Woodsmith magazine gave instructions on how to build a pine cupboard. Lumber will be needed for two shelves 11 1/4 inches long, two base sides 12 1/2 inches long, and two door stiles 28 1/8 inches long. Your lumber comes in 6 foot lengths.
a. How many feet of lumber will you need?

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

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.

Answer:

[tex]6\frac{1}{5}[/tex] or [tex]\frac{31}{5}[/tex]

Step-by-step explanation:

Answer:

31/5 OR 6 1/5  (Depends if your teacher wants an improper fraction or a mixed number.)  

Step-by-step explanation:

First, rewrite the decimal as a fraction with 1 as the denominator.  

6.2 = 6.2/1

Nest, multiply to remove one decimal place so it's easier to solve.  

6.2 x 10 = 62 and 1 x 10 = 10 so... that would be 62/10

Find to GCF of both 62 and 10, or in other words something that they are both divisible by.  That would be 2, and now you can simplify the fraction further.  

62/2 = 31 and 10/2 = 5 so that would be 31/5, which is 6 1/5 as a mixed number.  

I hope this was useful!! :)

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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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 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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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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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:

≈150cm²

Step-by-step explanation:

area is calculated by firmula pir²

r=6.9cm

pi=3.142

3.142×6.9² = 149.59062 cm²

How can AA criterion be used to show that ΔPOR and ΔXYZ are similar: 2. Rotate the image of ΔPQR so that the image of side QP aligns with side YX and the image of side QR aligns with side YZ.

In Mathematics, the AA criterion states that the third angle is equal on two (2) similar triangles when two (2) angles of one of the triangle are respectively equal to the two (2) angles of the other triangle.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or an anticlockwise (counterclockwise) direction.

By applying AA criterion to triangle PQR (ΔPQR) and triangle XYZ (ΔXYZ), we have the following:

side QP ≅ side YX.

side QR ≅ side YZ.

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Answe:

Step-by-step explanation:

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.

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 fact that and allows you to conclude that the system is consistent because if two vectors are equal, then their components must be equal.

Since and , we can set up the following linear system of equations:

Ax = b

where A is the matrix and x and b are the vectors. Since we know that and , then the system of equations is consistent. This is because if two vectors are equal, then their components must be equal. Therefore, if and , then

a1x1 + a2x2 = b1

a3x1 + a4x2 = b2

Since the two vectors are equal, then the components must be equal as well, so

a1x1 + a2x2 = a3x1 + a4x2

which can be rearranged to

(a1 - a3)x1 + (a2 - a4)x2 = b1 - b2

Since b1 - b2 is a constant, then the coefficient of x1 and x2 must both be 0, meaning that the system is consistent.

The fact that and allows you to conclude that the system is consistent because if two vectors are equal, then their components must be equal. This means that if and , then we can rearrange the system of equations to get (a1 - a3)x1 + (a2 - a4)x2 = b1 - b2, which implies that the coefficients of x1 and x2 must both be 0, meaning that the system is consistent.

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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:

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

Answer:

y = 8

Step-by-step explanation:

2/3 x+1/2y = 2

2/3 x - y = -10

3/2y = 12

y = 8

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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The proof of the trigonometry identity is shown below

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

Prove: (sec (x) + csc (x))^2 = 2 sec (x) csc (x) +(cot (x) + tan (x))^2.

So, we have

(sec (x) + csc (x))^2 = 2 sec (x) csc (x) +(cot (x) + tan (x))^2.

Open the bracket

sec^2(x) + csc^2(x) + 2 sec(x) csc(x) = 2 sec (x) csc (x) +(cot (x) + tan (x))^2.

Evaluate the like terms

sec^2(x) + csc^2(x) = (cot (x) + tan (x))^2.

Expand

sec^2(x) + csc^2(x) = cot^2(x) + tan^2(x) + 2

So, we have

sec^2(x) + csc^2(x) = cot^2(x) + 1 + tan^2(x) + 1

As a general rule:

tan^2(x) + 1 = sec^2(x)

csc^2(x) = cot^2(x) + 1

This means that

sec^2(x) + csc^2(x) = sec^2(x) + csc^2(x)

Hence, the identity has been proved

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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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Answer:

SAS

Step-by-step explanation:

2 sides if 20in. , the middle one is the same for both, and both have 22° angles

Answer:

  0.042563 km

Step-by-step explanation:

You want the distance 4256.3 cm expressed in km.

The prefixes centi- and kilo- refer to 1/100 and 1000, respectively.

  4256.3 cm = 4256.3 (1/100 m) = 42.563 m

Then 1 km = 1000 m, so 1 m = 1/1000 km, and we have ...

  42.563 m = 42.563 (1/1000 km) = 0.042563 km

Answer:

0.042563 km

Step-by-step explanation:

To convert centimeters to kilometers, divide the number of centimeters by 100,000.

So, 4256.3 cm = 4256.3 cm / 100,000 cm/km = 0.042563 km.

Mathematical induction is a method used to prove statements for all positive integers.

To prove the formula 1 + 2 + 3 + ... + (n-1) + n = n(n+1)/2 using induction,

we first show it holds for the base case n = 1.

When n = 1, the formula becomes 1 = 1(1+1)/2, which is true.

Then, we assume the formula holds for some integer k, and prove it holds for k+1.

Inductive step: Assume that the formula holds for some integer k, i.e., 1 + 2 + ... + (k-1) + k = k(k+1)/2. We need to prove that the formula also holds for k+1.

So, 1 + 2 + ... + (k-1) + k + (k+1) = k(k+1)/2 + (k+1) = (k+1)(k+2)/2, which shows that the formula holds for k+1 as well.

By repeating this process, we conclude the formula holds for all positive integers.

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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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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!

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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There are 97 people who ate pizza last Friday night.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

We have

184 = watched TV

183 = hung out with friends

37 = watched TV and ate pizza, but did not hang out with friends

31 = watched TV and hung out with friends, but did not eat pizza

40 = hung out with friends and ate pizza, but did not watch TV

29 = watched TV, hung out with friends, and ate pizza

74 = he did not do any of these three activities

We need to find out the number of people eating pizza by deducting the number of people not eating pizza from the total number.

So the people not eating pizza are listed as A, B, D, G

Total = 549

Those who only ate pizza= total - (A+B+D+G)

                                          = 549- (184+183+37+31)

                                          = 549- 415= 97

There are 97 people who ate pizza, last Friday night.

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In A bar graph, The Verical axis should start at 0 rather than 100 .

What does a bar graph explain?

Graphs are used to represent information in bar graphs. To represent value, bars that stretch to various heights are used. Bar graphs can be made using stacked bars, horizontal bars, vertical bars, or grouped bars (several bars that compare values in a category) (bars containing multiple types of information).

                            An easy way to compare several sets of data among various groups is with the aid of a bar graph. Two axes are used to depict the relationship, with the discrete values on one axis and the categories on the other.

The Verical axis should start at 0 rather than 100 .

Reason: For Accurate presentationa and comparision the verical axis should start at 0 rather than 100

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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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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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Answer:

6,6.5

Step-by-step explanation: