what is the area principle? the area principle says that when images are used to compare amounts, the areas of the images should be proportional to the amounts. the images should be different for each amount. the area of the background should be clean and white, with no distractions. the images should be polygons, making it easier to assess the area.

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

Learn more about quadratic equation at:

https://brainly.com/question/1214333

#SPJ1

Answer:

i think it's Z = 8,4

I'm not sure

The number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

A permutation is an act of putting things or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.

Given that soccer player = 11

We have to find in many ways we can choose a captain and one alternate captain from a team of eleven soccer players

Out of 11 player, we have to pick one captain and one alternate captain

nCr ways

nCr = n!/r!(n-r)!

Here n = 11 and r = 2

= 11C2

= 11!/2!(11-2)!

= 11! / 2!.9!

= ((11x 10 x 9!)/2!.9!)

= (11 x 10)/2

= 110/2

= 55

Therefore the number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

To learn more about permutations and combinations visit

https://brainly.com/question/9283678

#SPJ4

Answer:

x=6

Step-by-step explanation:

you divide -25 on both sides

-25x=-150

divido todo por -25 lo que me da es

x=6

The smallest number of rectangles required will be  30.

Given:- The sides of the rectangle are in the ratio of 5:4

let, length=5x

breadth=4x

Area = 20x²

Area of smaller rectangle =2*3

                                           =6cm²

Now, take numbers which are in the ratio of 5:4;

suppose, Case 1=10:8

                 Case2 = 15:12

For Case 1;

number of rectangles needed =10*8/2*3

                                                     =13.3333

This means it is overlapping hence, not possible.

For Case 2;

number of rectangles needed=15*12/2*3

                                                  =30

therefore, the smallest number will be 30.

To learn more about areas of Rectangle visit;

https://brainly.com/question/20693059

#SPJ4

Answer:

the  length of the piece of rope in meters is 22

Step-by-step explanation:

The computation of the length of the piece of rope in meters is shown below:

= 2πr

= 2 × 3.14 × 3.5m

= 21.98

= 22 meters

Hence, the  length of the piece of rope in meters is 22

The problem of changing the word s into the word t can be stated in terms of finding a path in this graph from vertex s to vertex t, where each intermediate vertex (word) in the path differs from the previous one by only one character and belongs to D.

a. To model this as a graph problem, we can treat each word in the dictionary D as a vertex in the graph. Then, we can create an edge between two vertices (words) if they differ by only one character. For example, there would be an edge between 'hit' and 'hot', as they differ by only one character ('i' and 'o'). The problem of changing the word s into the word t can be stated in terms of finding a path in this graph from vertex s to vertex t, where each intermediate vertex (word) in the path differs from the previous one by only one character and belongs to D.

b. To construct the graph, we can iterate through all pairs of words in D and check if they differ by only one character. This takes O(n²) time. Once we have identified the edges in the graph, the size of the graph is also up to O(n²), since there can be at most n vertices and n² edges (when every vertex is connected to every other vertex). Therefore, constructing the graph takes O(n²) time, and the size of the graph is up to O(n²).

To know more about the vertex of a graph visit:

https://brainly.com/question/12520974

#SPJ11

If A and B are sets with A⊆B the a) A ∪B = B, b) A∩B = A.

a) Let A⊆B

Let x ∈ A∪B

Then x ∈ A or x ∈ B .....(i)

By definition of union we have

x ∈ A ⇒ x ∈ B .....(ii)

Using (i) and (ii), if x ∈ A, then x ∈  b. If x ∈ B, then clearly x ∈ B.

Thus given A⊆ B, then A∪B = B.

b) First assume A∩B which implies that x ∈ A and x ∈ B.

Hence we can implies the

A∩ B ⊆ A (we started with the element in A∩B and concluded that it is in A) ------(i)

Now, let x ∈ A which implies x ∈ B ( as A⊆ B)

Hence, x ∈ A∩B, which in turn imply

A ⊆ A∩B -----(ii)

From (i) and (ii) we get

A∩B = A

Therefore if A and B are sets with A⊆B, then A ∩B = B and A∩B = A.

To know more about the sets refer to the link given below:

https://brainly.com/question/13458417

#SPJ4

Answer:

YOU GOT THIS!!

Answer:

no point of intersection

Step-by-step explanation:

y=x-8

y=x^2-2x-3

Answer:

Step-by-step explanation:

25 favors ... $62.50

60 favors ... $x = ?

If you would like to know how much do the supplies for 60 favors cost, you can calculate this using the following steps:

25 * x = 60 * 62.50

25 * x = 3750    /25

x = 3750 / 25

x = $150

Result: The supplies for 60 favors cost $150.

Answer:

C. She could spin a spinner divided into five equal sections three times. On the spinner, four sections represent customers who buy goldfish and one section represents customers who do not buy goldfish.

Step-by-step explanation:

We are told that four out of five customers who bought pets chose goldfish.

Thus;

P(those who bought pets also chose gold fish) = 4/5

Therefore;

P(those who bought pets but do not buy gold fish) = 1 - (4/5) = 1/5

Now, she wants to know the estimated probability that three randomly selected customers buying pets would not buy goldfish.

The probability we have is 1/5.

Therefore,to accommodate the 3 randomly selected customers, we have to multiply the numerator and denominator for each probability by 3.

Thus;

P(those who bought pets also chose gold fish) = 4/5 × 3/3 = 12/15

P(those who bought pets but do not buy gold fish) = 1/5 × 3/3 = 3/15

Looking at the new probabilities, the simulation she can use is to divide a spinner into five equal sections three times so that for each section, we can have the probability of 1/5 and 4/5.

Thus, option C is correct.

The answer is B. Hope this helps

Answer:

It's C. " Which"

Step-by-step explanation:

The five Ws are Who, What, When, Where, and Why, not Which.

Answer:

The volume of the solid is (\(π/3)(b^3 - a^3).\)

Step-by-step explanation:

To find the volume of the solid, we need to set up the triple integral in spherical coordinates. We first note that the cone \(z^2 = x^2 + y^2\) is symmetric about the z-axis and makes an angle of π/4 with the z-axis. We can then use the bounds of integration for the spherical coordinates as follows:

ρ: from a to b (the distance from the origin to the surface of the spheres)

θ: from 0 to 2π (the azimuthal angle)

φ: from 0 to π/4 (the polar angle)

The volume element in spherical coordinates is given by ρ^2 sin φ dρ dθ dφ. The integral for the volume of the solid is then:

\(V = ∫∫∫ ρ^2 sin φ dρ dθ dφ\)

The bounds of integration for the integral are:

ρ: a to b

θ: 0 to 2π

φ: 0 to π/4

Substituting in the bounds and the volume element, we get:

\(V = ∫₀^(π/4)∫₀^(2π)∫ₐ^b ρ^2 sin φ dρ dθ dφ\)

Evaluating the integral, we get:

\(V = (1/3)(b^3 - a^3) (π/4)\)

Thus, the volume of the solid is (\(π/3)(b^3 - a^3).\)

To know more about spherical coordinates, refer here:

https://brainly.com/question/4465072

#SPJ11

The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26

To solve the quadratic equation f(x) = x² + 10x - 1

we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, a = 1, b = 10, and c = -1.

Substituting these values into the quadratic formula:

x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))

= (-10 ± √(100 + 4)) / 2

= (-10 ± √104) / 2

Simplifying further:

x = (-10 ± 2√26) / 2

= -5 ± √26

Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:

x = -5 + √26 and x = -5 - √26

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ1

Answer:

25%

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

True.

Not all variables retained in a regression model need to be statistically significant at a given level of significance (e.g., 5% level). The inclusion of variables in a regression model can be based on theoretical or practical considerations, and not solely on statistical significance. Moreover, some variables may have an important effect on the dependent variable even if they are not statistically significant in the model. However, it is important to assess the overall fit and predictive power of the model, and to consider alternative models and variable transformations if necessary.

Answer:56

Step-by-step explanation:

Answer:

5 pieces of wood

Step-by-step explanation:

1 7/8 = 1.875

3/8 = .375

1.875 / .375 = 5

Answer:

5 pieces of wood

Step-by-step explanation:

\(\frac{(1\frac{7}{8})}{\frac{3}{8}}=5\)

If you divide 1 7/8 by 3/8 you get 5.

Answer:

\(\textsf{Equations of bisectors:}\quad \begin{cases}3x+11y-10=0\\33x-9y=0\end{cases}\)

\(\textsf{Bisector of acute angle:} \quad 33x - 9y = 0\)

Step-by-step explanation:

To determine the equations of the angle bisectors of two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, we can use the formula:

\(\boxed{\dfrac{a_1x+b_1y+c_1}{\sqrt{{a_1}^2+{b_1}^2}}=\pm\dfrac{a_2x+b_2y+c_2}{\sqrt{{a_2}^2+{b_2}^2}}}\)

Let line 3x - 2y + 1 = 0 be defined by the equation a₁x + b₁y + c₁ = 0.

Let line 18x + y - 5 = 0 be defined by the equation a₂x + b₂y + c₂ = 0.

Therefore:

Substitute the values of a₁, b₁, c₁, a₂, b₂, and c₂ into both formulas.

\(\begin{aligned}\dfrac{3x-2y+1}{\sqrt{{3}^2+{(-2)}^2}}&=\dfrac{18x+y-5}{\sqrt{{18}^2+{1}^2}}}\\\\\dfrac{3x-2y+1}{\sqrt{13}}&=\dfrac{18x+y-5}{5\sqrt{13}}\\\\3x-2y+1&=\dfrac{18x+y-5}{5}\\\\5(3x-2y+1)&=18x+y-5\\\\15x-10y+5&=18x+y-5\\\\3x+11y-10&=0\end{aligned}\)

\(\begin{aligned}\dfrac{3x-2y+1}{\sqrt{{3}^2+{(-2)}^2}}&=-\dfrac{18x+y-5}{\sqrt{{18}^2+{1}^2}}}\\\\\dfrac{3x-2y+1}{\sqrt{13}}&=-\dfrac{18x+y-5}{5\sqrt{13}}\\\\3x-2y+1&=-\dfrac{18x+y-5}{5}\\\\5(3x-2y+1)&=-18x-y+5\\\\15x-10y+5&=-18x-y+5\\\\33x-9y&=0\end{aligned}\)

Therefore, the equations of bisectors of the angles between the given lines are:

\(\boxed{\boxed{\begin{aligned}3x+11y-10&=0\\33x-9y&=0\end{aligned}}}\)

\(\hrulefill\)

To identify the bisector of the acute angle, calculate the angle between any one of the bisectors and one of the lines.

The formula for the angle between two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is:

\(\tan \theta=\left|\dfrac{a_2b_1-a_1b_2}{a_1a_2+b_1b_2} \right|\)

Let's find the angle θ between the bisector 3x + 11y - 10 = 0, and the line 3x - 2y + 1 = 0.

Therefore:

Substitute the values of a₁, b₁, a₂ and b₂ into the formula for the angle between two lines:

\(\tan \theta=\left|\dfrac{3 \cdot 11-3 \cdot (-2)}{3 \cdot 3+11\cdot (-2)} \right|\)

\(\tan \theta=\left|\dfrac{33+6}{9-22} \right|\)

\(\tan \theta=\left|\dfrac{39}{-13} \right|\)

\(\tan \theta=\left|-3\right|\)

As tan θ > 1, the angle θ between the bisector and the line must be more than 45°. This means that the angle between the two given lines is more than 90°. So 3x + 11y - 10 = 0 is the bisector of the obtuse angle between the given lines. Therefore, the other angle bisector bisects the acute angle.

Therefore, the bisector of the acute angle is:

\(\boxed{\boxed{33x - 9y = 0 }}\)

Note: The attached diagram shows the given lines as black lines, the bisector of the acute angle as the red dashed line, and the bisector of the obtuse angle as the green dashed line.

The vertical component of velocity can be zero at specific points in the motion of an object.

What is Velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.

The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.

To learn more about Velocity, Visit

https://brainly.com/question/80295

#SPJ4

The correlation coefficient between the student's height and the distance they were able to jump is -1.13.

To compute the correlation coefficient (r) between the person's height and the distance they were able to jump, we need to use the given formula:

\(r = \sum (xi - \bar x)(yi -\bar y) / \sqrt{(\sum (xi - \bar x)^2 * \sum (yi -\bar y)^2)\)

Where:

In our case,

\(\bar x\) = 64.44

\(\bar y = 6.06\)

Square the differences and sum them:

\(\sum ((xi -\bar x)^2) =307.84\\\\\sum ((yi -\bar y )^2) = 2.7224\)

Calculate the correlation coefficient using the formula:

\(r = -32.63 / \sqrt{(307.84 * 2.7224)}\\\\r = -32.63 / \sqrt{838.74158}\\\\\r = -32.63 / 28.96\\\\r = -1.128\)

Therefore, the correlation coefficient (r) for the linear fit between height and jump distance is approximately -1.13.

Learn more about correlation coefficient here:

brainly.com/question/27246345

#SPJ1

Answer:

change to standard form

-9x+y=4

multiply through by -1

9x-y=-4

Answer:

The measures of interior angles of a triangle sum to 180°.

63+60=123

180-123=57

Angle AB is 57°

a) The probability that the specific engineer Jane and the specific manager Mary are on the committee is 2/45

b) The probability that the most experienced and least experienced engineers are on the committee is 2/45

The term called probability in math is known as the probability is the likelihood or chance that an event will occur

And it is calculated by using the general form that can be written as,

=> Probability = Expected/Total outcome

Here we know that if 2 managers were randomly selected from  10 managers, then the probability will be 2/10

AS we know that if 4 engineers were randomly selected from 18 managers, then the probability will be 4/18

On the other hand the probability that engineer Jane or manager Mary is on the committee will be calculated as,

=> 2/10 x 4/18

=> 8/180

When we simplify this then we get the value of the probability as 2/45.

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ4

Answer: 29

Step-by-step explanation:

4y + 4 + 60 = 180

4y = 116

y = 29

Answer:

7 1/3

Step-by-step explanation:

You turn 3 2/3 into 11/3 and then turn 11 into 33/3. Subtract 33/3-11/3 to get 22/3. Turn this into a mixed number: 7 1/3.

Hope it helps!

Answer:

? = 3.01

Step-by-step explanation:

I just divided 11 by 3 2/3 and rounded the answer to 3.01

The concentration of iodoacetone in the 3.00 mL of the original unknown solution is 9.45 x 10-6 M.

To find the concentration of iodoacetone, we can use the equation C1V1 = C2V2, where C1 is the concentration of the standard solution, V1 is the volume of the standard solution, C2 is the concentration of the unknown solution, and V2 is the volume of the unknown solution.

In this case, the concentration of the standard solution is 6.3 x 10-8 M, the volume of the standard solution is 10.00 mL, the concentration of the unknown solution is unknown, and the volume of the unknown solution is 3.00 mL.

We also have the concentration of the internal standard, which is 2.0 x 10-7 M, and the peak areas for both iodoacetone and the internal standard in the unknown solution, which are 633 and 520, respectively.

Using the equation C1V1 = C2V2, we can calculate the concentration of the unknown solution:

(6.3 x 10-8 M)(10.00 mL) = (C2)(3.00 mL)
C2 = (6.3 x 10-8 M)(10.00 mL)/(3.00 mL)
C2 = 2.1 x 10-7 M

So the concentration of iodoacetone in the 3.00 mL of the original unknown solution is 2.1 x 10-7 M.

Know more about concentration here:

https://brainly.com/question/30862855

#SPJ11

Answer:

Designate the remaining pair of coordinates as "set 2." Using the previous coordinates (3, 4) and (1, 2), the coordinate pair (1, 2) becomes "set 2" and will be your x2 and y2 values in the formula. Therefore, x1 is 3, y1 is 4, x2 is 1 and y2 is 2. Now that you have your values, you can plug them into the formula.