10. Logan places a mirror on the floor 220 cm from the base of a wall. He holds a flashlight 130 cm above the ground and shines the beam onto the mirror. How far must Logan stand back from the mirror so that the height at which the light shines on the wall is 100 cm greater than the height at which Logan holds the flashlight?

Answer:

she is incorrect because it is 1:5

Step-by-step explanation:

1000g in a kg

0.4kg:2kg

1:5

The location of the point k after dilation and reflection over the x-axis is (3,-1).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis.

Dilation of the point will be,

J(2,4) = j'(1,2

K(6,2) = k'(3,1)

The reflection over the x-axis of point k is,

k'(3,1) = ( 3,-1)

Hence, the point k will be (3,-1)

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Answer:

7/10

Step-by-step explanation\(\frac{9}{15} *\frac{2}{2} = \frac{18}{30} \\\frac{7}{10} *\frac{3}{3} =\frac{21}{30}\)

Using eric and Sue's result to work out the estimate of the probability he will get tail is 1/2.

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

As Aadi is going to throw the coin only once despite the given data we can say that the probability of getting tail in one go is 1/2

P = favorable outcome/total

P = [H,T] / 2

P ( tail) = 1/2

P = 1/2.

Using eric and Sue's result to work out the estimate of the probability he will get tail is 1/2.

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Answer:

9.8

Step-by-step explanation:

To solve, use the Pythagorean Theorem: a² + b² = c² or c² - b² = a².

"a" and "b" are both legs of the right triangle. "c" is the hypotenuse. In this case, we need to use this formula: 14² - 10² = a² or 196 - 100 = a². This simplifies to 96 = a². This can simplify further to 9.79795897 = a. Round this to the nearest tenth: 9.8 = a.

Hope it helps!

The plan with the smallest one-time membership fee is Plan D.

The point-slope formula will be used to determine the equation that models the cost of each plans.

(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x - x₁)

where (x₁, y₁) is the coordinates of point 1

(x₂, y₂) is the coordinates of point 2.

For the equation y = mx + b,

let x = number of discs rented

y = total cost

m = rental rate per disc

b = one-time membership fee

Plan A

(y - 14) = [(17 - 14)/(2 - 1)](x - 1)

y - 14 = 3x - 3

y = 3x + 11

Plan B

(y - 12) = [(16 - 12)/(2 - 1)](x - 1)

y - 12 = 4x - 4

y = 4x + 8

Plan C

(y - 10) = [(15 - 10)/(2 - 1)](x - 1)

y - 10 = 5x - 5

y = 5x + 5

Plan D

(y - 12) = [(21 - 12)/(2 - 1)](x - 1)

y - 12 = 9x - 9

y = 9x + 3

Hence, the plan with the smallest one-time membership fee, b, is Plan D.

Your question is incomplete, but most probably you are asking

"...Which plan has the smallest one-time membership fee?"

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Answer:

Hey there!

4t(5t)=20t^2

4t(-4)=-16t

5(5t)=20t

5(-4)=-20

Hope this helps  :)

Step-by-step explanation:

This is just a matter of multiplication. 4t x 5t = \(20t^{2}\), so that will be in your first box. 4t x -4 = -16t, so that'll be in your second box. 5 x 5t = 25t, so that will be in your bottom-first box, and 5 x -4 = -20, so that will be in your last one.

It will take 8 weeks to Tom to achieve his goal.

The amount earned by him is given by multipliy number or hours and eaning in a hour.

Given

Tom has a goal of saving enough money to buy a new set of rims for his car.

Tom makes $7. 50 an hour take home pay at his job working 15 hours per week.

The earning of Tom in an hour = $7.5

If tom worked 15 hours in a week, then the amount earned by him in one week is;

\(=15\times 7.5\\\\=112.5\)

The required amount to achieve his goal = $900

The number of week he need to work to achieve his target is;

\(= \dfrac{900}{112.5}\\\\= 8\)

Hence, It will take 8 weeks to Tom to achieve his goal.

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According to the question At least 16 days must pass before the class must repeat a seating arrangement.

To determine the number of days that must pass before the class must repeat a seating arrangement, we can consider the concept of permutations.

In the given scenario, there are 8 students and 8 desks, and we want to find out how many different seating arrangements are possible.

The first student can choose any of the 8 desks, the second student can choose any of the remaining 7 desks, the third student can choose any of the remaining 6 desks, and so on.

Therefore, the total number of seating arrangements is given by the product of the numbers from 8 down to 1, which can be calculated as 8 factorial (8!). Mathematically, it can be represented as:

\(\(8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320\)\)

So, there are 40,320 different seating arrangements possible.

Now, to find the number of days that must pass before the class must repeat a seating arrangement, we can use the concept of the pigeonhole principle. According to this principle, if we have more items (seating arrangements) than the number of containers (days), at least two items must occupy the same container.

Since there are 40,320 seating arrangements and we want to find the minimum number of days, we can use the formula for finding the minimum number of containers required for a given number of items:

\(\( \text{Minimum number of containers} = \lceil \log_2 (\text{number of items}) \rceil \)\)

Using this formula, we can calculate the minimum number of days required:

\(\( \text{Minimum number of days} = \lceil \log_2 (40,320) \rceil = 16 \)\)

Therefore, at least 16 days must pass before the class must repeat a seating arrangement.

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The volume of the box is \(4576 in^3.\)

The formula for the volume of a rectangular prism is V = lwh, where l and w are the length and width of the base, and h is the height of the prism. In this case, the base is a square, so l and w are equal. Since the base has an area , we can solve for l and w.

We can use the formula for the area of a square, \(A = s^2\), to solve for s, the length of one side of the base. \(A = 176 in^2, so s^2 = 176 in^2\), so s = sqrt(176) in.

Now that we have s, we can calculate l and w. l = w = sqrt(176) in.

Now that we have the dimensions of the box, we can calculate the volume. \(V = lwh = (sqrt(176))^2 * 26 in^3 = 4576 in^3\).

Therefore, the volume of the box is \(4576 in^3.\)

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It can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.

A quadrilateral is a four-sided polygon with four angles. It is a two-dimensional shape that is bounded by four line segments, each of which is called a side. The sum of the angles of a quadrilateral is 360 degrees. Types of quadrilaterals include rectangles, squares, trapezoids, parallelograms, and kites.

First of all, ABCD is a quadrilateral, which means it has four sides and four vertices. A, B, C and D are the vertices of this quadrilateral. It can be seen that A(2,3), B(4,6), C(7,4) and D(a,b) given in the question are coordinates of the vertices. Therefore, from these coordinates, we can conclude that A, B, C and D are the vertices of the quadrilateral ABCD.

Moreover, these coordinates can also be used to determine the length of the sides of the quadrilateral. The distance between A and B can be calculated by using the Pythagorean theorem. Similarly, the lengths of other sides can also be calculated by using the same theorem. Furthermore, the coordinates will also help us to calculate the angles formed by the sides of the quadrilateral ABCD.

Therefore, it can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.

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complete questions as follows-

If A(2,3),B(4,6),C(7,4) and D(a,b) are vertices of quadrilateral prove its true.

The quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

Given:

f(x) = 2(x+1)^2 - 8

= 2(x^2+1+2x) - 8

= 2x^2 + 2 +4x - 8

= 2x^2+4x-6(standard form)

Intercept form:

= 2x^2+4x-6

= (x-1)(x+3)

x-1 = 0

x = 1

x+3 = 0

x = -3

(1,0) and(-3,0).

Therefore the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

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Answer:

Step-by-step explanation

Remark

The likelihood of an event happening is 28 times out of a hundred.

The chances of it not happening is 72 chances out of a hundred.

Answer:

Unlikely!

Step-by-step explanation:

Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

p = 3

Step-by-step explanation:

Given

4(2 + px) = 12x

If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.

Distributing gives

8 + 4px = 12x ( equate the coefficients of the x- term )

4p = 12 ( divide both sides by 4 )

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4(2 + px) = 12x

8 + 4px = 12x

If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.

4p = 12

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

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To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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When a plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone, it forms a hyperbola.

A double-napped cone is a three-dimensional object with two identical nappes, or curved surfaces, that meet at a single vertex. The nappes extend infinitely in both directions away from the vertex.

When a plane intersects the double-napped cone, it cuts through both nappes, resulting in a curve that consists of two separate branches. These branches are symmetrical about the plane that contains the axis of the cone.

The resulting curve, known as a hyperbola, has two distinct arms or branches that open up in opposite directions. The hyperbola is characterized by its center, vertices, asymptotes, and foci. The plane intersects the cone at an angle, which determines the shape and orientation of the hyperbola.

Therefore, when a plane intersects both nappes of a double-napped cone but does not go through the vertex, it forms a hyperbola.

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Call the number : x

(1/3)x + 5 = x-6

=> (1/3)x + 5 - (x-6) = 0
=> (1/3)x + 5 - x + 6 = 0
Group (1/3)x with -x, 5 with 6

=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
=> x = -11 : (-2/3) = 33/2.

Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2

33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)

In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

Answer:

3

Step-by-step explanation:

Assuming that a regular triangle means an equilateral triangle, there are 3 lines of symmetry, by starting at the three angles of the triangle and drawing a line through the bisector of the side opposite to the angle.

Answer:

Tenths

Step-by-step explanation:

Answer:

X - north

Y - north

Step-by-step explanation:

I took the test!

Answer:

it y x

Step-by-step explanation:

Answer:

y = (-zvx)/w

........

Statistical time division multiplexing is sometimes called asynchronous time division multiplexing. The correct answer is "c. asynchronous."

Statistical time division multiplexing is sometimes called asynchronous time division multiplexing. However, it should be noted that statistical time division multiplexing is different from synchronous time division multiplexing, which divides the time slots in a fixed, predetermined manner. In statistical time division multiplexing, the time slots are allocated dynamically based on the data traffic, hence the term "statistical".

More specifically, asynchrony describes the relationship between two or more events/objects that interact in the same system but do not occur in a predetermined manner and are not necessarily dependent on each other's existence for escape. They do not cooperate with each other, which means they may or may not occur simultaneously as they have their own separate processes.

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Answer:

Josiah can jog 5/6 mile in 15 min. Find his average speed in miles per hour

Answer:

X = -52

Step-by-step explanation:

1/3x - 2/3 = - 18

1/3x = - 18 + 2/3

x = (52/3) / (1/3)

x = -52