Pie/Circle Graph: As a wildlife biologist, one of your duties is to catch, tag, and
release different species of mammals found in Oak Mountain, Alabama. Use
the data provided below to determine the percentage of each mammal
species caught and then label the different sections found in the pie graph
provided. During a 24 hour period, six cotton mice were caught, nine Norway
rats, 17 pine voles, and two eastern chipmunks.

The expression for f(x) that satisfies all the given conditions is:

f(x) = x

Given conditions:

f(x) is cubic: This means that f(x) can be expressed as a polynomial of degree 3 in the form: f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

f(x) ≥ 0 when x ≤ 2: This means that the curve of f(x) must be above or on the x-axis for x ≤ 2. In other words, f(x) must have a non-negative value for x ≤ 2.

f(x) < 0 when x > 2: This means that the curve of f(x) must be below the x-axis for x > 2. In other words, f(x) must have a negative value for x > 2.

f(0) = 4: This means that the curve of f(x) passes through the point (0, 4).

To satisfy the above conditions, we can start with the general form of a cubic polynomial, f(x) = ax^3 + bx^2 + cx + d, and find values of the coefficients a, b, c, and d that satisfy the given conditions.

Using the condition f(0) = 4, we can get d = 4.

Now, using the condition f(x) ≥ 0 when x ≤ 2, we can set up the inequality:

ax^3 + bx^2 + cx + 4 ≥ 0 for x ≤ 2

We can see that this inequality must hold for all x ≤ 2, so we can test the inequality at x = 2 to get:

8a + 4b + 2c + 4 ≥ 0

Simplifying this inequality, we get:

2a + b + 0.5c ≥ -1

Similarly, using the condition f(x) < 0 when x > 2, we can set up the inequality:

ax^3 + bx^2 + cx + 4 < 0 for x > 2

Again, we can test this inequality at x = 2 to get:

8a + 4b + 2c + 4 < 0

Simplifying this inequality, we get:

2a + b + 0.5c < -1

Now, we can solve these inequalities simultaneously to find the values of a, b, and c that satisfy all the given conditions. To do this, we can solve for c in terms of a and b from the first inequality:

c ≥ (-2a - b)/0.5

c ≤ (-2a - b)/0.5 - 8

Substituting these inequalities for c in the second inequality, we get:

2a + b + 0.5((-2a - b)/0.5 - 8) < -1

Simplifying this inequality, we get:

-3a - 2b > 13

Now, we can choose any values of a and b that satisfy this inequality, and then solve for the corresponding value of c using the first inequality.

For example, let's choose a = 1 and b = -5. Then, from the first inequality, we get:

c ≥ (-2(1) - (-5))/0.5 = 7

And from the second inequality, we get:

2(1) - 5 + 0.5c < -1

0.5c < 4

c < 8

So, we can choose c = 6, which satisfies both inequalities.

Therefore, the expression for f(x) that satisfies all the given conditions is:

f(x) = x

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Answer:

61

Step-by-step explanation:

thats right

Answer:

q = -1/8

Step-by-step explanation:

You're trying to solve for q
32q+4=0

Subtract 4 both sides
32q=-4

Now Divide -4 by 32 (This means you have to simplify)
-4/32 = -1/8 due to the common factor of 4.

q = -1/8

Answer:

4(8q+1)

Step-by-step explanation:

32q+4

4*8q+4*1

4(8q+1)

Answer: 36/12 = 3

Step-by-step explanation:

Answer:

The expression should be something like: 36/12

Answer:

D, dialation and rotation on edge

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

36 mph

Step-by-step explanation:

d = rt

d = (x)(3.6)

d = (x-4)(4)

3.6x = 4x - 16

-0.4x = -16

x = 40

Her speed was 40 on Thursday, so 36 on Friday

The speed of Debbie on Friday is 36 miles per hour.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Let d be the distance of her mother's house.

Let x be the speed of Debbie on Thursday.

x = d / 3.6

⇒ d = 3.6x

Speed on Friday = x - 4

Speed on Friday = d / 4

d / 4 = x - 4

⇒ d = 4 (x - 4)

Equating both the equations of d, we get,

4(x - 4) = 3.6x

4x - 16 = 3.6x

4x - 3.6x = 16

0.4x = 16

x = 40

Speed of Debbie on Thursday = 40 mile per hour

Speed of Debbie on Friday = 40 - 4 = 36 mile per hour

Hence the speed of Debbie on Friday is 36 miles per hour.

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Answer: 10

Step-by-step explanation:

Let the number be A

6 x A = 60

Hence, A = 60/6 = 10

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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Given:

The image of polygon MNOP after a similarity transformation is WXYZ.

Each side of MNOP is 2 times as long as the corresponding side of WXYZ.

To find:

The scale factor of the dilation in the similarity transformation.

Solution:

We know that, the scale factor is

\(k=\dfrac{\text{Side of image}}{\text{Corresponding side of original figure}}\)

We know that, MNOP is the original figure and WXYZ is the image. MN is corresponding side of WX.

\(k=\dfrac{WX}{MN}\)             ...(i)

Each side of MNOP is 2 times as long as the corresponding side of WXYZ.

\(MN=2WX\)

\(\dfrac{1}{2}=\dfrac{WX}{MN}\)

\(0.5=\dfrac{WX}{MN}\)           ...(ii)

From (i) and (ii), we get

\(k=0.5\)

Therefore, the correct option is B.

Answer:

On average, Elizabeth will earn $43.35 per week if her chickens lay 51 dozen per week.

Step-by-step explanation:

0.85x

x represents how many dozens

0.85(51) = 43.35

The number of people who ride the bus is 70 students.

From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.

Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.

This will be illustrated as:

4/7 = 40/x

Cross multiply

4x = 40 × 7

4x = 280

Divide

x = 280/4

x = 70

Therefore there are 70 students.

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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?

Step-by-step explanation:

here is ur answer with perfect solution

Answer:

The answer is (0)

Step-by-step explanation:

Answer:

(K+9)^2

Step-by-step explanation:

You have to find what two numbers muliply to 81 and add to 18, in this case the numbers that satisfy that are 9 and 9. So you then get (k+9)(k+9) which is the same as (k + 9)^2.

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

The converse of the parallelogram angle theorem is proved.

The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.

Here we are given that  LM ≅ ON and  LO ≅ MN

Here we have also know that ∠LNO and ∠NLM are alternative and interior angles

Then according to the reflexive property, it can be written as

=> LN ≅ LN

Then as per the SSS similarity the given triangle is written as,

ΔLNO ≅ ΔNLM

Here we have also it can be written as ∠OLN ≅ ∠MNL and  ∠LNO ≅ ∠NLM

Then it can be written as LM || ON and  LO || MN

Then the LMNO is a parallelogram

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Answer:

I think its 70in hope it helps

Step-by-step explanation:

Answer:

Quadrilaterals

Step-by-step explanation:

The slope-intercept of a line is given by

Where

"m" is the slope

and

"b" is the y-intercept

of the line.

The equation of the line given is

Comparing this with the slope-intercept form of a line, we have:

Thus,

The slope is 9 and the y-intercept is -5

\(\text{Area of parallelogram QRST} = QR \times TU = 20 ~in \times 18~in =360 in^2\)

Answer: The answer is 10.

Answer:

I don't see any answer choices, but read my explanation

Step-by-step explanation:

Any line with a slope of 3 would be parallel to y=3x+2.

For example,

y=3x+4

y=3x-1

y=3x

All of these lines are parallel to the original equation

Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

Answer:

The answer is 44!

Step-by-step explanation:

hehe ywww!!

renegade???

The dimensions of the open box made from rectangular piece of material will depend on the dimensions of rectangular material.

If an open box is made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides, then the dimensions of the box will depend on the size of the original rectangular piece of material and the size of the squares that are cut from the corners. The length and width of the box will be equal to the length and width of the original rectangular piece of material minus twice the size of the squares that are cut from the corners. The height of the box will be equal to the size of the squares that are cut from the corners.

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Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.

The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.

If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:

P = (2b + t) - d

Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

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The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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Answer: Find out how many eagles per ton hay costs:

(4/5 eagle)/ 1/6 ton  =  6/1  *  4/5   =   24/5  =  4.8 eagles per ton

THEN  2/3 ton would cost:

2/3 ton  *  24/5  eagles/ton =  (24*2) /(5*3) = 48/15 = 16/5 = 3.2 eagles

Step-by-step explanation: