\In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur. The climate in which these mice live has slowly gotten colder.

How will this change in the environment most likely affect the mouse population?

The adaptation of thinner fur will be selected over thicker fur, and the population will remain unchanged.
The adaptation of thicker fur will be selected over thinner fur, and the population will remain unchanged.
The adaptation of thinner fur will be selected over thicker fur, and the population will evolve.
The adaptation of thicker fur will be selected over thinner fur, and the population will evolve.

Step-by-step explanation:

the answer will be zero 0

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry.

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

2. Find the value of the supplementary angle of y for each polygon.

A.) For an isosceles triangle, using the base angle theorem we can write that the measure of the angle opposite to the congruent side will be equal. Therefore, the sum of the angles of the triangle can be written as,

y + y + 26° = 180°

2y = 154°

y = 77°

B.) The sum of the interior angles of a regular polygon is given as (n-2)180°, where n is the number of sides, also for a regular polygon the measure of each interior angle is equal. Since in a pentagon the number of sides is 5. Therefore, the measure of an interior angle can be written as,

y = [(n-2)180°]/n

y = [(5-2)180°]/5

y = 108°

3. The sum of the exterior angle of all the polygons is equal to 360°. Therefore, the sum of the exterior angles of the triangle and the pentagon will be the same, 360°

4. The formula to find the sum of the interior angles of a polygon, we can use the formula.

Sum of interior angles of an n-sided polygon = (n-2)180°

Where n is the number of sides.

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Answer:

The basic way to calculate the number of members is finding the area under the curve. The total members are 20

Step-by-step explanation:

The given graph shows that how many team members have a particular weight.

The first rectangle shows that 5 team members have a weight of 115kg.

The second rectangle shows that 3 team members have a weight of 115kg.

The third rectangle shows that 2 team members have a weight of 115kg.

The forth rectangle shows that 0 team members have a weight of 115kg.

The fifth rectangle shows that 3 team members have a weight of 115kg.

The sixth rectangle shows that 4 team members have a weight of 115kg.

The seventh rectangle shows that 3 team members have a weight of 115kg.

So, the total team members are = 5 + 3 + 2 + 0 + 3 + 4 + 3 = 20

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The proof is shown below

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given:

∠CBA ≅ ∠FBA; ∠CAB ≅ ∠FAB

Now, ∠BCA is congruent to ∠BFA      [reflexive property of congruence]

Also, AB= AB  (common)

Thus, we can conclude that Δ BCA≅ Δ BFA  by ASA criteria.

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Answer: a) 46 minutes
               b) 10:47

The basic knowledge for this is that 60 minutes = 1 hour

a) Question a asks for how long it took from a 10:34 bus from Mosley to reach Bamford. From the table you can see that the 10:34 bus reaches Bamford at 11:20. All you have to do is count from 10:34 to 11:20.
10:34 will become 11:00 at 10:60 right? Clock's generally don't show 10:60 but goes directly to 11:00 after 1 minute is passed at 10:59. So from 10:34 to 11:00, it takes 26 minutes. Remember the bus reaches at 11:20 so from 11:00 to 11:20, it takes 20 minutes. Now add them up:
26 minutes + 20 minutes = 46 minutes

Here you go! Total 46 minutes from Mosley to Bamford.

b) From question b, we can see that Trina did not ride the first bus or by any chance missed it because the bus left at 10:14 and she is at the station at 10:15. Now think it from your perspective! You missed the first bus and you are in a big rush. So to reach your destination as early as possible, you will obviously take the next earliest bus. The next bus is at 10:24 (Belton). So if we take the 10:24 bus in Belton, it reaches at 10:47 in Garton.

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The number of children ticket sold on Sunday is 210.

Given this equations:

x+y=370 equation 1

3x+7y=1750 equation 2

Multiply equation 1 by 7

7x + 7y = 2590 equation 3

Subtract equation 2 from equation 3

4y = 840

Divide both sides by 4

y = 840 / 4

y = 210

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Answer:

3  1/2

Step-by-step explanation:

Put '3' where 'y' is and compute :

[12 -3(3) ] / 2   + 3 [ (2(3)-4 )/3) =

   3/2              +   2  

    =   3  1/2

Answer:

to be honest i don't know

Step-by-step explanation:

uh

Answer: its all

Step-by-step explanation:

it does not matter which one you pic, you just have to pick one.

7.7278 g/ml is the most accurate density of the substance.

It is define as the quantity per unit volume, unit area, or unit length.

i.e. the mass of a substance per unit volume.

Mathematically,

[tex]\rho =\frac{m}{v}[/tex]       ----- equation  (1)

Where,

p is the density

m is the mass

v is the volume

According to the question,

Mass = 27.82 grams  

Volume = 3.6 ml

By substituting the Value of m and v in equation 1.

[tex]\rho =\frac{27.82}{3.6}[/tex]

[tex]\rho = 7.7277777 g/ml[/tex]

Therefore,

The most accurate density of the substance in g/ml is  7.7277777 g/ml.

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Answer:

a = 46. Look down to find out more↓:

Step-by-step explanation:

a = kb²

4 = k(3)²

4 = k9

k = 4/9

a = 4/9(9²)

a = 4/9 (81)

a = 324/9

a = 36

The probability that Alex takes out three red apples is 1/30.

The probability that Alex takes out one green apple and two red apples is 1/10.

The probability that Alex takes out three red apples = (number of red apples / total number of apples) x (number of red apples - 1 / total number of apples - 1) x (number of red apples - 2 / total number of apples - 2)

4/10 x 3/9 x 2 /8 = 1 / 30

The probability that Alex takes out one green apple and two red apples = (number of green apples / total number of apples) x (number of red apples / total number of apples - 1) x (number of red apples - 1 / total number of apples - 2)

6/10 x 4/9 x 3/8 = 1 / 10

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Answer:

this is what i got

Answer:

Step-by-step explanation:

Let's rearrange the equation (for my benefit):

y-3 = -(x + 6)

y = -x -6 + 3

y = -x -3

This is an equation of a straight line with slope of -1 and a y-intercept of -3 (y is -3 when x = 0).

See the attached graph.

The probability of student A is 15/44

Given student A is 70% of time and student B is 60% of time

We need to find the probability of student A

Using formula of conditional probability is P(X/Y) = P(X and Y) / P(Y)

Here X = A and Y = A or B

Therefore,

P(A/A or B) = P(A and (A OR B) / P (A or B)

Now, There is none complement for at least 1

We know that Student A attends 70 % of time

So , his absence is 30% of the time .

Hence the probability of absence is 0.3

Now Considering B in the similar way

We get,

Probability of the absence is 0.4

They are both absent (0.3)(0.4)= 0.12

Here we can say that 12 % of time both are absent

So one or another present on that time is 88%

The probability of present of the time is 0.88

Now calculating the probability,

P(A/A or B) = P(A and (A OR B) / P (A or B)

= 0.3/0.88

= 30/88

= 15/44

Hence the Probability Of A is 15/44

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The equation of line is y = 92x – 182631. The slope is 92 and the y-intercept is the negative 182631. And the health expenditure in 2010 will be 2289.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

In MODE, (second line), fix the number of decimal places to be 2.

Then the slope and the y-intercept values of the Lin Reg line will round to the nearest hundredth.

(x₁, y₁) → (1997, 1093)

(x₂, y₂) → (2002, 1553)

Then we have

y – 1093 = [(1553 – 1093) / (2002 – 1997)] (x – 1997)

y – 1093 = [460  / 5] (x – 1997)

y – 1093 = 92 (x – 1997)

           y = 92x – 182631

If x = 2010, then the value of y will be

y = 92 × 2010 – 182631

y = 184920 – 192631

y = 2289

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Answer:

The Fruit market is at -  6th Street and 11th Avenue

Step-by-step explanation:

Distance is a numerical measurement of how far apart objects or points are. to find the distance between two points is the length of the line segment connecting them we use distance formula.

for example :-

if (x, y) and (p, q) are the two points joining the line segment then distance between them is given by the formula :-

[tex]\sqrt{(p- x)^2 + (q-y)^2}[/tex] this is known as the distance formula.

using the above formula :

distance between points (4, 8)  and (12, 20) is:

[tex]\sqrt{(12-4)^2 + (20-8)^2}[/tex]

√(8² + 12²)

√208

14.42

Now the fruit market is Three-fourths the distance between Tia’s home to Lei's home.

therefore,

3/4×14.42  = 10.8

now we can check that option (A ) i.e. (6, 11)  distance from lei home i.e. (12, 20) is equal to 10.8

hence the fruit market is at the = 6th Street and 11th Avenue

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Answer:

A

Step-by-step explanation:

The amount of RENT forgot to write is $ 50.

A transaction is a completed agreement between a buyer and a seller to exchange goods, services, or financial assets in return for money.

Here, Total expected amount = $ 900

          Actual amount = $ 750

          Deposit forgot = $ 100

Amount of RENT = 900 - (750 + 100)

                              = 900 - 850

                             = $ 50

Thus, The amount of RENT forgot to write is $ 50.

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Answer:

[tex]x=\pm3\sqrt{2}[/tex]

Step-by-step explanation:

1) Add 25 to both sides.

[tex]x^2 = -7 + 25[/tex]

2) Simplify -7 + 25 to 15.

[tex]x^2=18[/tex]

3) Take the square root of both sides.

[tex]x=\pm18[/tex]

4) Simplify [tex]\sqrt{18}[/tex] to [tex]3\sqrt{2}[/tex].

[tex]x=\pm3\sqrt{2}[/tex]

(A) n=w by the corresponding angles theorem.

(B) This is the correct answer. n=s by the vertical angles theorem and s and x are supplementary by the same-side interior angles theorem. Thus, n and x are supplementary and not always equal.

(C) n=z by the alternate exterior angles theorem.

(D) s=w, so (s+w)/2 = (s+s)/2 = s. Since n=s by the vertical angles theorem, n=s.

(E) n and w are equal by the corresponding angles theorem, and w and y are supplementary as they form a linear pair. Thus, n+y=180, and it follows n=180-y.

3.5

The triangle shown is a 30-60-90 special right triangle. All right triangles that have a 30-degree angle will be, but if needed you can use the equation: 180 - (90 + 30) = x, to find the missing angle.

Special Right Triangles

Special right triangles are useful because they allow us to easily find missing sides without having to use sin, cos, or tan. All special right triangles have formulas that can be used to find missing sides.

Formulas

30-60-90 triangles have 3 sides: the hypotenuse (c), the short leg (b), and the long leg (a).

The formulas are as follows:

Solving for b

We are already given c, so the easiest way to find b is to use the formula b = 0.5c. Just plugin the c-value.

Once simplified the final answer is

Answer:

$72

Step-by-step explanation:

The 90% confidence interval for the population mean is 78.1905<x<81.8095

The formula for calculating the confidence interval is expressed as:

CI = x ± z*s/√n

Given the following parameters

mean "x" = 80

z = 1.645

s = 5.5

n = 25

Substitute

CI = 80 ± 1.645*5.5/√25

CI = 80 ± 1.8095

CI = {78.1905, 81.8095}

Hence the 90% confidence interval for the population mean is 78.1905<x<81.8095

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Answer:

[tex]c=4 \sqrt{2}[/tex]

Step-by-step explanation:

Pythagoras Theorem

    [tex]a^2+b^2=c^2[/tex]

where:

Given values:

Substitute the given values into Pythagoras Theorem formula and solve for c:

[tex]\begin{aligned}a^2+b^2 & = c^2 \\\implies 4^2+4^2 & =c^2\\16+16 & =c^2\\32 & =c^2\\ \sqrt{c^2}& =\sqrt{32}\\ c & =\sqrt{16 \cdot 2}\\& = \sqrt{16}\sqrt{2}\\& =4\sqrt{2}\end{aligned}[/tex]

Therefore, the measure of the third side of the given right triangle is [tex]4 \sqrt{2}[/tex]

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Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.

Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;

18 = 2 x 9

18 = 2 x 3 x 3

18 = 3 x 6

In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.

2. Now, to write f(x) as the product of (x-1) and another factor.

x³+5x²+2x-8 = (x-1)(x²-6x+8).

3. Now, to write f(x) as the product of three linear factors.

x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)

4. Look at the sketch below.

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An Event is the set of results from an experiment in probability. Assume you do an experiment by tossing a coin.

An Event is the set of results from an experiment in probability. Assume you do an experiment by tossing a coin. This experiment results in the coin landing 'heads' or 'tails.' These are the events that are associated with the experiment.

Scenario 1: You are taking a multiple-choice test. Event A is you choose the correct answer. Event B is you choose D as the answer.

The two of the given events will overlap since there is a possibility that the correct answer is option D.

Scenario2: You survey students in your school about what grade they are in. Event A is the person is a senior. Event B is the person who is a junior.

The two of the given events are mutually exclusive events since a person can not be a senior and a junior at the same time.

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Answer:

hope this is helpful.

putting values of X and y in the equation

Answer is 12

Answer:

answer is 39

Step-by-step explanation:

So, we start with the original problem:

3

x

2

−

4

y

2

Then we substitute the given

x

and

y

values into the expression:

3

(

5

)

2

−

4

(

3

)

2

Now, according to the order of operations, we simplify the exponential powers first, thus, reducing the expression to this:

3

(

25

)

−

4

(

9

)

Then, we use the order of operations again and do the multiplication next:

75

−

36

We then use the order of operations a final time and finish off the expression with subtraction:

39

Answer: 4

Step-by-step explanation:

Sides opposite congruent angles in a triangle are congruent, so:

So, MN = 1 + 3 = 4

Answer:

3rd option

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 1, 4 ] , then

f(b) = f(4) = 3³ + 2 = 27 + 2 = 29

f(a) = f(1) = [tex]3^{0}[/tex] + 2 = 1 + 2 = 3 , then

average rate of change = [tex]\frac{29-3}{4-1}[/tex] = [tex]\frac{26}{3}[/tex]