A teacher grades 27 tests in 3 hours.

find the constance of variation

Distance between (1,4) and (-2,8) is 5 units.

The separation between two points. The coordinates of two points in space are used in the formula.

In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula.

Let distance between two points ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) be 'd' then,

d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

We are given two points (1,4) and (-2,8)

So, using formula for distance we get,

d= [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

=[tex]\sqrt{(-2-1)^{2} + (8-4)^{2} }[/tex]

d [tex]\sqrt{(-3)^{2} + 4^{2} } \\=\sqrt{25} \\=5[/tex]

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The probability that no digit appears more than twice is 0.648.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

We will choose each digit of 5-digit numbers at random from digits 0,1,2,..,9.

We have to compute the probability that no digit appears more than twice.

So, we have to form a five-digit number say "abcde".

Now, for 'a' we have 10 choices.

For 'b' we have again 10 choices because a digit can appear at most two.

For 'c' we have 9 choices because the digit in 'a' can not be chosen as a digit can appear at most two.

For 'd' we have again 9 choices by a similar argument.

Finally, for 'e' we have 8 choices because the digit chosen previously can not be repeated more than twice.

The total number of such 5-digit numbers is = 10*10*9*9*8 = 64800.

Now, a total number of 5-digit numbers = 10*10*10*10*10 = 100000.

Hence, the probability that no digit appears more than twice is given by,

= 64800/ 100000

= 0.648

Hence, the probability that no digit appears more than twice is 0.648.

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Answer:

Use the formula y-3= 1/4(x--7) ---> y-3= 1/4(x+7)

4.75 is the y intercept

After Solving the provided question, the Michelle's point value after the third round is -4.5 by the third round

A value is computed using operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or numbers, the math operator's symbol has predetermined rules.

Mathematical operations like addition (+), subtraction (-), multiplication (*), and division (**) take precedence over one another. Neither of the two operators can be used to solve an equation by itself. The brackets in any equation, whether arithmetic or algebraic, must be evaluated first, according to the order of operations principles, which we must abide by. The second place is where the order will be determined. After evaluating addition and subtraction, we'll analyze multiplication and division.

[tex]she starts off with a negative 2.3 of you add positive 4.5 = > (-2.3) + 4.5 = 2.2[/tex]

but after that, she lost another 6.7 points, leaving her with a negative score of 4.5.

[tex]= > 2.2 - 6.7 = ( -4.5 )[/tex]

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In determining a mean, the 90% C.I. is more accurate than the 95% C.I.

A confidence interval is the mean of your estimate plus or minus the range of that estimate's variability.

You can reasonably anticipate that if you repeat the test, your estimate will fall within these values.  In statistics , confidence is another name for probability

A statistician who declares that they have a 95% confidence level has basically seen one possible interval out of many possible ones, and 19 out of 20 of those intervals include the correct value of the parameter.

In determining a mean, the 90% C.I. is more accurate than the 95% C.I.

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375 hours  should be the warranty period so that only 1% of them fail before the warranty is over.

As per the details share in the above question are as follows,

A certain type of electric bulb is a random variable that is normally distributed with a mean of μ=500 hours

The standard deviation σ=20 hours

We have to determine what should be the warranty period so that only 1% of them fail before the warranty is over?

Now let us consider,

Probablity Z=(X-μ)/σ

Solving further we get,

P(Any bulb fail before 500 hours)

= P(z < (500 - 500)/20)

= P(z < 0) = 0.50

Thus,

P( Failed before 500 hours)

[tex]= (0.50)^3[/tex]

= 0.125

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When working with rational functions, your main concern to not divide by 0.  Dividing by 0 can't be done.

So, you need to look at the denominator of your fraction and figure out what values of g will make that denominator become 0.

Option #1 is to plug in each option from your list to see which ones make the denominator equal 0.  If that g-value makes the denominator equal zero, then it has be excluded.

Option #2 is to set the denominator equal to 0 and solve that equation:
    g^3 - 4g^2 - 12g = 0

To solve this, you could do it by factoring.

    g^3 - 4g^2 - 12g = 0     

     g ( g^2 - 4g -12) = 0

   g ( g - 6 ) ( g + 2) = 0

This splits into:
   g = 0, g = 6, g = -2

So those are the three values of g that you cannot use.

g ≠ 0; g ≠ 6, g ≠ –2

To find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

The cost of 4 small greeting cards is 4 * $1.80 = 4 * 1.8 = $7.20.

The cost of 3 large greeting cards is 3 * $3.85 = 3 * 3.85 = 11.55.

The total cost of 4 small greeting cards and 3 large greeting cards is $7.20 + $11.55 = 7.2 + 11.55 = 18.75.

To find the cost of x small greeting cards and y large greeting cards, you can use the following equation:

cost = x * $1.80 + y * $3.85

Substituting the values of x and y into this equation will give you the total cost of the greeting cards.

Hence, to find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.

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Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.

What is the system of linear equations?

A system of linear equations is a collection of two or more linear equations, and a solution to a system of linear equations consists of values of each of the unknown variables in the system that satisfies all of its equations or makes them true.

Let L be the number of lions, T be the number of tigers, and B be the number of bears. We can set up the following system of equations to represent the given information:

L + T + B = 40

L = T + 4

B = T - 3

We can solve this system of equations using substitution. Starting with the second equation, we can solve for T:

T = L - 4

Substituting this expression for T into the third equation, we get:

B = L - 4 - 3

B = L - 7

Substituting this expression for B into the first equation, we get:

L + L - 4 + L - 7 = 40

3L - 11 = 40

3L = 51

L = 17

Now that we know the number of lions, we can substitute this value back into the equation T = L - 4 to find the number of tigers:

T = 17 - 4

T = 13

Finally, we can substitute these values for L and T into the equation B = L - 7 to find the number of bears:

B = 17 - 7

B = 10

Hence, Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.

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Answer:

Step-by-step explanation:

9 bytes2

Answer:

Step-by-step explanation:

You want the explicit formula for each of the geometric sequences, and the 7th term.

The explicit formula for a geometric sequence with first term a[1] and common ratio r is ...

  a[n] = a[1]·r^(n-1)

The explicit formula is ...

  a[n] = -4·(-3)^(n-1)

The 7th term is ...

  a[7] = -4·(-3)^(7-1) = -2916

The explicit formula is ...

  a[n] = 12·(1/4)^(n -1)

The 7th term is ...

  a[7] = 12·(1/4)^(7-1) = 3/1024

Answer:

27

Step-by-step explanation:

3*3*3 equals 27. I hope this helps.

Answer: The solution to this problem is 27.

If the scale of drawing is 1 inches : 10  feet and the real horse height is 25 feet, then the height of the horse in drawing is 2.5 inches

The scale of drawing the horse = 1 inch : 10 feet

Therefore in scale

The height of the horse in drawing = 1 inch

The  height of the horse = 10 feet

The original height of the horse = 25 feet

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 10 feet = x inches : 25 feet

1 / 10 = x / 25

1 × 25 = 10x

10x = 25

x = 25/10

x = 2.5 inches

Therefore, the height of the horse in drawing is 2.5 inches

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Answer: 38 nickels, 24 quarters

Step-by-step explanation:

x=number of quarters

y=number of nickels

x + y = 62

$0.25x + $0.05y = $7.90

solve for x in terms of y, then substitute into the 2nd equation:

x = 62-y

.25(62-y) + .05y = 7.90

15.5 - .25y + .05y = 7.90

15.5 - .20y = 7.90

-.20y = -7.6

y = -7.6/-.20

y = 38

now solve for x:

x  + 38 = 62

x = 62-38 = 24

x = 24

Browne County shows a population bigger than Orange County in 2015.

Herein we find the case of two cities in the United States that changes exponentially in time, the population of Browne County decrease in time, while the population of Orange County decreases at a lower rate in time in time. Exponential model is introduced below:

p'(n) = p · (1 + r / 100)ⁿ

Where:

Now we proceed to build the equation that explain the growth of the two cities:

Browne County (p = 87,000, r = - 10)

p'(n) = 87,000 · 0.9ⁿ

Orange County (p = 102,000, r = 16)

p'(n) = 102,000 · 0.84ⁿ

Now we evaluate the two functions at n = 5:

Browne County

p'(5) = 87,000 · 0.9⁵

p'(5) = 51,372

Orange County

p'(5) = 102,000 · 0.84⁵

p'(5) = 42,657

Browne County has more population than Orange County.

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Answer:85%, 135%

Step-by-step explanation:

2/40 is 5%. There is 17 2's in 34 so the percentage is 17x5=85.

There is 27 2's in 54 so the percentage is 27x5=135.

The inference from given boxplot is : The visiting team had more variability in the number of shots taken.

In this question we have been given two boxplots.

For the boxplots that the coach made,

for the home team:

Whiskers range is:16 to 32

So, the minimum value = 16

the maximum value = 32

the box ranges from 20 to 23. A line divides the box at 22.

so, the first quartile = 20

the third quartile = 23

the Median = 22

interquartile range(IQR) = 23 - 20

                                      = 3

And for the visiting team

Whiskers range :14 to 32

This means, the minimum value is 14 and the maximum value = 32

As the box ranges from 16 to 24 and a line divides the box at 18,

the first quartile is 16, the third quartile = 24 and the median = 18

So, the interquartile range (IQR) = 24 - 16

                                                   = 8

From above data analysis the inference is that the visiting team had more variability in their shots, because their distribution has a higher interquartile range (8 > 3)

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Given question is incomplete.

The complete question is:

A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.

Number of Shots Taken by Home Team Players

A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.

Number of Shots Taken by Visiting Team Players

Which describes an inference that the coach might make after comparing the medians of the two data sets?

Answer: y= -1x + 2

Step-by-step explanation:

The linear equation is y= mx + b

Y-intercept here is at (0,2), so b is 2

Let pick point (0,2) (2,0)

The slope is rise/run, and we see that the graph is going down by 2 and goes over by 2, so it is -2/2 = -1

So the equation is y=1x +2

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Answer: 24 units.

Step-by-step explanation: To find the perimeter of the right triangle, you need to add up the lengths of all three sides of the triangle.

The right triangle shown has a vertex at (-4, 4), another vertex at (4, 4), and a third vertex at (4, -2). The length of the side between the first two vertices can be calculated using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((4 - (-4))^2 + (4 - 4)^2)

= sqrt(8^2 + 0)

= sqrt(64)

= 8

The length of the side between the second and third vertices can be calculated using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((4 - 4)^2 + (-2 - 4)^2)

= sqrt(0 + (-6)^2)

= sqrt(36)

= 6

The length of the hypotenuse of the right triangle can be calculated using the Pythagorean theorem:

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

= sqrt(8^2 + 6^2)

= sqrt(64 + 36)

= sqrt(100)

= 10

To find the perimeter of the triangle, add up the lengths of all three sides: 8 + 6 + 10 = 24 units.

Therefore, the perimeter of the right triangle is 24 units.

Answer:

1) Associative

2) Distributive

3) Distributive

4) Associative

Length of the car is 12 inches equal to 192 feet.

Using measuring instruments like a ruler, measuring tape, etc., one can measure the length of any object. A ruler can be used to determine, for instance, how many inches a pencil is long. A feet scale can be used to gauge the height of each student in a class.

The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.

Given ,

3 inches : 4 feet

3 inches : 4*12

3 inches :48

1 inches : 16 feet

Length of the car is 12 inches = 12 * 16

Length of the car is 12 inches = 192 feet

The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, a rectangle's length and width are its dimensions.

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Answer:

  SL = 2.1 miles

Step-by-step explanation:

Given ∆LRS with RS extended to point T, and angles R = 35° and exterior angle LST = 70°, you want the measure of SL. You want to apply the process to finding distance to shore.

The exterior angle LST is the sum of interior angles SRL and SLR. In equation form, this is ...

  ∠LST = ∠SRL +∠SLR

  70° = 35° +∠SLR

  ∠SLR = 35°

The angles at either end of segment LR are both 35°, so the triangle is isosceles. That means sides SR and SL are congruent:

  SL = SR = 2.1 miles

The distance from the boat to the lighthouse has been found using an isosceles triangle. A similar method can be used to find the distance to shore. It requires the captain to be able to identify a point on shore, and measure the distance traveled parallel to the shore.

By using a 45° angle to start, and a 90° angle at the second measurement, the distance traveled between angle measurements will be exactly the (closest) distance to shore from the point of the second measurement.

Other angle measures can be used with trigonometric methods.

The expression for the cost of buying n book will be 20 + 13n.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

In this case, the person some books online for myself and friends and each book costs $13 and the store charges a one-time shipping fee of $20.

The expression for the cost of buying n books is:

= 20 + (13 × n)

= 20 + 13n

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Answer:

Geometric sequence

Step-by-step explanation:

A geometric sequaence is when the term is multiplied or divided to get to the next term.

each term is being multiplied by 5

To prove <ABC is congruent to <ABD

congruent figures are those that match in terms of size and shape or are the same size and shape. The geometry of congruent angles

Congruent refers to something that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

According to the question

Both the triangles are right-angled

From RHS criterion

∠ABC ≅ ∠ABD

Definition of angle bisector segment addition property

The line or line segment that splits an angle into two equal pieces is known as the internal angle bisector (internal angle bisector)

definition of congruent angle transitive property

According to the transitive property of congruence, all shapes are congruent to one another if two shapes are congruent to a third shape.

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According to given model income level corresponds to the minimum percent of charity contributions is 5%.

The given function is P(x)=0.0014x² - 0.1529x + 5.855, 5≤x≤10.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Check the critical points and end points to test for any absolute extrema over the given interval.

Absolute Maximum: (5,5.1255)

Absolute Minimum: (10,4.466)

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (54.60714285,1.68028392)

Focus: (54.60714285,180.2517125)

Axis of Symmetry: x=54.60714285

Directrix: y=−176.89114464

Now, P(5)=0.0014(5)² - 0.1529(5)+5.855

= 5.1255

≈5%

Therefore, according to given model income level corresponds to the minimum percent of charity contributions is 5%.

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Answer:

y^2(3+4)

7y^2

BTW isn't it too much to ask for high school level question?