what is the sum of the exponents of the prime factors of the square root of the largestperfect square that divides 12! ?

The distance from B to AC can be constructed as

The distance from G to EF can be constructed as

The distance from Q to SR can be constructed as

What is the distance of a line from a point?

A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.

For the first figure,

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the correct answer is A

Always concentrate on point where X or G(X) equals Zero.

For example, here point (0,2), G(X)=2 when X=Zero.

If u tried to Replace X and G(X) in the equations below with these numbers, you would figure out the right answer so easily. Have a nice day!

Check the picture below.

Systematic random sampling is the sampling method is the auditor using for each salesperson.

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

Given,

The sales force for a publishing company is constantly on the road trying to sell books. as a result, each salesperson accumulates many travel-related expenses that he or she charges to a company-issued credit card. to prevent fraud, management hires an outside company to audit a sample of these expenses. for each salesperson, the auditor prints out the credit card statements for the entire year, randomly chooses one of the first 20 expenses to examine, and then examines every 20th expense from that point on.

Systematic random sampling is the sampling method is the auditor using for each salesperson.

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Answer:

k = - 6 , c = 8

Step-by-step explanation:

f(x) = x² + kx + c

given f(2) = 0 , substitute (2, 0 ) into f(x)

0 = 2² + 2k + c

0 = 4 + 2k + c ( subtract 4 from both sides )

- 4 = 2k + c → (1)

given f(- 3) = 35 , substitute (- 3, 35 ) into f(x)

35 = (- 3)² - 3k + c

35 = 9 - 3k + c ( subtract 9 from both sides )

26 = - 3k + c → (2)

subtract (2) from (1) term by term to eliminate c

- 4 - 26 = 2k - (- 3k) + (c - c)

- 30 = 2k + 3k

- 30 = 5k ( divide both sides by 5 )

- 6 = k

substitute k = - 6 into (1) and solve for c

- 4 = 2(- 6) + c

- 4 = - 12 + c ( add 12 to both sides )

8 = c

then

k = - 6 and c = 8

A sampling distribution of the sample proportion with n=15 and p=0. 65 is stimulated here when The probability of tails of a weighted coin is 0. 65. The number of tails is noted each of the 15 times the coin is tossed.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

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Answer:

2.5 - 2(-3-0.5) + 2(n) > 10.75

Step-by-step explanation:

Step 1: two and 5 tenths is 2.5

Step 2: 2 times the quantity of the difference of negative three and one half is 2(-3-1/2)

Step 3:  two times a number is at least ten and three quarters = 2(n) > 10.75

Combine: 2.5 - 2(-3-0.5) + 2(n) > 10.75

Answer: 1424850

Step-by-step explanation:

2.3 x 10³ = 2300

5.9 x 105 = 619.5

2300 x 619.5 = 1424850

Pls thank and rate <3 (and branliest if ok with u :)))

The value of x that is a counterexample to the student's conjecture is (a) x = -1/4

From the question, we have the following statement that can be used in our computation:

x = Non-negative number

Student's conjecture:

x + 4 < x²

Using the options, we have:

(a) x = -1/4

x + 4 < x²

-1/4 + 4 < (-1/4)²

3.75 < 1/16 -- false

(b) x = -4

x + 4 < x²

-4 + 4 < (-4)²

0 < 16 -- true

(c) x = 1

x + 4 < x²

1 + 4 < (1)²

5 < 1 -- false

This cannot be used because x is non-negative

(c) x = 4

x + 4 < x²

4 + 4 < (4)²

8 < 16 -- true

The false statements are the counterexamples

Hence, the value of x is (a) x = -1/4

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Complete question

Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?

Responses

A. ​ x=−1/4 ​

​B. ​ x=−4 ​ ​

C. x = 1

D. x = 4

Answer:

  $1280

Step-by-step explanation:

You want the cost of flooring a cubic 4096 ft³ room at $5 per square foot.

Each dimension (length, width, height) of the room is the edge length of a cube with a volume of 4096 ft³.

  V = s³

  4096 = s³

  ∛4096 = s = 16 . . . . feet

The floor area is the square of the edge length:

  A = s²

  A = (16 ft)² = 256 ft²

At $5 per square foot, the cost of flooring will be ...

  ($5/ft²)(256 ft²) = $1280

The hardwood floors will cost $1280.

Answer: zero slope

Step-by-step explanation:

When the slope of a line is zero it creates a horizontal line.

What is Angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

From the figure, we can tell that a transversal is passing through the two parallel lines which makes corresponding angles.

In the given figure 14x+7 and 10x+5 are the two angles formed by the transversal.

14x+7=10x+5

Now take all the variable terms to one side

14x-10x=5-7

4x=-2

Divide both sides by 4

x=-2/4

Divide numerator and denominator by 4

x=-1/2

Hence the value of x is -1/2

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Answer:

y = 1x + -2

Step-by-step explanation:

Step 1: Calculating Slope (m).

m = y2 - y1 / x2 - x1

m =  -4 - 0 / -2 - 2

m = -4 / -4

m = 1

Now put value of m in equation...

y = 1x + b

Step 2: Calculating Y-intercept (b).

Lets choose the first point, ( 2, 0) for calculating y-intercept:

y = m ( x ) + b

0 = 1 ( 2 ) + b

0 = 2 + b

-2 = b

b = -2

Now put value of b in equation for your final answer...

y = 1x + -2

Hope this helps!

Answer:

y = -1.5

Step-by-step explanation:

use the method y2 - y1 / x2 - x1

The probability of having at least one employee not have a college degree is 0.595

Here it is given that the 74% of employees have a college degree.

Hence, the probability of one employee having a college degree is

74/100

= 0.74

The probability that an employee does not have a college degree is

1 - 0.74

= 0.26

Hence

The above problem is clearly a Binomial distribution. with n = 120 and p = 0.26

"success" is when one employee does not have a college degree.

Therefore the probability that at least 1 employee does not have a college degree is

P(X≥1)

= 1 - P(X = 0)

A binomial distribution with sample n and probability p has a PMF

ⁿCₓ  X  pˣ X  (1 - p)ⁿ⁻ˣ

where x is a random variable

Here

n = 3

p = 0.28

x = 0

Hence we get

³C₀  X  0.26⁰ X  (0.74)³

0.405

Therefore,

P(X≥1)

= 1 - 0.405

= 0.595

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Answer:

u=8

Step-by-step explanation:

48+3u=9u

-3u both sides

48=6u

divide by 6 on both sides

8=u

Answer:

87.08.

850.08 - 763 = 87.08.

Salinity and density decrease as temperature rises. Salinity and density, therefore, have a negative relationship with temperature. The density rises as salinity rises. As the temperature drops, ocean water becomes denser. Therefore, water becomes denser as it becomes colder. The density of seawater also rises as salinity does.

Water that is less dense floats above water that is denser. The warmer water will float on top of the colder water if there are two layers of water with the same salinity. However, there is a catch! Salinity has less of an impact on water density than temperature does. Therefore, if the layer with higher salinity is considerably warmer than the layer with lower salinity, the layer with higher salinity can actually float on top of the layer with lower salinity.

As you descend to the ocean's bottom, the temperature of the water continues to drop. So, as you descend to the ocean's bottom, the density of the water keeps rising. The deep ocean is divided into layers, with the lightest water at the top and the densest water at the bottom. The ocean's depths have horizontal circulation. In other words, water flows in strata of equal density.

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Answer:

x = 36

The measure of the exterior angle is 114°

The remote interior angles are 24° and 90°.

Step-by-step explanation:

The angle marked 3x + 6 is the exterior angle. The other two marked angles are called "remote interior angles"

The two remote interior angles added together equals the exterior angle.

3x+6 = 24° + 2x + 18

Combine like terms.

3x + 6 = 2x + 42

Subtract 2x from both sides.

x + 6 = 42

Subtract 6 from both sides.

x = 36

If required, use the x=36 to find the measure of the exterior angle.

3(36) + 6

= 108 + 6

= 114°

Or find the measures of the remote interior angles.

2(36) + 18

= 72 + 18

= 90°

The remote interior angles are 24° and 90°.

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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The equation of straight line having

(a) gradient -4 and coordinates (-2,1) is  4x + y [tex]=[/tex] -7

(b) gradient 0 and coordinates (-1,21) is y = 21 .

In the question ,

the gradient and coordinates of the point on the line is given .

we have to find the equation of the straight line .

Part(a)

the gradient of the line [tex]=[/tex] -4 ,

the coordinates of a point on the line = (-2,1)

So , the equation of the line is

(y - 1) = (-4)*(x -(-2))

y - 1 = -4(x + 2)

y - 1 = -4x - 8

4x + y = -8 + 1

4x + y = -7

the equation is 4x + y = -7  .

Part(b)

the gradient of the line = 0 ,

the coordinates of a point on the line = (-1 , 21)

So , the equation of the line is

(y - 21) = 0(x-(-1))

y - 21 = 0

y = 21

the equation of the line is y = 21  .

Therefore , The equation of straight line having  (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7  and (b) gradient 0 and coordinates (-1,21) is  y = 21  .

The given question is incomplete , the complete question is

Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

(a) -4, (-2 , 1)

(b) 0, (-1, 21)

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The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.

In this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:

y = m · x + b

Where:

And the relationship between the slopes of two perpendicular lines:

m · m' = - 1

Where:

And the slope of the original line can be found by the secant line formula:

m = Δy / Δx

And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:

M(x, y) = 0.5 · A(x, y) + B(x, y)

Where:

First, find the slope of the line segment by secant line formula:

m = [- 1 - (- 5)] / (- 5 - 9)

m = - 4 / 13

Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:

m' = - 1 / m

m' = - 1 / (- 4 / 13)

m' = 13 / 4

Third, determine the midpoint of the line segment by the midpoint formula:

M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)

M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)

M(x, y) = (2, - 3)

Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:

b = y - m' · x

b = - 3 - (13 / 4) · 2

b = - 3 - 26 / 4

b = - 3 - 13 / 2

b = - 19 / 2

The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.

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Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

In the given question,

Arianna is going to use a computer at an internet cafe.

The cafe charges an initial fee to use the computer and then an additional price per minute of usage.

Let C represent the total cost of using a computer for t minutes at the internet cafe.

We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

The additional change per unit = Slope of the linear function

The linear function C(t) given as;

C(t)=mt+b...............(1)

where m=slope and b=vertical intercept

Then, Slope = change in C(t)/change in t

Slope = ∆C(t)/∆t

We taking he given two point to find the slope

C(t) = 9.90 for t=1

C(t) = 15.30 for t=7

∆C(t)=15.30-9.90

∆C(t)=5.40

∆t=7-1

∆t=6

So, The required slope=5.40/6

The required slope=0.9=m

Now finding the value of b.

As we know that,

C(t) = 9.90 for t=1

The equation using this should be

9.90=m×1+b

Now putting the value of m in this equation

9.90=0.9×1+b

9.90=0.9+b

Subtract 0.9 on both side, we get

b=9

Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Putting the value in equation (1)

15.75=0.9t+9

Subtract 9 on both side

15.75-9=0.9t+9-9

0.9t=6.75

Divide by 0.9 on both side

0.9/0.9 t=6.75/0.9

t=7.5

Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

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(a) Probability that third apple is red from three selected apple one after one is 22/23.

(b) Probability that exactly two of the three apples are red is 0.3012

In the question we have,

total number of apples in a box = 25

number of red apples in a box = 22

number of green apples in a box = 3

Now, three apples are selected at random,one after other without replacement and first two apples are green .

(a) Then number of apples remained in a box after two green apples withdraw = 23

probability that third apple is red = 22/23

(b) The following are possible number of sample spaces for exactly two of the three apples are red

where , R--> red apple and G--> green apple

For first sample space , RGR i.e first and last apples are red

probability that first and last apples are red from three withdraw apples or P(RGR) = 22/25× 3/24× 21/23 = 0.1004

similarly, P(RRG) = 22/25×21/24×3/23 = 0.1004

P(GRR) = 3/25×22/24×21/23 = 0.1004..

Probability that exactly two apples are red = P(RRG)+ P(RGR)+ P(GRR) = 3(0.1004) = 0.3012

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Answer:

9:55 a.m.

Step-by-step explanation:

Sothy starts at 8 a.m. and plans for 10,000 steps. At 8:23 a.m., she walked 2000. We are solving for when she reaches 10,000 steps.

This means that she walks 2,000 steps in 23 minutes

If she walks 2,000 steps in 23 minutes, then we can multiply by 5 to get 10,000 steps in 115 minutes.

Now, we need to add 115 minutes to 8 a.m.

we can round 115 minutes to 120 minutes.

If you add 120 minutes to 8 a.m., you get 10 a.m.

Now subtract the 5 minutes you added earlier to get 9:55 a.m.

Answer:

(0.5, 1.5 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (- 4, 4 ) and (x₂, y₂ ) = B (5, - 1 ) ,then

M = ( [tex]\frac{-4+5}{2}[/tex] , [tex]\frac{4-1}{2}[/tex] ) = ( [tex]\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = (0.5, 1.5 )

Answer:

The midpoint is at ( 1/2, 3/2)

Step-by-step explanation:

Midpoint

To find the x coordinate of the midpoint

Add the x coordinates of the endpoints and divide by 2

( -4+5)/2 = 1/2

To find the y coordinate of the midpoint

Add the y coordinates of the endpoints and divide by 2

( 4+-1)/2 = 3/2

The midpoint is at ( 1/2, 3/2)

James average pay per hour is $17.40

How to find James average pay per hour

information given in the problem are

Last year, James earned £2,100 per month

This year, he's had a 6% increase in his monthly pay

35 hours per week for 46 weeks in the year

The question is a percentage problem

6% increase a factor of  1.16

2100 * 1.16 = 2436

number of hours in a month

35 hours = 1 week

? hours = 4 weeks

? = 4 * 35

? = 140 hours in 4 weeks = 1 month

James average pay per hour is gotten form the calculation below

if 140 hours pays 2436 then1 hour will pay ?

140 = 2346

1  =  ?

cross multiplying

? * 140 = 2436 * 1

? = 2436 / 140

? = $17.40

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The statement that describes the x-intercept of the graph is: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.

The x-intercept of a linear relationship between variable x and y can be described as the value of x when the value of y is zero.

On a graph, the x-intercept is the point on the graph where the line intercepts the x-axis. The value of y at this point is 0.

in the graph that shows a linear relationship between the number of monthly payments made and the remaining balance left on a loan, the line intercepts the x-axis at 60.

Therefore, it means: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.

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Step-by-step explanation:

those are the answers if I am wrong you can correct

There are 52 cards in the deck and so the probability of guessing the card right is 1/52.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

We can find this probability by seeing that

=1/4×1/13

=1/52

Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.

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