The diagonals of parallelogram ABCD intersect at P. Select all the statements that must be true.

Answer:

216 in^3

Step-by-step explanation:

Volume = 6 in. * 4 in. * 9 in. = 216 in^3

The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

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The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.

What is the definition of a function?

A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).

There are several types of functions in mathematics. Here are a few examples:

An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.

Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.

A polynomial function is a function composed of polynomials.

Functions that may be used to inverse another function are known as inverse functions.

Now,

Given function is F(x)=4(x+6)2+5

=(4x+24)2+5

=8x+48+5

=8x+53

hence,

          The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.

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Joan paid with $19.00, she should receive $19.00 - $12.00, which equals $11.30 in change.So Joan should receive 11.30 in change.

Joan should receive $11.30 in change. To calculate this, we must start with the total cost of her items, which comes to $10.20 ($1.20 for the milk, $4.70 for the sandwich, and $3.30 for the sherbet). To this we must add the tax, which was $1.80. This brings the total cost to $12.00. Joan should receive $11.30 in change. To get this answer, we can use the following formula: Change = Total Payment - (Cost of Items + Tax). In this case, the formula would look like this: Change = 19.00 - (1.20 + 4.70 + 3.30 + 1.80). After calculating, the answer is 11.30. So Joan should receive 11.30 in change.

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The solution to the equation is (b) x = -18

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

X

= 6

-3

Represent the equation properly

So, we have the following representation

x/-3 = 6

Cross multiply the equation

This gives

x = -3 * 6

Evaluate the products

x = -18

Hence, the solution is (b) x = -18

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Answer: H. -2 or 8/3

Step-by-step explanation:

3x^2-2x-16=0

Multiply 3 times 16

x^2-2x-48=0

find two numbers that will add up to equal -2 and will be multiplied to get -48. (-8 and 6)

(x-8)(x+6)

divide both numbers by 3 but since you cannot divide 8 and 3 you will move the 3 in front of the x.

(3x-8)(x+2)

Set both equal to 0.

3x-8=0    x+2=0

x= 8/3      x=-2

Answer:

Below

Step-by-step explanation:

Since the center (h,k) is (4,1)   and the circle passes through (4,-4) the radius is 5    ( from y = 1 to -4 ...a distance of 5 )

the equation for a circle is of the form  (x-h)^2 + (y-k)^2 = r^2

  becomes   (x-4)^2 + ( y-1)^2 = 5^2   < ==== graph this equation

radius = 5   then the diameter = 10  then     circumference = pi * d = 10 pi

Answer:

24 cans of soda for $8.89 is the better deal.

Step-by-step explanation:

Divide 24 cans of soda for $8.89 by 2. That way, with the same amount of cans, you can determine which one is more expensive.

1) 12 cans of soda: $4.75

2) 12 cans of soda: $4.445

The second one is cheaper.

Step-by-step explanation:

inscribed angles subtended by the same arc are equal.

the angle FGH is "based" on the same arc (FH) as the angle FJH.

so, FGH = FJH = 56°.

Answer:

y = (2/3)x + 3

Step-by-step explanation:

first we need to find the y-intercept

we can do this by using what is given, the point (-3,1) and the slope (2/3)

using the slope-intercept formula: y = mx + b.

m = slope

b = y intercept

we can plug in the x and y values we were given

so,

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

we can now easily solve for b

1 = (2/3)(-3) = b

first multiply

1 = -2 + b

then add 2 to both sides, this way we isolate b

3 = b

now that we have the y intercept we can write the equation of the line

y = (2/3)x + 3

if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.

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

multiply first

1 = -2 + 3

add the like terms

1 = 1

Answer:

Step-by-step explanation:

is A

We can write the equivalent expression as -

{5.95 × 10⁸ + 8.87 × 10⁸} = {10⁸ x 14.82}.

In mathematics, an expression or mathematical expression is combination of terms both constants and variables. For example -

23 + 54

2x + 5

3x + 5y + z

Given is that after gathering information, Kara decided to add up some distances. She decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. He wrote -

5.95 × 10⁸ + 8.87 × 10⁸

The given expression is -

5.95 × 10⁸ + 8.87 × 10⁸

10⁸ x (5.95 + 8.87)

10⁸ x 14.82

Therefore, we can write the equivalent expression as -

5.95 × 10⁸ + 8.87 × 10⁸ = 10⁸ x 14.82.

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{Question in english -

1) Operations with numbers written in scientific notation

a) After gathering information, Kara decided to add up some distances. decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. Here is what he wrote.

5.95×108 + 8.87×108

Do you know what the result is?}

Answer:

Solution and calculation given below.

The solution is, the distance of the towns is 11.88 km

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

here, we have,

So this can be solve by solving the distance of the plane and the town to the west and also the distance of the plane to the town to the east.  

So the town with an angle of depression of 34 degrees

Let x be the distance of the plane and town  

Cos 34 = x / 8

x = 8 cos 34

x = 6.63 km  

So the town with an angle of depression of 49 degrees

Let y be the distance of the plane and town  

Cos 49 = y / 8

y = 8 cos 49

y = 5.25 km  

so the distance of the towns is 5.25 + 6.63 = 11.88 km

Hence, The solution is, the distance of the towns is 11.88 km.

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complete question:

An airplane is flying between two towns at an altitude of 8km. One town is to the west of the plane and the other is to the east. The angle of depression to one town in de34grees and to the other town is 49degrees. What is the distance between the two towns

The required measure of angle m∠Q is 42 degrees, as of the given condition.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,

m∠O + m∠P + m∠Q = 180°

Using the given information,

m∠O = (6x - 14)°

m∠P = (2x + 16)°

m∠Q = (2x + 8)°

(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°

10x + 10 = 180°

10x = 170

x = 17

Substituting the value of x back into the expression for m∠Q,

m∠Q = (2x + 8)°

m∠Q = (2 * 17 + 8)°

m∠Q = 42°

So the value of m∠Q is 42 degrees.

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The greater probability is the probability of winning through the use of regular defense.

If out of the 100 games that were reviewed, the defense games were 50 and the prevent defense games were 50 as well

Out of the regular 50, there are 38 wins and then 12 loses. Out of the prevent games, there 29 wins and 21 loses.

The probability to win by regular is 38 / 50 = 0.76

the probability to win by prevent defense is 29 / 50 = 0.58

0.76 is greater than 0.58 hence the decision would be to win the game by playing the regular defense.

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A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?

Play the "regular" defense.

Play a "prevent" defense that guards against long gains but makes short gains easier.

The coach reviews the outcomes of 100 games.

Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.

Answer:

1 + 1 = 2

Step-by-step explanation:

you add one and add another one and together thetr is two. so you would have two left.

Students should be able to solve problems related to similar triangles on the Unit 6 test.

Triangle is a 3×3 sided only going with three angles and three side it is one of the most basic fundamental safe in the geometry and is used in many different area of Mithun science triangle are also after used in the architecture art in other area of the designing triangle came in many other different form.

Unit 6 tests on similar triangles require students to apply the knowledge they have learned in geometry class in order to solve problems related to similar triangles. The main topics covered in this test are the various theorems and properties that apply to similar triangles.

The first theorem students should understand is the AA Theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This theorem can be used to solve problems that involve similar shapes.

The second theorem students should understand is the SAS Theorem, which states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between those two sides is the same, then the two triangles are similar. This theorem can be used to solve problems in which two triangles have the same angles and sides that are in proportion to one another.

The third theorem students should understand is the SSS Theorem, which states that if three sides of one triangle are proportional to three sides of another triangle, then the two triangles are similar. This theorem can be used to solve problems in which two triangles have the same angles and sides that are in proportion to one another.

Finally, students should also understand the properties of similar triangles. These properties state that the sides of similar triangles are proportional to one another, the angles of similar triangles are congruent to one another, and the corresponding angles of similar triangles are equal.

By understanding these theorems and properties, students should be able to solve problems related to similar triangles on the Unit 6 test.

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The values of the x are:

1) x = 2,

2) x =11.

3) x = 51

4) x = 7

What is the Angle Bisector theorem?

the angle bisector of a triangle bisects the opposite side in such a way that the ratio of the two line segments is proportional to the ratio of the other two sides.

18)

Given:

Two parallel lines intersecting horizontally the three vertical line,

So, Their ratios are in proportion.

9/4 = 13.5 / x + 4

x + 4 = (13.5*4)/9 = 6

x = 6-4 = 2.

So,  the value of the x is 2.

19)

Given:

Two parallel lines intersecting horizontally the three vertical line,

So, Their ratios are in proportion.

12.8/x-3 = x+5/10

12.8 * 10 = (x-3) * (x+5)

128 = x²+2x -15

So, by solving this quadratic equation we get:

x =11.

21)

Given:

VT bisects the ∠STU

By using the Angle Bisector theorem,

9/33 = 12 / 3x+2

9(3x+2) = 33 * 12

27x + 18 = 1396

x =  1396 - 18 / 27

x = 51

22)

Given:

LM bisects the ∠JLK

By using the Angle Bisector theorem,

4/ (x-4) = (x +3) / 8

(x - 4) * (x + 3) = 8 * 4

x² - x - 12 = 32

x = 7.152

x = 7

Hence, the values of the x are:

1) x = 2,

2) x =11.

3) x = 51

4) x = 7

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If the array includes just the positive integers [tex]{\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}[/tex], the magic square is said to be normal. Some authors take magic square to mean normal magic square.

A magic square is a square grid of numbers that has the same sum for every row, column, and diagonal. It is a mathematical puzzle that has been known and studied for thousands of years. Magic squares can be of different sizes, but the most common are those with odd numbers of rows and columns.

The concept of magic squares dates back to ancient China, where they were believed to have mystical properties. In India, they were used for divination and as part of religious rituals. In Europe, magic squares were popularized in the 16th century, where they were used as a form of mathematical entertainment. Magic squares are not only interesting mathematical puzzles but also have practical applications.

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Complete Question: -

Fill the given squre with numbers from 0 to 8 ( using each of them exactly once) in such a way that the sum of the numbers in the first second and third rows are third rows are in the ratio 1 : 2 : 3. At the same time the sum of the numbers in the first second and third columns also have to be in the same ratio.​

Because angles 1 and 2 are adjacent, we will see that the measure of angle 2 is 77°.

Here we know that m∠1 = 103°, and we want to find the measure of angle 2, which is an angle adjacent to angle 1.

That means that if we add their measures, then we will get a plane angle, this means that:

m∠1 + m∠2 = 180°

Then we can write:

103° + m∠2 = 180°

m∠2 = 180° - 103° = 77°

That is the measure of angle 2.

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The simplified form of the expression √x × ⁴√x in rational exponent form is x^3/4.

Given that, square root of x times the fourth root of x.

√x × ⁴√x

To simplify the expression, rewrite using the least common index of 4.

Since ⁿ√xᵃ = x^(x/n)

√x = x^(1/2)

and

⁴√x = x^(1/4)

Hence, we have;

x^(1/2) ×  x^(1/4)

Using exponent rule

x^( 1/2 + 2/4 )

Add 1/2 and 1/4

x^( 1/2 + 1/4 )

x^3/4

Therefore, the simplified form is x^3/4.

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Answer:

              The greatest possible five-digit number you can create with the numbers 6, 0, 3, 2, and 4 is 64,320.

Step-by-step explanation:

               When it comes to creating the biggest number with a given set of digits, the one and only rule is to organize the digits from greatest to least, this way it ensures that you have the maximum possible values that aren't mitigated by having a small number before a larger one. Based on this, we can organize 6, 0, 3, 2, and 4 from greatest to least, which will be 64,320. Hence, the greatest possible five-digit number you can create with those given numbers is 64,320.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

J(t) = 230,600(1.009)^t

Step-by-step explanation:

J(t) = 230,600(1 + 0.009)^t, or

J(t) = 230,600(1.009)^t                                                                                                                                                                                                              If this is Wrong ill do. it again!!

The estimate for the number of the paintings that are over 70 years old is given as follows:

68 paintings.

The histogram shows the number of observations that appear in each range of the data-set.

24 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:

24/(3 x 4) = 2 units.

Then the estimate of those over 70 years old is given as follows:

Then the total amount is of:

2 x 22 + 24 = 68.

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For given circle, Area of shaded region is 52π cm².

What exactly is a circle?

A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.

The equation for a circle in the plane is:

(x-h)^²+ (y-k)² = r²

When the coordinate points are (x, y)

(h, k) is the coordinate of a circle's center.

where r is the circumference of a circle.

where circle area = πr²

Circle circumference=2πr

Now,

Radius of biggest circle = 8cm

radius of unshaded circle= 4cm and

radius of smaller shaded circle= 2cm

Then,

Area of shaded region= Area of biggest circle - area of white circle + area of smaller shaded circle

=π*8² - π*4² + π*2²

=64π-16π+4π

=52π cm²

hence,

           Area of shaded region is 52π cm².

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Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

What are points, lines, and planes?

Point: A point is a basic geometric object that represents a specific location in space.

Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.

Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.

Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.

Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.

Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.

Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.

Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

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Calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations.

When the equations are solved simultaneously, they are known as simultaneous equations.

Jogging be considered as x

Cycling be considered as y

Shelly spent 40 minutes jogging and 22 minutes cycling, and burned 620 calories to write this in equation we get,

40x + 22y = 620

Shelly swapped times,

22 minutes of jogging and 40 minutes of cycling and burned the same number of calories,

22x + 40y = 620

By multiplying two equation we get,

multiply equation 1 by 22 and equation 2 by 40 we get,

880x + 484y = 13640

880x + 1600y = 24800

Now subtracting equation 1 from 2 we get,

1116y = 11160

y = 11160/1116

y = 10

Therefore, putting value of y in equation 1 we get,

880x + 484(10) = 13640

880x = 13640 - 4840

x = 8800/880

x = 10

Therefore, calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

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The lemon are limiting ingredient  in lemonade recipe.

Here the limiting ingredient is lemon because here for 1 cup of sugar we have 1 lemon it's clearly seems that the juice of 1 lemon never melt the 1 cup of sugar that's why here limiting ingredient   is lemon.

A limiting reagent is a substance that is completely consumed upon completion of a chemical reaction. They are also called limiting agents or limiting reactants. According to the stoichiometry of a chemical reaction, a certain amount of reactants is required for the reaction to go to completion. Consider the following reactions involving the formation of ammonia.

[tex]3H_{2} +N_{2} - > 2NH_{3}[/tex]

In the above reaction, 3 moles of hydrogen gas are required to react with 1 mole of nitrogen gas to produce 2 moles of ammonia. But what if only 2 moles of hydrogen gas and 1 mole of nitrogen were available during the reaction? Not all nitrogen can be used in this case (because 3 moles of hydrogen gas are required to react all the nitrogen). Hydrogen gas is therefore called the limiting reagent for this reaction as it limits the reaction.

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The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The length of the ladder is 10 feet. And the inclination angle is 65°. Then the distance from the bottom of ladder to the wall is given as,

cos 65° = x / 10

x = 4.23 feet

If the ladder reaches a window 9.6 feet above the ground, then the angle is given as,

sin θ = 9.6 / 10

sin θ = sin 73.74°

     θ = 73.74°

The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.

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