Solve the problem below. Be sure to show all calculations. Explanations given to justify your solutions must be given in complete sentences.

Given the figure to the right and the fact that m∠ABD= 133°, find the measurements of the angles below.

m∠ABC=___ m∠BCD=___ m∠ACB=___

The carrying capacity is impacted by both biotic and abiotic processes. The carrying capacity develops as these conditions improve. The carrying capacity decreases as the factors grow scarcer. When resources are depleted faster than they are replaced, the species has reached its carrying capacity.

The average population size of a species in a given habitat is referred to as carrying capacity.

Environmental considerations such as appropriate food, shelter, water, and mates limit the species population size.

The carrying capacity is impacted by both biotic and abiotic processes. The carrying capacity develops as these conditions improve.

The carrying capacity decreases as the factors grow scarcer. When resources are depleted faster than they are replaced, the species has reached its carrying capacity.

Thus, in this way abiotic factors and biotic factors affect population growth.

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Answer:

f = p + 0.75

Step-by-step explanation:

The width of the border frame can be modeled as follows:

f = p + 0.75

where p represents the width of the pool.

The expression is simplified to ;

1. 10n² - 15n + 20xn - 30x

2. 5n(2n - 5) + 10x(2n - 3)

An algebraic expression can be described as an expression that is composed of coefficients, variables, terms, factors, and constants.

These expressions are also comprised of arithmetic operations, which includes;

From the information given, we have that;

10n3 − 15n2 + 20xn2 − 30xn

Now, let's factor the greatest common variable, n, we get;

10n² - 15n + 20xn - 30x

To factor the entire expression, we get;

(10n² - 15n) + (20xn - 30x)

5n(2n - 5) + 10x(2n - 3)

Hence, the expression is 5n(2n - 5) + 10x(2n - 3)

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Answer:

Method 1: Calculate 40% discount on original price, then subtract discount from original price.

Amount of discount = 40% of $30

= 0.40 × $30

= $12

New price = $30 - $12 = $18

Method 2:

New price = (100% - discount percentage) of original price

= 60% of original price

= 0.60 × $30

= $18

At the end of the week, the flower is 96.5 inches tall.

The probability of at most 4 threes appearing when 20 dice are tossed is 0.0756 and The probability of at most 2990 threes appearing when 12000 dice are tossed is 0.054.

a. The probability of at most 4 threes appearing when 20 dice are tossed can be calculated using the cumulative distribution function of the binomial distribution with parameters n = 20 and p = 1/4 (the probability of rolling a three on a single die). Using a binomial cumulative distribution calculator or a statistical software package, the result is approximately 0.0756.

b. The probability of at most 2990 threes appearing when 12000 dice are tossed can be calculated using the cumulative distribution function of the binomial distribution with parameters n = 12000 and p = 1/4. Using a binomial cumulative distribution calculator or a statistical software package, the result is approximately 0.0544.

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Answer:

6,6.5

Step-by-step explanation:

The amount of money he will have after paying these bills each month is $2002.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The health insurance plan he selected has an average monthly premium of $297 .

The average monthly cost of his electric bill is $281.

The phone/internet/cable package he wants costs an average of $220 each month.

The monthly salary is $2800.

Now,

Total cost.

= 297 + 281 + 220

= 798

Now,

The amount remaining.

= 2800 - 798

= $2002

Thus,

The amount of money he will have is $2002.

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The area of the lake is 252000 square meters.

In geometry, the dimensions of a rectangle refer to its length and width. The length of a rectangle is its longer side, while the width is its shorter side. The length and width of a rectangle can be thought of as the horizontal and vertical sides of the rectangle, respectively.

A rectangle can be specified by its dimensions in the form (length, width). For example, a rectangle with length equal to 5 units and width equal to 3 units can be written as (5, 3).

It's important to note that the length and width of a rectangle can be interchanged without changing the shape of the rectangle. In other words, a rectangle with dimensions (5, 3) is the same shape as a rectangle with dimensions (3, 5).

To determine the area of the lake, we first need to determine the size of the clay rectangle in terms of meters. We can do this by multiplying the dimensions of the rectangle on the map by 100 (since 1 centimeter on the map represents 100 meters in real life).

So, the dimensions of the clay rectangle in meters would be:

4.5 cm * 100 = 450 meters (width)

5.6 cm * 100 = 560 meters (length)

Next, we can find the area of the rectangle by multiplying its length by its width:

450 meters * 560 meters = 252000 square meters

Therefore, the area of the lake is 252000 square meters.

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Option C is the correct representation of the solution of the inequality equation.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given the equation, [tex]\frac{x^{2} + 9x - 22 }{x + 4}[/tex] ≥ 0

factors of x² + 9x - 22 are,

x² + 11x - 2x - 22

x(x + 11) - 2(x + 11) = (x + 11)(x - 2)

[tex]\frac{(x + 11)(x - 2)}{x +4}[/tex] ≥ 0

x - 2 ≥ 0

x ≥ 2

so the line should be greater than and equal to 2.

so x + 11 ≥ 0

x ≥ -11

1/(x + 4) ≥ 0 or x + 4 < 0

x < -4

and line varies from,

-4 > x ≥ 11

graph of inequality is between -11 and -4 in which -4 is not included and -11 is included.

only the graph of option C satisfied the conditions.

Hence Option C is correct.

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F(x)=a(x−h)2+k , where (h,k) is the Vertex of the parabola. X=h is the axis of symmetry

A quadratic function’s Vertex Form is provided by: f(x)=a(xh)2+k, where (h,k) is the parabola’s Vertex. The axis of symmetry is x=h. To convert f(x) to Vertex Form, use the completing the square approach.

In vertex form, the quadratic equation is y = a(x-h)2+k. The axis of symmetry is defined as the point at where the vertex crosses the parabola (h, k). The x coordinate is denoted by h. The axis of symmetry is the vertical line that passes through the vertex of a parabola, ensuring that the left and right sides are symmetric. To put it simply, this line divides the graph of a quadratic equation into two mirror images.

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The difference between depths in January and July is 18 feet.

We know that the average depth of the river is 20 feet.

We know that the depth on January was 6ft, while the depth on July was 22ft, the difference is just the subtraction between these two values, we will get:

Difference = 22 feet - 6 feet = 16 feet.

Then the correct option is the fourth one, the difference between the depths is 16 ft.

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a four-story office building has interior columns spaced 30 ft apart in two perpendicular directions

Determine the service live load for a first floor interior column direction

following ASCE-7  guidelines

Area = 20 * 25 = 500 ft^2 which is > 400 ft^2

Nominal live load on every floor = 80 psf

Hence the reduced service live load ( L )

L = Lo [ 0.25 + 15 / √AI ]  ------ ( 1 )

Lo = unreduced load

AT = Tributary area = 500 * number of floors = 2000 ft^2

AI ( influence area ) = AT * number of floors = 2000 * 4 = 8000 ft^2

Lo = 1.6 * 80 psf * 2000 ft^2 = 256 kips

Input values into equation 1 above

L = 106 kips

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Answer:

≈150cm²

Step-by-step explanation:

area is calculated by firmula pir²

r=6.9cm

pi=3.142

3.142×6.9² = 149.59062 cm²

The SQL statement to select the author IDs of authors who have published at least 10 books would use a subquery and the GROUP BY and HAVING clauses.

The subquery would count the number of books for each author and group the authors based on their ID. The HAVING clause would then filter the results to only include author IDs where the count of books is greater than or equal to 10. The final SQL statement would look like this:

SELECT author_id

FROM authors_books

GROUP BY author_id

HAVING COUNT(book_id) >= 10;

This statement would return a list of author IDs where each author has published at least 10 books.

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The function f(x) when the value of x = -x is f(-x) =  -3x² + 2x - 5.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given function is f(x) = -3x² - 2x - 5.

In order to find f(-x), substitute -x in place of x.

f(-x) = -3(-x)² - 2(-x) - 5

      = -3x² + 2x - 5

Hence the function f(-x) =  -3x² + 2x - 5.

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Answer:

a. They are proportional

b. 11

Step-by-step explanation: They table is said to be proportional because all their ratios are the same/equal.

b. 5.5 multiplied by 2 is 11.( cross check the other values of wet dog food by multiplying the values by 2)

Answer: like terms

Step-by-step explanation:

To simplify the equation, combine like terms.

Step 1: Add the x terms together and then add the y terms together.

5x + 7x = 12x

3y + 4y = 7y

Put the x terms and y terms together from step 1.

12x + 7y

The force acting on the adult and the student, both stuck to the wall, is determined by their weight and the centripetal force acting on them.  This means that the net force acting on both of them must be equal to zero.

The quadratic equation in LaTeX:

$ax^2 + bx + c = 0$

The weight of an object is proportional to its mass, and the centripetal force acting on an object is proportional to its mass and the square of its velocity.

Therefore, the ratio of the force acting on the adult to the force acting on the student will be equal to the square of the ratio of their masses and the square of the ratio of their velocities.

Let the mass of the student be 'm' and the mass of the adult be '2m'. Then, the ratio of the forces acting on them will be (2m) / m * (v_adult / v_student)^2, where 'v' represents velocity.

Since the ride remains stationary against the wall for both the student and the adult, this means that the net force acting on both of them must be equal to zero, i.e. their weight must be balanced by the centripetal force acting on them.

Thus, (2m) / m * (v_adult / v_student)^2 = 1.

This equation shows that the mass of the rider does not determine if the ride will remain stationary against the wall while rotating. The ride's velocity and the distribution of mass on the ride will determine whether it remains stationary or not, not the mass of the rider.

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Answer:

(-2, -2) and ( 4, 1) is the answer.

In a parking lot, let x stand in for the length of the vehicles. This would be regarded as a discrete form of variable.

What exactly are discrete variables?

The procedure used to ascertain a discrete variable's value is counting. One illustration is the number of students present. how many red marbles there are in the jar. How many heads are present after the flip of three coins? students' grade level.

                         The discrete distributions most frequently used by statisticians and analysts are the multinomial, Poisson, Bernoulli, and binomial distributions. There are further instances, including the negative binomial distribution and the geometric and hypergeometric distributions.

The number of vehicles in the parking lot is a discrete numerical variable rather than a continuous one because there are only a finite number of possible values rather than an infinite number and because it must be an integer and cannot be a value between integers. In this instance, discretion is the best course of action.

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Answer:

9/64

Step-by-step explanation:

[tex]=0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\=0.75\times \frac{0.25}{1.3}\\=0.75\times 0.1875(\left a.k.a\:\frac{3}{16}\right)\\\frac{\left(3\times 0.1875\right)}{4}\\\mathrm{\left(Clarification:\:The\:\:math\:\:above\:\:is\:\:a\:\:broken\:\:down\:version\:of\:the\:original\:problem.\right)}\\=\frac{0.5625\left(\frac{9}{16}\right) }{4}\\=0.1406\left(\frac{9}{64}\right)[/tex]

Hope this helps!

Answer:

C. 6

Step-by-step explanation:

The range is the difference between the highest and lowest numbers so you do 8-2 which gets you 6.

The volume of the solid obtained by rotating the region in the first quadrant can be found using the method of cylindrical shells.  

The volume of the solid is obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3.

The formula for the volume is:

where a is the value of x such that y = tan(x) intersects y = 3, and y = tan(x) is the equation of the upper boundary of the region being rotated. To find a, we need to solve the equation tan(x) = 3 for x. The exact value of a can then be plugged into the integral.

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A parallelogram with base of 3 m and perpendicular height of 3m have an area of 9m²

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

The area of a parallelogram is the product of its base and its perpendicular height. It is given by:

Area = base * perpendicular height

If Height of parallelogram is 3m and Area is 9m². Let h represent the height, hence:

Area = base * perpendicular height

Substituting:

9 = 3 * h

h = 3 m

A parallelogram with base of 3 m and perpendicular height of 3m have an area of 9m²

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The low tide on Tuesday is -1/6 less than the low tide on Monday.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

An inappropriate fraction is created by adding the numerator to a mixed fraction after multiplying the denominator of the proper fraction by the whole number it is related to.

Given that,

The low tide on Monday = -1 1/2 ft.

Convert the mixed fraction to a improper fraction:

-1 1/2 = -1/2 ft

The low tide on Tuesday = -1 1/3 ft.

Convert the mixed fraction to a improper fraction:

-1 1/3 = -2/3 ft

Take the difference between the two tides:

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

= - 4/6 + 3/6

= -1/6

Hence, the low tide on Tuesday is -1/6 less than the low tide on Monday.

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Answer:

So, the difference of the rates at which the pools are being filled is 1/18 inch per minute.

Step-by-step explanation:

We can find the rate of filling of each pool by dividing the inches filled per hour by the number of minutes it takes to fill them.

Rate of Pool A = 4 inches / 12 minutes = 1/3 inch per minute

Rate of Pool B = 7 inches / 18 minutes = 7/18 inch per minute

The difference in the rates of filling the two pools is:

(7/18) - (1/3) = (7/18) - (6/18) = 1/18 inch per minute.

So, the difference of the rates at which the pools are being filled is 1/18 inch per minute.

The solution to the equation [tex] {6}^{(4x - 3)} = - 4[/tex] is x = 0.3019.

To solve the equation [tex]{6}^{(4x - 3)} = - 4[/tex], we need to isolate the variable x. Here are the steps to solve this equation:

First, we need to take the logarithm base 6 of both sides of the equation. This will help us to isolate the exponent.

log6 [tex]{6}^{(4x - 3)}[/tex]= log6 -4

Use the logarithmic property that [tex] log(b) {b}^{x} = x[/tex] to simplify the left-hand side.

4x - 3 = log6 -4

Use a logarithmic table or calculator to find the value of the right-hand side.

4x - 3 = log6 -4

4x - 3 = -1.7924

Finally, we can isolate the variable x by adding 3 to both sides of the equation and then dividing both sides by 4.

4x = 3 - 1.7924

4x = 1.2076

x = 1.2076 ÷ 4

x = 0.3019

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Answer:

y = 8

Step-by-step explanation:

2/3 x+1/2y = 2

2/3 x - y = -10

3/2y = 12

y = 8