\right)[/tex]

[tex]\bf 6p^2-4p+9p-6[/tex]

[tex]\bf 6p^2+5p-6[/tex]

Therefore, option B. 6p²+5p-6, is your answer!

__________________

Hope this helps!

Have a great day!

The maximum number of zeroes in a generic equation with the form axe? + bx4 + cx3 + dx2 is 5.

a) [tex]$ax^{5}[/tex]

b) Factor 2x3 - 9x2 + 7x + 6  is

(x - 3) (x -2) (2x + 1)

c) x = -b / 2a

Replace x by -2, from the vertex:

-2 = -b / 2a

Solve for b:

-b = -4a

Or

b = 4a

By evaluating the equation with the vertex's x-value, we can determine the y-value from the vertex:

y = ax2 + 4ax - 6

Simplify, 6 for y, and -2 for x:

6 = a(-2)2 + 4a(-2) - 6

6 = 4a - 8a - 6

solve for a:

a = -3

Simplifying the above equation,

b = 4a, b = -12

The value for a is -3.

The value for b is -12

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The solution for the inequality |x +1|>-3 is x > -4 or x < -4.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To solve the inequality |x + 1| > -3, we need to consider two cases:

x + 1 > -3: In this case, we can subtract 1 from both sides to get x > -4.

x + 1 < -3: In this case, we can subtract 1 from both sides to get x < -4. However, we also need to reverse the inequality symbol because we are multiplying or dividing by a negative number.

So the solution for the inequality is x > -4 or x < -4.

To get the final solution, we need to consider the combined solution from both cases:

x < -4 or x > -4

This represents as follows:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

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A statistical test is more likely to find a significant increase in mean life expectancy if it is based on a very large random sample and a 1% significance level is used.

As per the given data

Vigorous exercise helps people live several years longer.

The mild activities like slow walking extend life is not clear.

The added life expectancy from regular slow walking is just 2 months.

Here we have to determine that when a statistical test is more likely to find a significant increase in mean life expectancy.

The increase in life expectancy regarding regular slow walking should be considerably greater than 2 months, which means that the a larger sample is needed to give a more precise result

The chances of finding significant results increases when we increase sample size or use a higher significance level.

So, among the given options, significant results will be achieved

If it is based on a very large random sample and a 1% significance level is used.

Therefore option (b) is correct.

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y = ln( [tex]\frac{x^2+1}{2}[/tex])  is the required equation.

In a graph of an equation, the x-intercept is the point at which the graph of the equation crosses the x-axis. It is the point where the y-coordinate is equal to 0. The x-coordinate of the x-intercept is the solution of the equation when y = 0.

Given that the slope at point (x,y)

and we know that slope at any find is dy/dx

so dy/dx = [tex]xe^-^y[/tex]

=> dy/[tex]e^-^y[/tex] = xdx

=> [tex]e^y[/tex] dy = x dx

intergrating both side we get:

[tex]e^y[/tex] = x²/2 + c

where c is a constant

given x intercept is 1

[tex]e^0[/tex] = 1²/2 + c

=> 1 = 1/2+c

=>  c= 1/2

so [tex]e^y[/tex] = x²/2 + 1/2

taking ln on both side we get:

y = ln( [tex]\frac{x^2+1}{2}[/tex])  is the required equation.

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It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

Option(B) is the correct answer. The answer is - Adding data from a student who is 154 cm tall and weighs 69kg.

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To determine the service fee as a percentage of the deposited amount, we can use the following formula:

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Service fee percentage = (Service fee / Deposited amount) x 100

In this case:

Service fee percentage = (31.74 / 2239.10) x 100 = 1.41%

So, the service fee for depositing the amount of R2239.10 was 1.41% of the deposited amount.

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The two equivalent expressions that could be used to find the total number of chocolate pieces that Luisa has are given as follows:

To obtain the number of pieces that Luisa has, we must consider that:

Hence the multiplication operation giving the number of pieces is given as follows:

4 x 10 x 8.

The associative property of multiplication states that the order in which 3 or more terms are multiplied does not change the product, hence the equivalent expressions are given as follows:

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The value of TU is 117.

What is a line segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

Here, we have

Given: U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3.

We have to find the value of TU.

TV = TU + UV

20x − 3 = 11x − 15 + 10x

20x − 3 = 21x - 15

-3 + 15 = 21x - 20x

12 = x

Now, we have TU = 11x − 15.

We put the value of x on TU and we get

TU = 11x − 15

TU = 11(12) - 15

TU = 132 - 15

TU = 117

Hence, the value of TU is 117.

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Answer:

-----------------------

The line of sight is the hypotenuse of the 45° right triangle.

As per the property of the 45° right triangle, the length l is:

Answer:77.7f

Step-by-step explanation: pythagorean theorem

55*55=3025

3025*2=6050

square root 6050=77.7

The puffs that the patient will take daily include:

1 puff every 4 hours for 24hrs = 6

1 puff every 6 hours for 24hrs =4

2 puffs every 4 hours for 24hrs =12

2 puffs every 6 hours for 24 hrs =8

From the information, a physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.

In this case, it should be noted that puff every 4 hours for 24hrs will be 6 times. Also, 1 puff every 6 hours for 24hrs will be 4 times.

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The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.

The probability of randomly landing in a particular region of a circular dartboard is 1/6. This means that each region of the dartboard is equivalent in size, and thus has the same central angle. Since the dartboard is circular, the total measure of the central angles must add up to 360 degrees. Therefore, the measure of the central angle of each section of the dartboard is 360 divided by 6, which is equal to 60 degrees.

The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.  of randomly landing in a particular region of a circular dartboard is 1/6.

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Answer:

x=32

x+1=33

Step-by-step explanation:

let the first consecutive integer be 'x'

let the second consecutive integer be 'x+1'

x+x+1=65

2x+1=65

2x=65-1

2x=64

x=64÷2

x=32

x+1=(32+1)

x+1=33

The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption.  P(terriers) = 85% is likely Option B

Generally, Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.

A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.

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The number of combinations that can be made among eight people is given as follows:

56 combinations.

As there are different roles, the order is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

For this problem, two people are selected from a set of 8, hence the number of combinations is given as follows:

P(8,2) = 8!/6! = 8 x 7 = 56 combinations.

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except point (5, 7) all given coordinates are on the line.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

given, an equation 2x−y=20

to check what are the coordinate of the equation:

The easiest way to find out if a point falls on a specific line is to plug the first value of the point in for x and the second value for y.

Thus, For Coordinates(10, 0)

2x−y=20

=> 2 * 10 - 0 = 20

=> 20 = 20

Thus Coordinates are on the line.

Thus, For Coordinates(15, 10)

2x−y=20

=> 2 * 15 - 10 = 20

=> 30 -10 = 20

=> 20 = 20

Thus Coordinates are on the line.

Thus, For Coordinates(5, 7)

2x−y=20

=> 2 * 5 - 7 = 20

=> 3 = 20

Thus Coordinates are not on the line.

Thus, For Coordinates(-4, -28)

2x−y=20

=> 2 * -4 - (-28) = 20

=> -8 + 28 = 20

=> 20 = 20

Thus Coordinates are on the line.

Therefore, except point (5, 7) all given coordinates are on the line.

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We can substitute the given values into the expression to find the result:

3s - 4q - m² = 3(-24) - 4(-3) - 4² = 72 + 12 - 16 = 60.

So the expression equals 60 when m= 4, q= -3, and s = -24.

The answer for  2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3 is 32185024125880310

Let x = 2, y = 56799065, z = 569050890562, a = 69, b = 420 and c = 9.

The equation is: 2x + y × z + a × b + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × y × 3 × z × 3

We can calculate this equation as follows:

2 × 2 + 56799065 × 569050890562 + 69 × 420 + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × 56799065 × 3 × 569050890562 × 3

= 4 + 32185023742042530 + 28380 + 145800 - 1365466177461590

= 32185024125880310

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Answer: your answer is c

Step-by-step explanation:

You prοbably know our football and basketball teams, but we have 21 Divisiοn I varsity programs that all raise the bar whenever they compete.

There were 465 people whο were surveyed in all.

The attendance at the FSU-Marist game was (M), n(M)=240.

The attendance at the FSU-Butler game was (B), n(B)=200.

The tοtal number οf spectators for the FSU-NC State game was n(NCS)=240.

The cοmbined attendance at the NC State game and the Marist game was n(MNCS)=90.

The cοmbined attendance at the Butler vs. NC State game was n(NCSB)=80.

The cοmbined attendance at the Butler and Marist games was n(BM)=100.

n(MBNCS)=30 peοple attended all three of the games.

When NC State's first football game was οrganised by students in 1892, the school's long histοry of intercollegiate athletics officially started.

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The number of times that you would expect to roll the numbers, when rolling an unbiased dice is:

a. 100 times

b. 300 times

c. 300 times

d. 200 times

e. 200 times

There is only a single 1 in a six sided unbiased dice so the number of rolls is:

= 1 / 6  x 600

= 100 times

There are 3 even numbers ( 2, 4, and 6) so the number of rolls :

= 3 / 6 x 600

= 300 times

There are 3 odd numbers ( 1, 3, 5 ) so number of rolls is:

= 3 / 6 x 600

= 300 times

There are 2 numbers less than 3 which are 1 and 2 :
= 2 / 6 x 600

= 200 times

There are 2 prime numbers ( 2 and 3 ):

= 2 / 6 x 600

= 200 times

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The measure of the angle opposite the side of length 3 is approximately 53.13 degrees.

To find the measure of the angle opposite the side of length 3, we need to use the inverse sine function. The inverse sine function can be written as sin^−1(x). We can use the Pythagorean Theorem to calculate the side length of the triangle, which is 3^2 + 4^2 = 5^2. Therefore, we can use the inverse sine function to calculate the measure of the angle opposite the side of length 3. To do this, we will take the ratio of the side of length 3 to the hypotenuse, which is 3/5. We can then plug this value into the inverse sine function, which gives us sin^−1(3/5). Calculating this value gives us approximately 53.13 degrees, which is the measure of the angle opposite the side of length 3.

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The answer is D. I and II only. The number of people who chose A as their favorite brand could be 30 or 35 since x is rounded to the nearest integer, which is 3. However, it cannot be 45 since 3 is the nearest integer.

1. x is rounded to the nearest integer, which is 3

2. If x is equal to 30, then the number of people who chose A as their favorite brand would be 30

3. If x is equal to 35, then the number of people who chose A as their favorite brand would be 35

4. If x is equal to 45, then the number of people who chose A as their favorite brand would be 45

5. Since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45

6. Therefore, the answer is D. I and II only.

1,150 respondents were asked to select their preferred brand among brands A, B, and C of laundry detergent. x% of those polled indicated that A was their preferred brand. The outcome is 3 if x is rounded to the nearest integer. This means that x could be 30, 35, or 45. However, since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45. Therefore, the answer is D. I and II only, meaning that the number of people who chose A as their favorite brand could be 30 or 35. This is because if x is equal to 30, then the number of people who chose A as their favorite brand would be 30 and if x is equal to 35, then the number of people who chose A as their favorite brand would be 35.

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Answer:

2/5 of income put into savings

Step-by-step explanation:

Let Kory's income be X

1/3 of his income goes to taxes so taxes are X/3

Remaining is (1-  2/3) of income = (2/3 ) X

He spends 4/5 of this remaining amount

So balance after expenditure = (1- 4/5) = 1/5 of the remaining income and this amount is put into savings

Fraction of income in savings = 1/5 x 2/3 X = (2/15)X

So fraction put into savings account is 1/5 of total income

If you find it confusing to work with fractions such as these, I suggest an alternate approach which may make it easier to understand

Pick an amount for total income. Since the denominators are 3 and 5, choose an amount which is divisible by both 3 and 5 or in other words divisible by 15

Let's choose 300, a convenient number

Tax Paid = 1/3 x 300 = 100

Income after tax = 300 - 100 = 200
which is same as 2/3 x 300

Spending = 4/5 x 200 = 160

Balance in savings = 200 - 160 = 40 same as 1/5 x 200

So amount in savings as a fraction of income = 40/300 = 2/15

Karen divided 560.9 by 10³ and got a quotient of 0.5609 ,therefore he is right.

What do you mean by division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

What do you mean by quotient ?

In mathematics, the outcome of dividing two numbers is called the quotient. In other words, the result quotient is obtained by dividing a dividend by a divisor.

How to Divide a Long Number by Decimals?

Hence, Karen divided 560.9 by 10³ and got a quotient of 0.5609.

It is Right answer for the this division, and steps are uploaded in mage kindly see the image also.

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