14. A clear box has the shape of a rectangular prism and is filled with sand. Find the volume of the box. 8¹1 in. 41⁄/in. 6 in.​

The answer of the given question based on the pentagon is , the perimeter of the pentagon is approximately 122.

A regular pentagon is polygon with five sides of equal length and five angles of equal measure. It is type of regular polygon, which is a polygon with all sides and angles of equal measure. In a regular pentagon, each interior angle measures 108 degrees, and each exterior angle measures 72 degrees.

The formula for the perimeter of a regular pentagon is P = 5s, where s is the length of a side.

To find the length of a side of the pentagon, we can use the fact that the radius of the circle is 20. If we draw radii from the center of the circle to the vertices of the pentagon, we divide the pentagon into 5 congruent isosceles triangles. Each of these triangles has a base of length 20 and two equal angles at the base, so they are also similar triangles.

Let x be the length of one of the equal sides of a triangle. Then, by the Pythagorean theorem, we have:

x² + (20)² = (2x)²

x² + 400 = 4x²

3x² = 400

x² = 400/3

x ≈ 12.2474

Therefore, the length of a side of the pentagon is s = 2x ≈ 24.4948.

The perimeter of the pentagon is P = 5s ≈ 122.474.

Rounding to three significant digits, the perimeter of the pentagon is approximately 122.

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Answer:

do how to do this is 16 x 16=256 and 8 x 8 =64 so 256+64=320

The sentence can be rewritten using De Morgan's Laws as:

It is false that Tina likes Sprite and Tina likes 7-Up.

In other words, Tina does not like both Sprite and 7-Up.

Answer:

2004

Step-by-step explanation:

There are 250 students in the sixth grade.

First, let's define some variables:

The total number of sixth-grade students is called "x."

The number of students who purchased their lunches will be referred to as "p."

The number of students who brought their lunch from home will be referred to as "h."

We know that from the problem statement that

p + h = x (since all students either purchased their lunch or brought their lunch from home)

p = 0.24x (since 24% of the students purchased their lunch)

h = 190 (since 190 students brought their lunch from home)

We can use these equations to solve for x:

p + h = x

0.24x + 190 = x (substituting in the value of p and h from the other equations)

0.76x = 190 (subtracting 0.24x from both sides)

x = 250 (dividing both sides by 0.76)

Therefore, there are 250 students in the sixth grade.

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Thus, the area of the wrapping paper that is used by lainey to cover all of the sides of cubical box is 486 sq. in.

A solid shape having six square faces is called a cube. Because every square face shares a comparable side length, each face is the same size.

Given data:

Volume of cubical box =   729 cubic inches   ...eq 1

Let 'x' be the side of the cube:

Formula for the volume of cube = x³   ...eq 2

Equation eq 1 and eq 2

x³ = 729

x = ∛729

x = 9 inches

Now, surface area of cube = 6x²

surface area of cube = 6*(9)²

surface area of cube = 6*81

surface area of cube = 486 sq. in.

Thus, the area of the wrapping paper that is used by lainey to cover all of the sides of cubical box is 486 sq. in.

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The TRUE statement in the given situation is (B) "Individuals #3 and #4 must both possess the trait in heterozygosity."

Pedigree analysis is a different method that researchers have developed to investigate how genes are passed down in people.

When there is a lack of progeny data from numerous generations in any group being studied, pedigree analysis is also helpful.

When analyzing a species' pedigree, one can learn a lot about the long-lived generations of that species.

The examination of an inherited trait in a group of related people to ascertain its pattern and properties, such as its mode of inheritance, age at which it manifests, and phenotypic variability.

It is possible to determine the likelihood that a child will have a specific ailment or condition using human pedigree analysis.

An organism with two distinct alleles for a trait is said to be heterozygous for that trait.

A person who possesses two copies of a genetic marker is said to be heterozygous.

So, the correct statement is (B).

Therefore, the TRUE statement in the given situation is (B) "Individuals #3 and #4 must both possess the trait in heterozygosity."

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Complete question:

This pedigree chart tracks the inheritance of a recessive trait that is not sex-linked. Based on the information in the chart, which of the following statements is true?

This pedigree chart shows three generations. The individuals are numbered from left to right, starting at the top left of the chart. Squares represent males and circles represent females. If the symbol is gray, that individual exhibits the recessive trait. If the symbol is white, the individual exhibits the dominant trait. On the first row there are two couples mated together. The first couple is made up of individuals #1 (recessive) and #2 (dominant). They have four offspring on the second row that all exhibit dominant traits: #5 (dominant), #6 (dominant), #7 (dominant), and #8 (dominant). The second couple in Generation #1 is made up of individual #3 (dominant) and individual #4 (dominant). They have three offspring in Generation 2: #9 (dominant), #10 (recessive), and #11 (dominant). Individual #8 from the first family and individual #9 from the second family mated together and produced three offspring in Generation 3. These offspring are #12 (recessive), #13 (dominant), and #14 (recessive).

A. Individual #11 must be homozygous for the recessive trait.

B. Individuals #3 and #4 must be heterozygous for the trait.

C. Individual #2 must be heterozygous dominant for the trait.

D. Individual #9 must be homozygous dominant for the trait.

Answer:

8.36

Step-by-step explanation:

67 - 1

8. 82

= 2747 - 4

328

=2743

328

= 8.36

Answer:

7.96 cm .

Step-by-step explanation:

7.96 cm .

The expression represented by the model is 4. 6/13 - 2/7.

Expression in math is a combination of numbers, symbols, and operators, such as variables and constants, used to represent a mathematical relationship. It can be used to represent the solution of a problem or the evaluation of a function. Expressions are used in algebra, calculus, and other branches of mathematics to describe the relationships between different elements.

This expression can be seen by looking at the model; the shaded portion represents the fraction 6/13 and the portion that was subtracted from it is 2/7. Thus, the expression represented by the model is 6/13 - 2/7.

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Answer:

step by step explanation:

All you have to do is expand and reduce the expressions

then evaluate -2 being a root of the expressions

To do that you need to substitute -2 into the simplified expressions

if the result comes as zero then f(-2) is factor of f(x) according to the factor theorem.

Example 1.

simplify (-5x-2)(7x-4)-2x+3

if you substitute f(x) as f(-2)

then substitute x with -2

when you simply and evaluate the expression you will get that the expression is equal to -137

which means -2 isn't a root since the expression must be equal to 0

-2 is not a root

do the same for the other expressions

The answer in a fraction in reduced form is 0.52.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

Numbers from 1 - 40

Let's find the probability of:

Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 20 numbers

Even numbers that are at least 12 = 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 15 numbers.

Numbers that are at least 12 = 29 numbers

Therefore, the probability that a number chosen at random is even given that it is at least 12 is 0.52

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The probability of getting a multiple of 3 given that the number chosen is greater than 15 is 8/25 or 0.32 as a decimal.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

Fractions are a way of representing a part of a whole or a portion of a quantity. They are written as two numbers separated by a line, with the number on top called the numerator and the number on the bottom called the denominator.

The probability of getting a multiple of 3 given that the number chosen is greater than 15, we need to first determine the number of integers between 16 and 40 that are multiples of 3. There are 8 such integers: 18, 21, 24, 27, 30, 33, 36, and 39.

Next, we need to determine the total number of integers between 16 and 40. There are 25 such integers: 16, 17, ..., 40.

Therefore, the probability of getting a multiple of 3 given that the number chosen is greater than 15 is 8/25 or 0.32 as a decimal.

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Answer:-133.69

Step-by-step explanation:

5.96 x 106 -7.29 x 105

631.76 -7.29 x 105

631.76 - 765.45

= -133.69

There are 49 possible outcomes in the sample space of Alex's experiment.

The multiplication principle of counting, states that if an event can occur in m ways and another independent event can occur in n ways, then the two events can occur in m x n ways.

Here we have

Alex has a spinner with 2 pink sections and 5 purple sections.

He spins the spinner twice.

Since Alex spins the spinner twice, the total number of possible outcomes is the product of the number of outcomes for each spin.

For each spin, there are 2 + 5 = 7 possible outcomes (2 pink sections and 5 purple sections).

Total number of possible outcomes = 7 x 7 = 49

Therefore,

There are 49 possible outcomes in the sample space of Alex's experiment.

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Answer:

voila j'espere que ca va t'aider

Answer: Option A:

To calculate the total amount Owen will spend on Option A, we need to calculate the monthly payment and then multiply it by the number of months:

First, we need to calculate the total amount of the loan. Owen is making a down payment of $3200, so he will be borrowing $28,820 (the price of the car minus the down payment).

Next, we can use the formula for calculating the monthly payment for a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where P is the monthly payment, r is the monthly interest rate, A is the total amount of the loan, and n is the number of months.

For Option A, the monthly interest rate is 1.3% / 12 = 0.01083, the total amount of the loan is $28,820, and the number of months is 36. Plugging these values into the formula, we get:

P = (0.01083 * 28,820) / (1 - (1 + 0.01083)^(-36)) = $860.45

Therefore, the total amount Owen will spend on Option A is:

36 * $860.45 = $30,975.98

Option B:

For Option B, we need to take into account the $1500 cash back that Owen will receive as part of the down payment. This means that the total amount of the loan will be $32,020 - $3200 - $1500 = $27,320.

To calculate the monthly payment, we can use the same formula as before:

P = (r * A) / (1 - (1 + r)^(-n))

For Option B, the monthly interest rate is 5.2% / 12 = 0.04333, the total amount of the loan is $27,320, and the number of months is 36. Plugging these values into the formula, we get:

P = (0.04333 * 27,320) / (1 - (1 + 0.04333)^(-36)) = $825.53

Therefore, the total amount Owen will spend on Option B is:

36 * $825.53 + $1500 = $30,316.08

Therefore, Option A will cost Owen a total of $30,975.98, and Option B will cost him a total of $30,316.08. Therefore, Option B is the cheaper option for Owen.

Step-by-step explanation:

If the area of a rectangle is 1 1/2 square feet and the width of the rectangle is 3/5 feet then the length of the rectangle is  5/2 square feet.

We can use the formula for the area of a rectangle, which is: Area = (length x width) We know that the area of the rectangle is 3/2 square feet, and we also know that the width of the rectangle is 3/5 feet. So we can plug in these values and solve for the length:3/2 sq. ft. = length x 3/5 ft.

To solve for the length, we can start by multiplying both sides of the equation by the reciprocal of  1 1/2 =3/5:

(3/2 sq. ft.) / (3/5 ft.) = length

(3/2 sq. ft.) x (5/3 ft.) = length

(3 x 5) / (2 x 3) sq. ft. = length

15/6 sq. ft. = length

5/2 sq. ft. = length

Therefore, the length of the rectangle is 5/2 square feet.

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The side length x round to the nearest tenth is 3.8 units

The figure in the image is a right-triangle.

Angle θ = 40°

Adjacent to angle θ = x

Hypotensue = 5

To find the measure of x, we use the trigonometric ratio.

cosine = adjacent / hypotensue

Plug in the values

cosθ = x / 5

cos( 40 ) = x / 5

Solve for x

x = cos( 40 ) × 5

x = 3.8

Therefore, the value of x is 3.8.

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The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is

Substituting the values in the equation, we get

Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A

Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil

And , number of cups of vegetable oil used by Colin to make 8 cakes A =

A = 8 x number of cups of vegetable oil used by Colin to make 1 cake

On simplifying the equation, we get

[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]

[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]

Therefore, the value of A is 5 1/3 cups

Hence, the number of cups of vegetable oil required is 5 1/3 cups

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Complete question is-

Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.

If Colin made 8 cakes, how much oil did Colin use in all?

A. 5 1/3 cups

B. 7 1/3 cups

C. 8 2/3 cups

D. 16 1/3 cups​

The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

In the given question,

There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH)

We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:

P(HHT) = (1/2) * (1/2) * (1/2) = 1/8

P(HTH) = (1/2) * (1/2) * (1/2) = 1/8

P(THH) = (1/2) * (1/2) * (1/2) = 1/8

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8

Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

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If each person drove at a constant rate,than Laura drove the fastest

Displacement is the measurement of  the how far an object is out of place,therefore distance refers to  the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.

The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.

to compute who drove the quickest by Using this   formula

speed=Distance /time,

first of all the convert times into hours:

Hank: 3.2 hours x 3 hours and 12 minutes.

Laura: 2.5 hours is 2 hours and 30 minutes.

Nathan: 2.25 hours is 2 hours and 15 minutes.

Raquel: 4 hours plus 24 minutes equals 4.4 hours.

now to calculate the speed by above formula

Hank: 55 miles per hour for 176 miles in 3.2 hours.

Laura: 60 miles per hour equals 150 miles in 2.5 hours.

Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.

Raquel: 65 miles for 286 miles in 4.4 hours.

As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.

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Answer: Dan

Step-by-step explanation: In Mrs. Barkley's class, only Dan followed the directions of using the ratio of 4 gems for every 3 flowers.

Dan:

4    20

3  = 15  You can use cross-products to check to see if they are equivalent.

3 x 20 = 4 x 15

60 = 60

Mary:

4       22

3    = 18

4 x 18 = 3 x 22

72 is not equal to 66

Nancy:

4       18

3    = 24

4 x 24 = 3 x 18

96 is not equal to 54

Jason:

4        26

3   =   20

4 x 20 = 3 x 26

80 is not equal to 78

The distance from Link to the Green Soldier so Link can attack is unit c = 5.

Triangle is a three-sided polygon with three angles. It is one of the most basic and fundamental shapes in geometry. Triangles can be classified by the lengths of their sides, by the size of their angles, or by the relationship between their sides. There are three basic types of triangles: equilateral, isosceles, and scalene. An equilateral triangle has three equal sides and three equal angles, an isosceles triangle has two equal sides and two equal angles, and a scalene triangle has all three sides and angles unequal.

The distance between Link and Ganon is the hypotenuse of a triangle, which is the geometry that is being displayed.

The Pythagoras rule can be used to determine this:

c² = a² + b²

The hypothenuse is c.

Triangle formula: a = base * 4 units

b = height = three units

c² = 4² + 3²

c² = 16 + 9

c² = 25

c = √25

unit c = 5

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If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.

Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.

Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.

Since NP and QS are parallel lines, we have:

∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)

Also, the alternate interior angles NOM and POM are equal, so:

∠NOM = ∠POM

Substituting this into the first equation gives:

∠POM + ∠MOP = 180°

We can now solve for ∠POM by substituting the given value:

130° + ∠POM = 180°

∠POM = 50°

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The correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:

OB. f(x) = x³ - 5x² - 7x + 35

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

The polynomial function of lowest degree with only real coefficients and having the given zeros can be obtained by multiplying the factors (x - √7), (x + √7), and (x - 5) since the zeros are √7, -√7, and 5.

Expanding the product, we get:

(x - √7)(x + √7)(x - 5) = (x² - 7)(x - 5) = x³ - 5x² - 7x + 35

Therefore, the correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:

OB. f(x) = x³ - 5x² - 7x + 35

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Value of indicated point is 2.

In mathematics, a straight line is a geometric object that extends infinitely in both directions and is perfectly straight, meaning that it does not curve or bend. A straight line is defined by any two points on the line, which can be connected by a line segment that lies entirely on the line.

The equation of a straight line can be written in various forms, such as slope-intercept form, point-slope form, or standard form, but they all describe the same line. The equation of a straight line is y = mx + b in slope-intercept form.

Given equation;

3x-y=1

Given coordinate (1,y)

Putting the value of coordinate in equation, we get

3-y=1

3-1=y

y=2

Hence, value of indicated point is 2.

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We will substitute he value 3 for a.

We will substitute he value 4 for b.

Required function is[tex]f(n) = 3(4)^{(n-1)}[/tex]

What is function?

A function is a mathematical concept that maps an input value or set of values to a unique output value or set of values. In computer programming, a function is a block of code that can be called by its name, and may take inputs (arguments) and return outputs.

We can observe that each term in the sequence is obtained by multiplying the previous term by 4. Therefore, the common ratio of the sequence is 4.

To write the explicit formula for the nth term, we can use the formula for a geometric sequence,

[tex]f(n) = a(b)^{(n-1)}[/tex]

We know that f(1) = 3, so we can substitute n=1 into the formula to get,

[tex]f(1) = a(b)^{(1-1)} = a[/tex]

Therefore, a = 3.

We also know that the common ratio between consecutive terms is 4. We can use this information to find the value of b,

12/3 = 4

48/12 = 4

192/48 = 4

768/192 = 4

The ratio between consecutive terms is 4, so b = 4.

Putting it all together, the explicit formula for the nth term in the sequence is [tex]f(n) = 3(4)^{(n-1)}[/tex]

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Correct question is "The first five terms of a sequence are shown

3, 12, 48, 192, 768, ...

We are going to write an explicit function to model the value of the nth term in the

sequence such that f(1) = 3.[tex]a(b)^{n-1}[/tex]

Our function will be written in this form: f(n)

What value will we substitute in for a?

What value will we substitute in for b?

What will be the function?"