what is the definition of prime and composite numbers??please answer fast
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Answer:

A and C

Step-by-step explanation:

multiplying the value by a fraction < 1 will give a value less than the original value.

multiplying the value by an integer greater than 1 will give a value greater than or equal to the original value

A and C have 6,766 multiplied by a fraction < 1 , then

A and C have a value less than 6,766

Answer: A and C

Step-by-step explanation: Every time you multiply a fraction by a whole number, you get less than the whole number

Answer:

A. 18/16 + 22/24 = 49/24

B. 23/13 + 42/15 = 297/65

C. 27/16 + 15/12 = 47/16  

Step-by-step explanation:

18/16 + 22/24

= 54/48 + 44/48

= 98/48

= 49/24

…………………

23/13 + 42/15

=(23×15)/(13×15) + (42×13)/(13×15)

= 345/195 + 546/195

= 891/195  (divide both sides by 3)

= 297/65

……………………………………

27/16 + 15/12

= 81/48 + 60/48

= 141/48  (divide both sides by 3)

= 47/16  

The solution of the equation is given by (-2,-1), This is represented by option C.

A system of equations is a set of equation that have a common solution.

The solution of the equations can be determined by using the Elimination and Substitution method

3x-5y = -1

2x-y = -3

-7x = 14

x = -2

Substituting this value in the equation

3 * (-2) -5y = -1

-6 -5y = -1

-5y = 5

y = -1

Therefore, the solution of the equation is given by (-2,-1), This is represented by option C.

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1. There's so much wrong with the suggested solution that it's hard to pinpoint the exact error. The "logic" is inconsistent - why do the [tex]x[/tex] and constant term stay in the denominator but the [tex]x^2[/tex] term does not?

What should be done is factorization in the numerator and denominator:

[tex]x^2 + 2x - 8 = (x + 4) (x - 2)[/tex]

[tex]x^2 + 6x - 16 = (x + 8) (x - 2)[/tex]

Then in the quotient, the factors of [tex]x-2[/tex] cancel so that

[tex]\dfrac{x^2+2x-8}{x^2+6x-16} = \dfrac{(x+4)(x-2)}{(x+8)(x-2)} = \boxed{\dfrac{x+4}{x+8}}[/tex]

2. Use the same strategy: factorize everything everything you can, then cancel anything you can.

[tex]x^2 - 9 = (x-3) (x+3)[/tex]

[tex]x^2+x-2 = (x+2)(x-1)[/tex]

[tex]x^2+x-12 = (x+4)(x-3)[/tex]

[tex]x^2+6x+8 = (x+4)(x+2)[/tex]

Then using the algebraic properties of multiplication/division, we have

[tex]\dfrac{x^2-9}{x^2+x-2} \div \dfrac{x^2+x-12}{x^2+6x+8} = \dfrac{x^2-9}{x^2+x-2} \times \dfrac{x^2+6x+8}{x^2+x-12} \\\\ ~~~~~~~~= \dfrac{(x-3)(x+3)(x+4)(x+2)}{(x+2)(x-1)(x+4)(x-3)} \\\\ ~~~~~~~~= \boxed{\dfrac{x+3}{x-1}}[/tex]

Applying the distance formula, DE = a. Therefore, the missing information is: A. a.

Distance Formula for determining the distance between two points on a coordinate plane is given as: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

In the proof given, applying the distance formula to find DE, we have:

DE = √[(a + b -  b)² +  (c - c)²}

Simplifying this, we would have:

DE = √(a² + 0²) = √(a²)

DE = a

Therefore, the missing information in the proof is: A. a.

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Answer:

A. a

Step-by-step explanation:

got it right on edge23

Answer:

all real numbers or [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

since both f(x) and g(x) are polynomials, neither of them have restrictions on their domains. Since they can be defined for all real numbers. It's not like the square root which has a domain of (0, infinity), or log x which is defined only from (0, infinity). So adding these two polynomials would result in a domain of all real numbers.

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

m = (y2 - y1)/(x2 - x1)

Using the points on the graph, we have:

m = (2 - 3)/(3 - 4)

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

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Answer:

13400 m

Step-by-step explanation:

The slope is defined as:

[tex]Slope=\frac{Rise}{Run}[/tex]

Substitute slope=13.4, Run=1 km=1000 m :

[tex]13.4=\frac{Rise}{1000}[/tex]

Solve for Rise:

[tex]Rise=13.4\cdot 1000=13400 ~m[/tex]

Step-by-step explanation:

what is the question. what am I to do with those random numbers without a question, I'm just writing all this because they said at least 20 characters so don't get offended but pls give a detailed question

The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

From the question:

Mars: F(x) = 2/3[tex]\sqrt{64x}[/tex]

Therefore, If x = 15

Then:

f (15) =  2/3 [tex]\sqrt[8]{15}[/tex]

= 16/3[tex]\sqrt{15}[/tex]

= 20.7ft/s

Hence, The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

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Answer:

-2

Step-by-step explanation:

The cat will be waiting and meowing at his bowl for 18.3 seconds.

The time it takes the cat to reach the bowl = 3.7 seconds (17/10 + 2)

The time it takes the woman to reach the bowl = 17 seconds (17/1)

The total time it takes the woman to put the food = 22 seconds (17 + 3 + 2)

Waiting time = 18.3 seconds (22 - 3.7)

Distance to the cabinet = 12 meters

Distance to the bowl = 5 meters

Total distance to be covered = 17 meters

Speed of the cat = 10 meters/s

Speed of the woman = 1 meter/s

Thus, since the time it takes is dependent on the speed of both, the cat will be waiting and meowing at his bowl for 18.3 seconds.

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Answer:

24-100, 12-5-22, -4, 37

Step-by-step explanation:

Solving a system of equations, we will see that Nora bought 2 apples and 6 bananas.

Let's define the variables:

We know that She buys 3 times as many bananas as apples.

y = 3*x

The total cost is $5.

x*$1 + y*$0.50 = $5

Then we have a system of equations:

y = 3*x

x*$1 + y*$0.50 = $5

Replacing the first equation into the second one we get:

x*$1 + (3x)*$0.50 = $5

Now we can solve this for x.

x*$1 + x*$1.50 = $5

x*$2.50 = $5

x = $5/$2.50 = 2

So She bought 2 apples, and:

y = 3*x = 3*2 = 6

And 6 bananas.

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Answer: its the last one

Step-by-step explanation:

i guessed and got it right

Answer:

168 kg oats and 252 kg corn

Step-by-step explanation:

2 equations and 2 unknowns

eq 1: x + y = 420

x is the amount of oats

y is amount of corn

eq 2: 9.4x + 3.4y = 5.8*420

solve equation 1 for x

x = 420 - y

substitute the value of x in eq 2

9.4(420-y) + 3.4y = 2436

y = 252

substitute y in eq 1

x + 252 = 420

x = 168

The equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym and has an area of 7000ft²

Let x be the width of the rectangle.

As the area of track along the walls of the gym is 7000ft²

(x - 12)(3x - 12) = 7000

After simplifying:

3x² - 48x + 6856 = 0

Thus, the equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

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[tex]|\Omega|=12+5+6+4=27\\|A|=12+5=17\\\\P(A)=\dfrac{17}{27}\approx63\%[/tex]

Answer: 2

Step-by-step explanation:

By the angle bisector theorem,

[tex]\frac{8}{24}=\frac{DC}{6}\\\\DC=2[/tex]

The length of DC is 2

Angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Given:

AB = 24, AC = 8, and BD = 6

Now, using angle bisector theorem

AB/ AC = BD / DC

24 / 8 = 6 / DC

3 DC= 6

DC = 2

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Using the above conditions ; If m ∠LOM = m ∠JKI,  if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.

An angle is known to be Congruent if its angles do have equal measure."

Note that question, In the said figure of the angles (image attached),

m ∠LOM = m ∠JKI  (congruent angles)              taken as 1      

m ∠MON = m ∠IKH  (congruent angles)             taken as 2  

The one should sum up both the side angle  of m ∠MON in (1) we obtain;

m ∠LOM + m ∠MON = m ∠JKI + m ∠MON

Then one should replace angle  m ∠MON = m ∠IKH from (eqn. 2)  on right hand side and then it will be:

m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH      taken as (3)

Then:

m ∠LOM + m ∠MON = m ∠LON  ( M is said to be the interior point of ∠LON)    taken as (4)

Since m ∠JKI + m ∠IKH = m ∠HKJ  ( I is said to be the interior point of ∠HKJ)            taken as number (5)

Using Number (3) , (4) and (5)  in the image attached, we obtained:

m ∠LON = m ∠HKJ  (Congruent angles)

Therefore, Using the above conditions ; If m ∠LOM = m ∠JKI,  if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.

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Answer:

it took her 18 month

Step-by-step explanation:

if you divide 4500 with 250 you get the ans

The toroid formed by rotating the rectangular figure gives;

a. A toroid

b. 374•π

c. 400•π

d. The surface area will be 4 times the initial surface area

The volume will be 8 times the initial volume

Taking the distance from the y-axis as 8

Width of the rectangle; 2.5

Length; 6

We have;

a. The solid of revolution is a toroid, having sharp corner edges

b. The surface area is found using the surface area of a hollow cylinder as follows;

Outer radius = 8 + 6 = 14

Inside radius = 8

Width = 2.5

Outer area = 2• π × 14 × 2.5 = 70•π

Inner area = 2• π × 8 × 2.5 = 40•π

[tex]{\pi \cdot 14 }^{2} - {\pi \cdot 8 }^{2} = 132 \cdot\pi[/tex]

The surface area of the figure is therefore;

c. The volume of the solid of revolution is found as follows;

[tex]{\pi \cdot 14 }^{2} \times 2.5 - {\pi \cdot 8 }^{2} \times 2.5= 400 \cdot \pi[/tex]

e. When the dimensions are doubled, we have;

The linear scale factor = 2

The area scale factor = 2^2 = 4

Therefore;

The volume scale factor = 2^3 = 8

The volume of the solid following the enlargement, is therefore;

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The degrees of freedom for the numerator of the F ratio can be calculated to be 9.

The degrees of freedom for the numerator can be found to be:

= number of exams graded - 1

Solving gives:

= 10 - 1

= 9

In conclusion, the degrees of freedom for the numerator of the F ratio is 9.

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Consider repeating the study using a larger sample.

Too small a sample may prevent the findings from being extrapolated, whereas too huge a sample may additionally increase the detection of differences, emphasizing statistical variations that are not clinically relevant.

Selecting the proper sample length will increase the chance of detecting an impact, and ensures that the look is both ethical and value-powerful. Repeated measures designs are widely used due to the fact they have got blessings over pass-sectional designs.

Larger sample sizes provide extra accurate mean values, perceive outliers that would skew the information in a smaller pattern and provide a smaller margin of blunders.

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The value of x in the given sector is determined as 7.1.

Total area of the sector = area of the shaded + area of the unshaded

Since shaded and unshaded areas are equal, the value of x is calculated as follows;

πr²θ/360 = πx²60/360 +  πx²60/360

πr²θ/360 = 2(πx²θ/360)

πr² = 2(πx²)

r² = 2x²

x² = r²/2

x² = (10²)/2

x² = 50

x = √50

x = 7.1

Thus, the value of x in the given sector is determined as 7.1.

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The first angle is 33.8° and second angle is 56.2°.

If the sum of the two angles is equal to the measurement of a right angle then the pair of angles is said to be complementary angles.

Complementary angles are the angles whose sum makes 90⁰.

Let's say our first angle is x:

x = first angle

According to the question,

The other angle is 22.4° more than the complementary angle.

Therefore, 22.4° will be added to the other angle.

first angle  = x

second angle = x + 22.4°

Since, complementary angle is equal to the sum of the two angles to be 90°.

∴ x + x + 22.4°  = 90°

    2x = 90 ° - 22.4°

    2x = 67.6°

     x = 67.6° / 2

     x = 33.8°

Thus, the first angle is 33.8° and second angle is 56.2°.

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It is to be noted that the flow rate is 50mL/h for the first instance, and;

100mL/h for the second instance.

Flow rate (Fr) is computed with the following formula:
Fr (mL/h) = Volume (mL)/ Time (Hours)

Time = 1 hour

Volume = 50 mL

It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence,

Hourly flow rate = unknown

To compute for Flow Rate (Fr)

Recall that:

Fr (mL/h) = Volume (mL)/ Time (Hours)

Inserting the values we have
Fr = 50/1

Fr = 50mL/h

We have been given the following:
Time = 0.5 hours (30 minutes = 0.5 hours)

Volume = 50mL

It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence

Fr = 50/0.5

Fr = 100 mL/h

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The two general approaches are qualitative and quantitative.

Forecasting is a technique that uses past data as inputs to make future predictions by determining the direction of trends in the future.

It is an estimation methodology that uses judgment, other than numerical analysis. This type of forecasting depends upon the knowledge of most experienced employees and consultants to provide predictions for future outcomes.

It is a data-based math process that teams use to understand performance and predict future based revenue on the data and the patterns. Forecasting results gives businesses the ability to make informed decisions on strategies and processes to ensure continuous success

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Answer:

Step-by-step explanation:

if the ratio of red to blue circles is 1:3 how many more red circles need to be added to make it a ratio of 3:1

add 8 red =

9/3 = 3/1