Assume that a pair of mice produces 6 offspring, and that half the offspring are male and half are female. Further, assume that no offspring die. If each pair of mice breeds only once, how many offspring would be produced each year for 5 years?.

The polynomial function of least degree with integral coefficients is equal to f(x) = x³ - 4x² + x + 6 with the given zeros 3, 2, -1.

As given in the question,

Given zeros of the polynomial function are :

3, 2, -1

⇒ ( x - 3 ) =0 or ( x - 2 ) = 0 or ( x + 1 ) = 0

Polynomial function of the given factors  ( x - 3 ) =0 or ( x - 2 ) = 0 or

( x + 1 ) = 0 is given by :

f (x ) = ( x - 3 )( x - 2 )( x + 1 )

⇒ f(x) = ( x² - 3x - 2x + 6 ) ( x + 1 )

⇒ f(x) = ( x² - 5x + 6 ) ( x + 1 )

⇒ f(x) = x³ + x² -5x² - 5x + 6x + 6

⇒f(x) = x³ - 4x² + x + 6

Therefore, the required polynomial function of least degree with integral coefficients using given zeros is equal to f(x) = x³ - 4x² + x + 6.

The complete question is:

Write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?

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Answer: Acute Triangle

Step-by-step explanation:

Because when we look at it we can actually see each of the angles, they are less than 90 degrees then they are consider as acute angles, if it's greater than 90 degrees and smaller than 180 degrees then it will be consider as a obtuse, and if it's equal to 90 degrees then it's a right angle. This is not a equiangular, if it's then it should be have three 60degrees angles.

The rental fee for each tube is $18.50 for the 15 tubes for a float down the ichetucknee river.

The cost is determined as the amount of money spent on some causality and thus it is calculated as the total of money that is spend from the money deposited form.

Here we have A group spent $277.50 to rent 15 tubes for a trip down the Ichetucknee River.

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Answer:

16.2

Step-by-step explanation:

By the Segment Addition Postulate,

AB+BC+CD+DE=AE

x+(x+4)+(2x+1)+(x−6)=80

5x−1=80

5x−1+1=80+1

5x=81

5x÷5=81÷5

x=16.2

AB=x=16.2

The slit-width-to-wavelength ratio for 30 degrees will be 2; for 60 degrees will be 0.87, and lastly, for 90 degrees angles will be 1.

The computation of slit-width-to-wavelength ratio for each of the angles after assuming that the small-angle approximation as invalid, has been given, as below,

sin θ = λ / a

sin30∘ = λ / a

0.5 = λ / a

a / λ = 2

Similarly,

sin θ = λ / a

sin60∘ = λ / a

0.87 = λ / a

a / λ = 0.87

And lastly, for 90 degrees

sin θ = λ / a

sin90∘ = λ / a

1 = λ / a

a / λ = 1

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The angle x of the isosceles triangle is 64 degrees.

The side and angle of the similar polygon are 7.5 units and 20 degrees.

The triangle above is an isosceles triangle. An isosceles triangle is a triangle that has 2 sides equal to each other and two angles equal to each other.

Therefore, the base angle of the isosceles triangle are equal.

Hence,

52 + x + x = 180

52 + 2x = 180

2x = 180 - 52

2x = 128

x = 128 / 2

x = 64 degrees

Similar polygons are two polygons with the same shape, but not the same size.  Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

Therefore, let's find x and y in the polygon.

x / 5 = 6 / 4

cross multiply

4x = 30

x = 30 / 4

x = 7.5

y - 73 = 360 - 90 - 61 - 116

y - 73 = 93

y = 93 - 73

y = 20

Therefore, the angle x of the isosceles triangle is 64 degrees and the sides x of the polygon is 7.5 units and the angle y of the polygon is 20 degrees.

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By using unitary method, it can be calculated that

30 mm is the length of the patio in the drawing.

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, unitary method will be used

9000 mm in actual is equivalent to 10 mm in the drawing

1 mm in actual is equivalent to [tex]\frac{10}{9000}[/tex] mm in the drawing

27000 mm in actual is equivalent to [tex]\frac{10}{9000}\times 27000[/tex] mm in the drawing

27000 mm in actual is equivalent to 30 mm in the drawing

27 m in actual is equivalent to 30 mm in the drawing

30 mm is the length of the patio in the drawing.

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The loan's APR is 246.7%. Buck takes out a $235,000 mortgage at 4.3%. He plans to make monthly payments of $1,136 over the course of 30 years.

The interest charged for borrowing that reflects the real yearly cost of the loan stated as a percentage is called the annual percentage rate (APR). the annual percentage cost of borrowing, which takes into account interest and other costs. Example. An APR of 9% is calculated using a $1000 loan with an annual interest rate of $80 and a service charge of $10.

Given,

Without a doubt, given that

Buck borrowed $235,000 in all.

$1136 in monthly payments

Loan term:

30 years

30 × 12

360 months

Buck's repayment amount equals monthly payments length of the loan

= 360 x 1136

= $408960

APR

= Amount paid back by buck - Amount borrowed by buck/Amt borrowed × Duration

= 408960 - 235000/235000 × 30

= 2.467 × 100

= 246.7%

The loan's APR is 246.7%. Buck takes out a $235,000 mortgage at 4.3%. He plans to make monthly payments of $1,136 over the course of 30 years.

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Answer:

4.3%

Step-by-step explanation:

correct on odyssey

The change in elevation will be 12 feet.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

When the train exits the gate, it climbs 170 feet up the first hill before dropping 164 feet down,the change in elevation will be:

= 176 - 164

= 12

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Answer:

19

Step-by-step explanation:

9 1/2 divided by 1/2 is 19

Answer:

[tex]y=\frac{1}{2}x+4[/tex]

Step-by-step explanation:

[tex]y-3=\frac{1}{2}(x+2) \\ \\ y-3=\frac{1}{2}x+1 \\ \\ y=\frac{1}{2}x+4[/tex]

The required markup from the cost of $270 is 20% of the sale price.

The selling price of an item is ​$360. It is marked down by ​%10, but this sale price is still marked up from the cost of ​$270.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Selling price after 10% marked down,
= [1 - 0.10] × 360
= 324
Now,
Percentage marked up of cost price of $270
= 324 - 270 / 270 × 100
= 20%

Thus, as of the given condition markup cost of $270 is 20% of the sale price.

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Answer:

To determine if there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit, we need to see if the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is constant.

On the first day, the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is 20°C / 68°F = 5/17.

On the second day, the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is 10°C / 50°F = 1/5.

Since the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is different on the two days, there is not a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.

Step-by-step explanation:

Since both data points satisfy the proportional relationship equation, we can conclude that there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.

To determine if there is a proportional relationship between the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F), we can check if the data points given for both temperatures satisfy the proportional relationship equation:

°F = (9/5) * °C + 32

Let's calculate the proportional relationship using the given data points:

1. First data point: 68°F and 20°C

  °F = (9/5) * 20 + 32

  °F = 36 + 32

  °F = 68

  The first data point (68°F and 20°C) satisfies the proportional relationship equation.

2. Second data point: 50°F and 10°C

  °F = (9/5) * 10 + 32

  °F = 18 + 32

  °F = 50

The second data point (50°F and 10°C) also satisfies the proportional relationship equation.

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Step-by-step explanation:

Angle 2 would be 49 ° because it's congruent to the other vertical angle.

Angle 3 in the left triangle is 68° and now that we know 2 is 49° we can solve that triangle.

The left triangle is 180° in total, to figure this out, listen to these steps

68 + 49 = 117°

180 - 117 = 63°

Angle 1 in left triangle is 63°

Angle 4 is 93 - 49 = 44°

and angle 3 would be = 87

49 + 44 + 87 = 180

Answer:

60/52

Step-by-step explanation:

Answer: 15/13

Step-by-step explanation:

When multiplying improper fractions, we multiply the numerator by the numerator and the denominator by the denominator. So here we have:

5/4 * 12/13

= 60/52

= 15/13

the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined which shape is formed as Square

When the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined, a square is formed. The sides are equal length and the angles are all 90 degrees.The coordinates (1,1), (7,3), (8,0) and (2,-2) are points on a two-dimensional plane. When the points are connected, a square is formed. A square is a four sided shape with four 90 degree angles and four equal length sides. The length of each side can be calculated by finding the distance between the two points. For example, the distance between (1,1) and (7,3) is 6 units. Therefore, the length of each side of the square is 6 units.

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so,  -11-[tex]\sqrt{2}[/tex]i and 3 + 4i are roots of polynomial function f(x) so 11 + [tex]\sqrt{2}[/tex]i and

3 - 4i are roots of f(x)  

Therefore, option D is correct

Polynomial function:

A polynomial function, in general, is also stated as a polynomial or polynomial expression, defined by its degree. The degree of any polynomial is the highest power present in it.

given that

Patricia is studying a polynomial function f(x). three given roots of f(x) are

-11-[tex]\sqrt{2}[/tex]i , 3 + 4i and 10 . Patricia concludes that f(x) must be a polynomial with degree 4.

so -11-[tex]\sqrt{2}[/tex]i and 3 + 4i are roots of polynomial function f(x) so 11 + [tex]\sqrt{2}[/tex]i and

3 - 4i are roots of f(x)  

Therefore, option D is correct

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Answer:

A Square Root of 80 to the nearest tenth, means to calculate the square root of 80 where the answer should only have one number after the decimal point.

Here are step-by-step instructions for how to get the square root of 80 to the nearest tenth:

Step 1: Calculate

We calculate the square root of 80 to be:

√80 = 8.94427190999916

Step 2: Reduce

Reduce the tail of the answer above to two numbers after the decimal point:

8.94

Step 3: Round

Round 8.94 so you only have one digit after the decimal point to get the answer:

8.9

To check that the answer is correct, use your calculator to confirm that 8.92 is about 80.

Answer:

You're answer is 8.9. Hope it helps.

Answer:

C) [tex]y=3x-8[/tex]

Step-by-step explanation:

[tex]y-16=3(x-8) \\ \\ y-16=3x-24 \\ \\ y=3x-8[/tex]

The two numbers whose difference is 86 and whose product is a minimum. The numbers are (43,-43) and therefore, the smaller number is  -43 and largest number is 43.

Given :

Two numbers whose difference is 86 and whose product is a minimum.

To find : The numbers

Let the largest number be x,

and smallest number be y.

According to question,

Two numbers whose difference is 86.

i.e.  x - y = 86                   -----------------------------(1)

Product of two number is minimum.

i.e.   xy = 86                     -------------------------------- (2)

where P is minimum.

Now substitute x from (1) in (2),

     x (x -86) = P

⇒ y(x) = x² - 86x = P               ------------------------------ (3)

Differentiating Equation (3), we get:

y'(x) = 2x - 86

and y'(x) = 0

After subtracting we get:

    2x - 86 = 0

⇒ x = 86 /2

⇒ x = 43

The vertex of the equation occur at x = 43.

Putting the value of x = 43 in equation (1) , we get:

    48 - y = 86

⇒ -y = 86 - 48

⇒ y = -43

So, the value of y is - 43.

Therefore, the numbers are (43,-43).

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, that is, the INPUT never repeats, Check the picture below.

now, to check on the graph if it's a function or not, simply recall the vertical line test, if you can draw a vertical line on the graph and it only touches it ONCE, then it's a function, if however a vertical line touches it more than once, then is not.

The function that can be used to determine the amount of money he has left over after x rides is  y = 70 - 5x .

In the question ,

it is given that ,

the amount that Charlie has to spend on the school carnival is = $125 ,

the amount spend on entry is = $15 ,

the amount spend on food is = $40 ,

the cost for each ride is = $5 ,

so , let the number of rides be = "x"

So , let y represents the amount of money left with Charlie .

According to the question ,

the function that represents the money left is

y = 125 - (15 + 40 + 5x)

y = 125 - (55 + 5x)

y = 125 - 55 - 5x

y = 70 - 5x

Therefore , the function is y = 70 - 5x .

The given question is incomplete , the complete question is

Charlie has $125 when he goes to the school carnival. he spends $15 to enter the carnival and $40 on food. rides at the carnival cost $5 each to play. which function can be used to determine how much money he has left over after x rides ?

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Answer:

To find the volume of water that was pumped from container A, we first need to find the volume of each container. We can use the formula for the volume of a cylinder to do this. The formula is V = πr^2h, where r is the radius of the cylinder and h is the height.

For container A, the volume is V = π * 13^2 * 18 = 8640π cubic feet

For container B, the volume is V = π * 11^2 * 20 = 7320π cubic feet

Since the water from container A completely filled container B, the volume of water that was pumped from container A is 8640π - 7320π = 1320π cubic feet.

To find the percent of container A that is full, we need to divide the volume of water remaining in container A by the total volume of container A and multiply by 100%. The total volume of container A is 8640π cubic feet, and after the water was pumped into container B, the volume of water remaining in container A is 8640π - 1320π = 7320π cubic feet.

Therefore, the percent of container A that is full is 7320π / 8640π * 100% = approximately 84.9% to the nearest tenth.

Answer:

15/4

Step-by-step explanation:

[tex]\ell=5/2 \\ \\ w=1 \\ \\ h=3/2 \\ \\ V=lwh=(5/2)(1)(3/2)=15/4[/tex]

Answer:

3.75 so i believe the answer might be 15/4?

Step-by-step explanation:

im sorry if this is not the right answer

Answer: Jayden would practice for 630 minutes.

Step-by-step explanation:

You know that he practices for 420 minutes in 2 weeks. Divide them by each other. [tex]\sqrt[2]{420}=210[/tex]

If one week is 210 minutes, 210x3=630 minutes.

The limit of x/|x|  as x approaches 0 does not exists.

We need to find the limit of x/|x| as x approaches 0.

Consider left hand limit.

lim x -> 0- (x/|x|)

x/|x| = -1 for all negative values of x.

So, lim x -> 0- (x/|x|) = -1

Consider right hand limit.

lim x -> 0+ (x/|x|)

x/|x| = 1 for all positive values of x.

So, lim x -> 0+ (x/|x|) = 1

lim x -> 0- (x/|x|) ≠ lim x -> 0+ (x/|x|)

Therefore, the limit of x/|x| does not exists.

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The complete question is:

What is the limit of x/|x| as x approaches 0?

Total Coins in the collection are 450 units

What is Percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is commonly used, however the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

Solution:

Given that 9 is 2% of the total collection

Let, total collection be x

2% of x is 9

2/100 * x = 9

x = 9 * 50 = 450

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It is NOT necessary for two triangles to be congruent just because the three angles (AAA) connecting them are congruent.

Given,

The congruent angles;

Angles of equal measure are said to have congruent angles. Thus, all angles with the same measure are referred to as congruent angles. They can be found everywhere, such as in isosceles triangles, equilateral triangles, and situations where a transversal intersects two parallel lines.

That is,

The triangles do not necessarily need to be congruent just because the three angles (AAA) between two triangles are similar. They have the same shape (or something similar), but we have no idea how big they are.

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The fraction that is equivalent to a terminating decimal between 0.25 and 0.50 will be 2/5.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.

The decimal numbers are 0.25 and 0.50.

The decimal number that comes between the decimal numbers 0.25 and 0.50 will be an infinite number. Let the number be 0.40 which comes between the numbers 0.25 and 0.50.

Convert a decimal number into a fraction number. Then we have

0.40 = 0.40 x 10 / 10

0.40 = 4 / 10

0.40 = 2 / 5

The fraction that is equivalent to a terminating decimal between 0.25 and 0.50 will be 2/5.

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The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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