Alan is 77 inches tall. He casts a shadow 14 feet long. His dad casts a 12-foot shadow at the
same time. How much shorter is Alan's dad than Alan? Draw a picture before you begin!

Answer:

6W + W = 770
==> 7W = 770

W = 110 and L = 660 in case you are looking for the solution

Step-by-step explanation:

Let L -= length and W the width of the rectangular field

six times as long as it is wide translates to:
L = 6W

Perimeter of field = 2(L + W)

Given perimeter = 770 feet
2(L + W) = 770
L + W = 770/2 = 385

Since L = 6W, substitute for L in the above equation:
6W + W = 770

7W = 770

W = 770/7 = 110 feet

L = 6W = 6(110) = 660 feet

the width = 55 feet and the length = 330 feet

so basically we take the width as x and the length as 6x then since the perimeter of a rectangle = 2*width + 2*length we will form the equation 6x + 6x + x + x = 770
then we'll solve this equation
14x = 770
x = 55
then multiply x by 6 to get the length which is 330

False. Despite not being continuous at that point, a function can nevertheless be defined there. For instance, even when a function is defined at a certain place, it may nevertheless have a finite jump there.

False. Despite not being continuous at that point, a function can nevertheless be defined there. Functions that have a limit that is equal to their value at a particular point are said to be continuous functions. A function is said to be continuous at a particular location if it is. A function can, however, be defined at a location yet not be continuous there. For instance, even when a function is defined at a certain place, it may nevertheless have a finite jump there. This suggests that the function is not continuous at that point since the left-hand limit and the right-hand limit of the function at that point are not equal. So, even though a function is defined at a certain location, it may not be continuous there.

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The value of the angle x is 18. 4°

it is important to note the six types of trigonometric identities, they are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have the opposite and adjacent sides, then;

tan x = 4/12

Divide the values

tan x = 0. 3333

take the tangent inverse of the value

x = 18. 4°

Hence, the value is 18. 4°

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Let's call the number of players on Team A as "A" and the number of players on Team B as "B".

We know that 1/5 of the players on Team A score a goal, so:

5 players / (1/5) = A players

5 * (1/5) = A

A = 25

We also know that 1/11 of the players on Team B score a goal, so:

2 players / (1/11) = B players

2 * (1/11) = B

B = 22

So there are 25 players on Team A and 22 players on Team B.

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By using quadratic formula we solve 9n² = 4 + 7n, we get [tex]n = \frac{7 \pm \sqrt{193} }{18}[/tex]

Quadratic formula is the simplest way to find the roots of a quadratic equation. There are certain quadratic equations that cannot be easily factorized, and here we can conveniently use this quadratic formula to find the roots in the quickest possible way. The roots of the quadratic equation further help to find the sum of the roots and the product of the roots of the quadratic equation. The two roots in the quadratic formula are presented as a single expression. The positive sign and the negative sign can be alternatively used to obtain the two distinct roots of the equation.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Given:

The equation:

9n² = 4 + 7n

First rearrange the terms

9n² = 4 + 7n

9n² 7n + 4

9n² = 7n + 4

9n² - 7n - 4 = 0

By using quadratic formula, we get

a = 9, b = - 7, c = - 4

n = [tex]\frac{-(-7) \pm \sqrt{(-7)^2 - 4 .9.(-4)} }{2.9}[/tex]

[tex]n = \frac{7 \pm \sqrt{(-7)^2 - 4.9.(-4)} }{2.9}[/tex]

[tex]n = \frac{7 \pm \sqrt{49 - 4.9(-4)} }{18}[/tex]

[tex]n = \frac{7 \pm \sqrt{49 + 144} }{18}[/tex]

[tex]n = \frac{7 \pm \sqrt{193} }{18}[/tex]

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

[tex]n = \frac{7 + \sqrt{193} }{18}[/tex] or [tex]n = \frac{7 - \sqrt{193} }{18}[/tex]

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The solution is Option A.

The number of data points that are incorrectly marked on the scatter plot is none

Dots are used in a scatter plot to show the values of two different numerical variables. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, utilize scatter plots.

The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from near the origin out to high y-values, the variables are said to have a positive correlation.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

Given data ,

Let the equation of graph be represented as A

Now , the value of A is

Let the values of x be = { 1 , 2 , 3 , 4 , 6 , 8 , 10 , 12 }

Let the values of y be = { 2.5 , 7.6 , 12.5 , 17.1 , 24.3 , 37.9 , 49.2 , 54.9 }

So , the points on the graph will be

A ( 1 , 2.5 ) , B ( 2 , 7.6 ) , C ( 3 , 12.5 ) , D ( 4 , 17.1 ) , E ( 6 , 24.3 ) , F ( 8 , 37.9 ) , G ( 10 , 49.2 ) , H ( 12 , 54.9 )

There are no points marked incorrectly on the scatter plot

Hence , the graph is plotted and there are no incorrect data points on the scatter plot

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Answer:

the water would most likely become more acidic.

Step-by-step explanation:

this is due to carbon dioxide being slightly acidic, it dissolves into the water inturn decreasing the pH.

Answer:

could have walked straight

through the forested area at 1km/h, did the troop save any time by going around

Answer:

3.75

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

bc=12.605

The horizontal distance between the base of the ladder and the wall is  8.9 feet.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

If we draw a right triangle with the ladder being the hypotenuse, the angle between the ladder and the ground is given as 69 degrees.

We can use trigonometric functions to solve for the horizontal distance between the base of the ladder and the wall.

Let x be the horizontal distance between the base of the ladder and the wall.

cos(69°) = x/26

Solving for x, we get:

x = 26 cos(69°)

Using a calculator, we find that cos(69°) ≈ 0.342, so:

x ≈ 26 × 0.342 ≈ 8.892

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.9 feet.

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let's convert the mixed fractions to improper fractions first.

[tex]\stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{4}\div \cfrac{20}{3}\implies \cfrac{3}{4}\cdot \cfrac{3}{20}\implies \cfrac{9}{80}[/tex]

9/80.

[tex]\frac{\frac{3}{4}}{(6+\frac{2}{3} )}[/tex]

[tex]6+\frac{2}{3}=\\ \\\frac{18}{3}+\frac{2}{3} =\\ \\\frac{18+2}{3} =\\ \\\frac{20}{3}[/tex]

[tex]\frac{\frac{3}{4}}{(\frac{20}{3} )}[/tex]

Check the attached image.

[tex]\frac{3}{4} *\frac{3}{20}=\frac{3*3}{4*20} =\frac{9}{80}[/tex]

9/80.

As the firm develops a specific sort of sensor and ships them in boxes of four, each sensor weighed 10 grams at first.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let's call the original weight of each sensor "w". The total weight of 4 sensors would be 4w.

With the new design, each sensor weighs 9 grams more, so each sensor weighs w + 9 grams. The total weight of 4 sensors is 76 grams, so we can write an equation:

4(w + 9) = 76

Expanding the left-hand side and solving for w, we have:

4w + 36 = 76

4w = 40

w = 10

So each sensor originally weighed 10 grams as company manufactures a special type of sensor, and packs them in boxes of 4 for shipment.

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La solución de la ecuación diferencial dy / dx = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] es la ecuación y = - 3 · ㏑ |x³ - 4 · x + 4| + C.

En este problema tenemos el caso de una ecuación diferencial ordinaria con variables separables, esto es, que las variables x, y pueden ser apartadas a cada lado de la identidad. A continuación, se presenta el procedimiento de la solución de la ecuación diferencial.

Primero, se escribe la ecuación diferencial y se separan las variables:

dy = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] dx

Segundo, se simplifica la expresión y se aplica la integral a ambos lados:

∫ dy = - 3 ∫ [(3 · x² - 4) / √(x³ - 4 · x + 4)] dx

Tercero, emplear la fórmula de sustitución algebraica u = x³ - 4 · x + 4:

du = 3 · x² - 4 dx

∫ dy = - 3 ∫ [du / u]

Cuarto, integral la expresión resultante:

y = - 3 · ㏑ |u| + C, donde C es la constante de integración.

Quinto, reversar la fórmula de sustitución algebraica:

y = - 3 · ㏑ |x³ - 4 · x + 4| + C

No existen problemas verificados en español, de modo que se añade una pregunta en inglés.

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Therefore , the solution of the given problem of quadrilateral comes out to be x value is  8.13 .

A rectangle is a four-sided, four-cornered object in mathematics. Either the Latin quartet or creative portfolio are the terms' sources (meaning "side"). Four states, corners, and provincial assemblies make up the three divisions of a rectangle. Convex and curved surfaces can be broadly divided into two categories. Convex quadrilaterals also include parallelograms, triangles, rhombuses, rectangles, and trapezoids as subcategories.

Here,

Given :

=> 11x + 4 , 18x - 2 and 114 degree ,

Let m∠B is x:

So ,

According to angle sum property :

=> 11x + 4 + 18x - 2 + 114 + x = 360

=> 116 + 30x = 360

=> 30x = 360 - 116

=> 30x = 244

=> x = 244/30

=> x = 8.13

Therefore , the solution of the given problem of quadrilateral comes out to be x value is  8.13 .

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The probability that the student chooses both math and Spanish is 0.5.  

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that professor is deciding which classes to teach in the fall.

The chooses math 341 with probability 3/7 and math 340 with probability 1/4 and neither class with probability 1/2.

P(M) = 3/7

P(S) = 1/4

P (M' ∩ S') = 1/2

According to De-Morgans law

P (M ∩ S) = P(M) + P(S) - P (M' ∩ S')

P (M ∩ S) =1/2

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The probability is 1/144 which can be computed by product of Q-matrix probabilities of transition.

Consider the absorbing states 0 and 6 and utilize both the Q-matrix of transition probability from 1, 2, 3, 4, and 5 to itself, as well as the S matrix of probabilities from 1, 2, 3, 4, and 5 to 0, 6.

The probability of the next three states being 4, 5, 0 in that order depends on the transition probabilities from one state to the next. If we know the transition matrix, we can calculate the probability as the product of the transition probabilities from one state to the next.

Q = Image is uploaded.

S = Image is uploaded.

The (1,6) item in the matrix corresponds to the desired probability.

[tex](1-Q)^-1S[/tex] = Image is uploaded.

This matrix's rows are labelled 1,2,3,4,5, and its columns are 0,6, respectively. 1/144 is the necessary probability.

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Megan tiled a rectangle with an area of 24 square centimeters, the Megan ‘s rectangle is 2 centimeters by 12 centimeters.

Megan tiled a rectangle with an area of 24 square centimeters,

A = 24 square centimeters

Area of the rectangle = length x breadth

A = l x b

24 = 12 x 2

Therefore, length= 12cm and breadth is 2 cm.

The area occupied by the rectangle within its perimeter may be calculated using the formula for the area of a rectangle. A rectangle's area is calculated by multiplying its length by its width (breadth). As a result, the area of a rectangle whose length and breadth are "l" and "w," respectively, may be calculated using the following formula. L * W = the rectangle's area. Therefore, the area of a rectangle is equal to (length width).

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Complete question:

Megan drew a rectangle that has an area of 24 square centimeters. Which of the following could be the dimensions of her rectangle?

By applying the properties of a parallelogram, it can be concluded that the quadrilateral would be a parallelogram since the opposite sides EF and GH are congruent and parallel.

Parallelogram is a 2-D shape formed by two pairs of sides, each of which is the same length (congruent) and parallel to its pair, and has two pairs of angles, each of which is equal to the angle opposite it.

Distance between two points is the length of the line segment that connects the two points in a plane.

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Slope of a line is its vertical change divided by its horizontal change.

m = (y₂ - y₁) / (x₂ - x₁)

We have these points E (-7,-4), F (2,-3), G (0,-7), and H(-9,-8), and we want to prove that they formed a parallelogram.

To do so, we have to prove that EF and GH are congruent by calculating the distance between EF and GH:

EF = √((x₂ – x₁)² + (y₂ – y₁)²)

    = √((2 + 7)² + (-3 + 4)²)

    = √(9² + 1²)

    = √82

GH = √((x₂ – x₁)² + (y₂ – y₁)²)

     = √((-9 – 0)² + (-8 + 7)²)

     = √((-9)² + (-1)²)

     = √82

Because EF = GH = √82, they are congruent.

In the second step, we have to prove that EF and GH are parallel by calculating their slope:

slope of EF = (y₂ - y₁) / (x₂ - x₁)

                   = (-3 + 4) / (2 + 7)

                   = 1/9

slope of GH = (y₂ - y₁) / (x₂ - x₁)

                    = (-8 + 7) / (-9 – 0)

                    = 1/9

Because EF and GH have the same slope, they are parallel.

Thus, since the opposite sides EF and GH are congruent and parallel, so the quadrilateral would be a parallelogram.

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Answer:

10/6 or 1 4/6

Step-by-step explanation:

Just add the numerators together 10/6. If you need a simplified version it would be 1 4/6.

Answer:12/5

Step-by-step explanation:

tan(x)=opposite/adjacent

tan(x)=12/5

Answer:

2.4

Step-by-step explanation:

This is a right-angled triangle:

where:
Side XY = hypotenuse

              = 13 units

With respect to Angle X:

Side YZ = opposite side

             = 12 units

Side XZ = adjacent side

              = 5 units

Trigonometric function:

Tan∅= [tex]\frac{opposite}{adjacent}[/tex]

 ∴TanX = [tex]\frac{SideYZ}{SideXZ}[/tex]

             = [tex]\frac{12}{5}[/tex]

             = 2.4

Answer:

The equation "3(g + h) = 12" can be translated into a sentence as: "Three times the sum of g and h equals 12."

Hope this helps.

Answer: 3 times g plus h equals 12

Step-by-step explanation:

3 times g + h = 3(g+h)

equals 12 = =12

Hope this helps!

Answer:

6/5

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

1/2×3/5×4

=12/10

divide by 2.

=6/5.

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold.

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold. This is because there is only one raffle winner and it is impossible to predict which ticket will be picked.

It's also crucial to remember that his odds of winning are entirely independent of those of any other ticket holder; nobody else's ticket will affect the outcome of the raffle. As a result, Isaac has the same chance of winning as any other ticket holder. It's also vital to remember that regardless of how many tickets are sold, the likelihood of winning stays the same. Therefore, regardless of how many raffle tickets are sold, there is a 2.5% chance of winning.

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The exponential function is given as follows:

y = 64(0.5)^(x/5).

The standard definition of an exponential function is given as follows:

y = a(b)^(x/n).

In which the parameters are given as follows:

Considering the initial value of 64, along with the fact that the amount halves each five days, the parameter values are given as follows:

a = 64, b = 0.5, n = 5.

Hence the function is defined as follows:

y = 64(0.5)^(x/5).

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I. the elements of (Anb)'uc = {1,2,4,5,6,7}

Ii. The elements of (Auc) 'n B = { 5}

III. The elements of( Aubuc)' = { }

A Venn diagram illustrates the relationships between two or more data sets. Venn diagrams are especially useful for highlighting similarities and differences and are commonly used to compare and contrast the characteristics of different data sets. In a Venn diagram, circles are used to represent each data set.

(Anb)' = {1,2,4,5,6,7}

(Anb)'uc = {1,2,4,5,6,7}

(Auc)' = {5,6}

(Auc) 'n B = { 5}

(Aubuc)' = { }. this means there is no elements for this.

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In a histogram, the width of the bars represents the range of values that fall into each specific category or bin. The spacing between the bars has no meaning in terms of the data being represented.

The ordering of the bars is based on the range of values within each bin, with the bars typically ordered from left to right in ascending order of value.

This is different from a bar graph, where the width and spacing of the bars can have meaning in terms of the comparison of the values being represented. For example, if the width of the bars in a bar graph represents the value of a data point, then a wider bar would indicate a higher value.

The spacing between the bars in a bar graph can also be used to show the relative difference between values. In a bar graph, the ordering of the bars may or may not have meaning, depending on the specific context and the purpose of the graph.

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There is only one point missing on the scatter plot graph.

And the point is (10, 2.6).

Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane.

The data for the gasoline purchases are given in the table.

From the diagram:

The missing point on the scatter plot graph is,

(10, 2.6)

Hence, the point is (10, 2.6).

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Answer:

in form of what?and what's the question

For the given nonlinear equation for population growth ax where a>0,  a0 the equation exhibits exact compensation  whereas b) it has a non-trivial steady state.

The equation describes a population that grows at a rate that is proportional to its size. Specifically, the equation states that the population growth rate is equal to the product of a constant multiplier, a, and the size of the population, x. This means that when the population size increases, the rate of growth increases in proportion, causing the population to grow at a steady rate. the equation expresses a population growth rate that is proportional to the population size.

This means that when the population size is large enough, any further increases in the population size will be met with an equal increase in the population growth rate. This causes the population growth rate to remain constant, which is the definition of a non-trivial steady state

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Answer:

The result is 9000.

Step-by-step explanation:

The calculation is done as follows:

600 ÷ 50 = 12

12 + 30 x 100 = 3200

3200 - 600 ÷ 0 = 9000

However, dividing by 0 is undefined and results in an error.