HELP!!!


Josiah is on a hiking trail that goes north to south. If Josiah hikes x miles north, his
elevation, in feet, can be found using the function ƒ(x) = (x − 3)² + 200.
Negative values would find the elevation if Josiah hiked south. Find and interpret
the given function values and determine an appropriate domain for the function.

Answer: 2280000000

Step-by-step explanation: Yes, I know it is a long number, but 10 cubed = 10 x 10 x 10, which simplified, would be 100 x 10, which is 1000. So, now you do 2.4 x 1000 to get 2400. Now you take that and multiply that by 9.5. Then, you do 10 to the 5th power, which is 100000. Now, you connect it all together, to get 2280000000. Hopefully, I did it right, if not I am sorry :/

Answer:

(6,-1)

Step-by-step explanation:

(4 +2,1 -2)

right/left is X

Up/Down is Y

right/up is +

left/down is -

Answer: \(1\dfrac{29}{60}\text{ minutes}\)

Step-by-step explanation:

Given: A total eclipse solar eclipse in 2003 lasted \(5\dfrac{3}{20}\) minutes

\(=\dfrac{5(20)+3}{20}=\dfrac{103}{20}\text{ minutes}\)

& a total eclipse solar eclipse in 2005 lasted \(3\dfrac{2}{3}\)minutes

\(=\dfrac{3(3)+2}{3}=\dfrac{11}{3}\text{ minutes}\)

Difference= \(\dfrac{103}{20}-\dfrac{11}{3}=\dfrac{103\times3-11\times20}{60}\)

\(=\dfrac{309-220}{60}\\\\=\dfrac{89}{60}\text{ minutes}\\\\=1\dfrac{29}{60}\text{ minutes}\)

So, 2003 solar eclipse was \(1\dfrac{29}{60}\text{ minutes}\) longer than solar eclipse in 2005.

Answer:x - 4

Step-by-step explanation:6x + 6 - 5x - 10 = x-4

The shape with a series of parallel cross sections that are congruent circles is a cylinder.

The cross-section that results from cutting a cylinder parallel to its base is a circle that is congruent to all other parallel cross-sections. This is true for any plane that is perpendicular to the cylinder's base. The only shape that has parallel cross-sections that are congruent circles is a cylinder, for this reason.

Two parallel, congruent circular bases that lay on the same plane make up the three-dimensional shape of a cylinder. A curved rectangle connecting the bases makes up the cylinder's lateral surface. Congruent circles are produced when a cylinder is cut in half parallel to its base.

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Based on the calculations, the values that could be the length of the third side are B. 10 and E. 8. Therefore, the correct options are B. 10 and E. 8.

To determine the possible values for the length of the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given sides of lengths 5 and 13, we can check which values satisfy the triangle inequality:

The sum of the lengths of the two sides must be greater than the length of the third side:

5 + 13 > Third side

18 > Third side

Now let's check each given value:

A. 2: Not possible, since 18 > 2 does not hold true.

B. 10: Possible, since 18 > 10 holds true.

C. 24: Not possible, since 18 > 24 does not hold true.

D. 5: Not possible, since the given length is already one of the sides.

E. 8: Possible, since 18 > 8 holds true.

F. 19: Possible, since 18 > 19 does not hold true.

Based on the calculations, the values that could be the length of the third side are B. 10 and E. 8.

Therefore, the correct options are B. 10 and E. 8.

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Answer:

To compare the purple paints that Madelyn and Arturo made, you need to find the ratio of red to blue in each mixture. You can do this by dividing the amount of red paint by the amount of blue paint.

For Madelyn, the ratio of red to blue is:

10 / 3 = 3.33

For Arturo, the ratio of red to blue is:

4 / 1 = 4

Since Arturo has a higher ratio of red to blue, his purple paint will be redder than Madelyn’s.

Answer:

The new surface area would be 9 times larger than the original surface area.

Step-by-step explanation:

Here we do not know what was the original shape, but we will see that it does not matter.

Let's start with a square of side length L.

The original area of this square will be:

A = L^2

Now if each dimension is tripled, then all the sides of the square now will be equal to 3*L

Then the new area of the square is:

A' = (3*L)^2 = (3*L)*(3*L) = 9*L^2 = 9*A

So the new surface area is 9 times the original one.

Now, if the figure was a circle instead of a square?

For a circle of radius R, the area is:

A = pi*R^2

where pi = 3.14

Now if the dimensions of the circle are tripled, the new radius will be 3*R

Then the new area of the circle is:

A' = pi*(3*R)^2 = pi*9*R^2 = 9*(pi*R^2) = 9*A

Again, the new area is 9 times the original one.

If the figure is a triangle?

We know that for a triangle of base B and height H, the area is:

A = B*H/2

If we triple each measure, we will have a base 3*B and a height 3*H

Then the new area is:

A' = (3*B)*(3*H)/2 = (3*3)*(B*H/2) = 9*(B*H/2) = 9*A

Again, the new area is 9 times the original area.

So we can conclude that for any shape, the new area will be 9 times the original area.

The p-value is option (A) 0.0500

Under the null hypothesis, the expected number of defective peaches in the sample of 400 would be:

p = 0.10 (since the null hypothesis assumes a maximum of 10% defective peaches)

n = 400

expected number of defective peaches = np = 0.10 x 400 = 40

We can then use the binomial distribution to calculate the probability of getting 50 or more defective peaches in a sample of 400, assuming that the null hypothesis is true.

P(X ≥ 50) = 1 - P(X < 50)

where X is the number of defective peaches in the sample, assuming the null hypothesis is true.

Using a binomial calculator or a statistical software, we can find:

P(X < 50) = 0.3081

Therefore,

P(X ≥ 50) = 1 - P(X < 50) = 1 - 0.3081 = 0.6919

This is the p-value of the hypothesis test. Since this is a one-tailed test , we can compare the p-value to the significance level, α. If α = 0.05, then the p-value is greater than α, which means we fail to reject the null hypothesis.

Therefore, the correct answer is A. 0.0500.

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The expression for modelling the pattern is n² + 2

Charlie can observe 38 guppy fish in month 6.

Given,

Number of guppy fish in Charlie's fish tank for the first time = 3

Number of guppy fish after one month = 6

Number of guppy fish in the following month = 11

The increasing pattern of guppy fish in the tank:

First month = 6 - 3 = 3

Second month = 11 - 6 = 5

So, we get that the number of guppy fish is increasing by odd numbers.

That is, 3, 6, 11, ........

Now, we have to find an expression for this pattern.

First term is 3.

That is, first term² + 2 = 1² + 2 = 3

Let n be the number of term.

n = 3

So, third term be:

3² + 2 = 9 + 2 = 11

So the expression for modelling the pattern is n² + 2

Now, we have to find the number of guppy fish in month 6.

That is,

n = 6

So,

n² + 2

6² + 2 = 36 + 2 = 38

That is, Charlie can observe 38 guppy fish in month 6.

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5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

When we use the formula A = A0(1 - r)t,

(1/2)A₀ = A₀(1 - 0.11)t

[Divide both sides by A₀ results in:

1/2 = (0.87)t

Using the log of both sides;:

log(1/2) = log(0.87)t

Using a logarithm property, we can bring the "t" to the front, giving us:

log(1/2) = t.log(0.89)

[Dividing both sides with log(0.89) gets us:

t =  log(1/2)/log(0.89)

Using calculator for soling the values.

t = 5.94 seconds

Thus, 5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

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The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.

A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.

On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.

A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.

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Answer:

x = 18311.61 m

Step-by-step explanation:

It is given that, An observer (O) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. The distance from the observer (O) to the bird (B) is 15,000 ft. We need to find the distance between the bird and the nest. It is based on trigonometry. So,

\(\sin (35)=\dfrac{\text{opposite}}{\text{hypotenuse}}\)

Let x is the distance between the bird and the nest

So,

\(\sin (55)=\dfrac{15000}{x}\\\\x=\dfrac{15000}{ \sin(55)} \\\\x=18311.61\ m\)

So, the distance between the bird and the nest is 18311.61 m.

Answer:

8,604

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(2^3)^2/2^3X2^2 = 6/4 = 3/2

Step-by-step explanation:

(2^3)^2 = 6^2 = 36

2^3 X 2^2 = 6 X 4 = 24

Answer:

(2^3)^2 is 32 greater than 2^3 * 2^2

Step-by-step explanation:

(2^3)^2 = 2^(3 * 2) = 2^6 = 64

2^3 * 2^2 = 8 * 4 = 32

Difference:

64 - 32 = 32

Answer: (2^3)^2 is 32 greater than 2^3 * 2^2

Answer:

29.40-19.80=9.6

9.6/6=1.6

So the answer is $1.60

Step-by-step explanation:

Answer:

Inequality:  100x + 5400 ≤ 27500

x ≤ 221

Step-by-step explanation:

100x + 5400 ≤ 27500

100x ≤ 22100

x ≤ 221

Thus, the shipping container can contain no more than 221 100 kg crates to not exceed 27500 kg.

Answer: A rotation of 180° around the origin.

Step-by-step explanation:

When we have a point (x, y) and we want to reflect it over a given line, the distance between the point and the line remains invariant under the transformation.

This is equivalent as a rotation around a point, the "radius" of the circle that we are creating when we do a rotation is constant.

Now, let's analyze our case:

First a reflection over x-axis, and then a reflection over the y-axis.

This means that if our point starts in quadrant 1 then:

-The reflection over the x-axis will leave our point in quadrant 4.

-The reflection over the y-axis will leave our point in quadrant 3.

Now, if our point stated on quadrant 2.

-The reflection over the x-axis will leave our point in quadrant 3.

-The reflection over the y-axis will leave our point in quadrant 4.

So essentially, these transformations "move" our point to the opposite quadrant, such that the rules of the reflection are applied.

This means that:

The distance between our point and the x-axis does not change.

The distance between our point and the y-axis does not change.

But if the distances to both axes do not change, then the distance between our point and the origin also does not change.

This means that we can find a rotation that is equivalent to this transformation.

So we must look at a rotation that moves our point 2 quadrants.

a rotation that moves our point 2 quadrants will be:

A rotation of 180° around the origin.

The length of the rectangle is 6m - 2.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area = 30m² - 20m - 10

Width = 5m - 5

Now,

Area = Length x Width

30m² - 20m - 10 = Length x (5m - 5)

10(3m² - 2m - 1) = Length x (5m - 5)

10(3m² - (3 - 1)m - 1 = Length x (5m - 5)

10 (3m² - 3m + m - 1) = Length x (5m - 5)

10 (3m(m - 1) + 1(m - 1)) = Length x (5m - 5)

10 (3m + 1)(m - 1) = Length x 5(m - 1)

(m - 1) gets canceled.

10(3m - 1) = Length x 5

2(3m - 1) = Length

Length = 6m - 2

Thus,

6m - 2 is the length of the rectangle.

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Answer:

The price to make maximum revenue is 1 and the maximum revenue is 2000.

Step-by-step explanation:

Consider the provided information.

Revenue is the product of the number of sales and the sales price.

Here, \(p\) is the price of a cookie and the number of cookies sold is \(x =- 2000 p + 4000\).

\(\text{Revenue}=p(-2000 p + 4000)\)

\(\text{Revenue}=-2000 p^2 + 4000p\)

The above equation is a quadratic equation and the graph of the above equation will be a downward parabola because the coefficient of \(p\) is negative.

The vertex(axis of symmetry) of a downward parabola has the maximum point.

The axis of symmetry is  \(x=\frac{-b}{2a}\)  for the quadratic equation \(ax^2+bx+c=0\).

By compare Revenue equation with \(ax^2+bx+c=0\), we get:

\(x=p, a=-2000, b=4000 \text{ and } c=0\)

Now put the respective values in the formula \(x=\frac{-b}{2a}\) .

\(p=\frac{-4000}{2(-2000)}\)

\(p=1\)

So revenue will be maximum for \(p=1\).

Now put \(p=1\) in \(\text{Revenue}=-2000 p^2 + 4000p\)

\(\text{Revenue}=-2000 (1)^2 + 4000(1)\)

\(\text{Revenue}=-2000 + 4000\)

\(\text{Revenue}=2000\)

Hence, the price to make maximum revenue is 1 and the maximum revenue is 2000.

Maximum revenue generated = $2000

Price at which the maximum revenue is generated = $1

Steps to find the maximum revenue,

Given in the question,

        x = -2000p + 4000

Expression for the revenue generated = Price of one cookie × Number of cookies sold

R = p(-2000p + 4000)

R = -2000p² + 4000p

For the maximum revenue,

"Find the derivative of the expression for revenue and equate it to zero"

R' = -4000p + 4000 = 0

4000p = 4000

p = $1

For p = 1,

R = -2000(1) + 4000

R = $2000

       Therefore, for the price of one cookie as $1, maximum revenue generated will be $2000.

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None of the graphs with the given degree sequence (4,4,4,4,4,4,2) can be bipartite.

To understand why none of the graphs with the given degree sequence (4,4,4,4,4,4,2) are bipartite, let's first define the key terms:

1. Degree: The degree of a vertex in a graph is the number of edges incident to it.
2. Sequence: A degree sequence is a list of the degrees of each vertex in a graph.
3. Bipartite: A graph is bipartite if its vertices can be partitioned into two disjoint sets such that no two vertices within the same set are adjacent.

Now, let's analyze the given degree sequence (4,4,4,4,4,4,2):

1. There are 7 vertices in the graph.
2. The sum of the degrees is 4+4+4+4+4+4+2 = 26, which is even (a necessary condition for a graph to be bipartite).

For a graph to be bipartite, it must satisfy the Handshaking Lemma. The Handshaking Lemma states that the sum of the degrees of all vertices in a set should be equal to the sum of the degrees of all vertices in the other set. In other words, the sum of the degrees of all vertices in one set is equal to the number of edges crossing between the two sets.

Let's assume we can divide the vertices into two disjoint sets, A and B. Since each vertex with degree 4 is adjacent to 4 vertices, it must be connected to vertices in the opposite set. However, we have six vertices with degree 4, so the total sum of degrees of vertices in set A would be 6 * 4 = 24, while the vertex with degree 2 in set B would only account for 2. This contradicts the Handshaking Lemma, as 24 ≠ 2.

Hence, none of the graphs with the given degree sequence (4,4,4,4,4,4,2) can be bipartite.

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n = 37, and tenth term = 18

Given progression,

36, 34, 32, ...

The sum of the first n terms is 0

First term(a1) = 36

The common difference (d)= 34-36 = -2,

The formula of the sum of the first n term is,

\(Sn = \frac{n}{2} [2a_{1} + (n - 1)d]\)

substitue the values Sn= 0, a1= 36, d= -2 in the above equation to find n

\(0\)= \(\frac{n}{2} [2(36) + (n-1) (-2)]\)

\(0 = \frac{n}{2}[72- 2n+ 2]\)

\(0 = \frac{n}{2}[74 - 2n]\)

\(74 - 2n = 0\)

\(2n = 74\)

\(n = \frac{74}{2}\)

\(n = 37\)

n = 37

The formula for finding the nth term(10th term):

\(a_{n} = a1 + (n - 1)d\)

n = 10, a1 = 36, d = -2

\(a_{10} = 36 + (10-1)(-2)\)

\(a_{10} = 36 + 9(-2)\)

\(a_{10} = 36 - 18\)

\(a_{10} = 18\)

\(a_{10}\) = 18

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Answer:

Step 2 was the first mistake and the second option is the answer.

Step-by-step explanation:

Julia incorrectly factored the -1 from the second group of terms.

The correct option is (B)

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

2x^4 + 2x³ -x²-x

While solving the above expression in the third step

x(2x²(x+1)) - 1(x-1)

should be

x(2x²(x+1)) - 1(x + 1)

Hence, Julia incorrectly factored the -1 from the second group of terms.

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x = -31/40 or -0.775
y = 41/40 or 1.025
z = 9/4 or 2.25

To solve the given system of equations:

Step 1: Write the system of equations:
x - y + z = 0
3x + y + 2z = 2
2x + y - z = -3

Step 2: Choose a method to solve the system. In this case, let's use the method of elimination.

Step 3: Multiply the first equation by 3 to make the coefficient of x in both equations 3:
3(x - y + z) = 3(0)   -->   3x - 3y + 3z = 0

Step 4: Rewrite the second and third equations:
3x + y + 2z = 2
2x + y - z = -3

Step 5: Add the equations together to eliminate y:
(3x - 3y + 3z) + (3x + y + 2z) = 0 + 2
6x - 2y + 5z = 2

Step 6: Add the second and third equations to eliminate y again:
(2x + y - z) + (2x + y - z) = -3 + (-3)
4x + 2y - 2z = -6

Step 7: Now we have a new system of equations:
6x - 2y + 5z = 2
4x + 2y - 2z = -6

Step 8: Add the equations together to eliminate y again:
(6x - 2y + 5z) + (4x + 2y - 2z) = 2 + (-6)
10x + 3z = -4

Step 9: Solve the equation 10x + 3z = -4 for x in terms of z:
10x = -4 - 3z
x = (-4 - 3z) / 10

Step 10: Substitute the expression for x back into the first equation:
(-4 - 3z) / 10 - y + z = 0

Step 11: Simplify and solve for y in terms of z:
-4 - 3z - 10y + 10z = 0
7z - 10y = 4
10y = 7z - 4
y = (7z - 4) / 10

Step 12: Substitute the expressions for x and y back into the second equation:
3((-4 - 3z) / 10) + ((7z - 4) / 10) + 2z = 2

Step 13: Simplify and solve for z:
(-12 - 9z + 7z - 4 + 20z) / 10 = 2
16z - 16 = 20
16z = 36
z = 36 / 16
z = 9 / 4 or 2.25

Step 14: Substitute the value of z back into the expressions for x and y to find their values:
x = (-4 - 3(9/4)) / 10
x = -31/40 or -0.775

y = (7(9/4) - 4) / 10
y = 41/40 or 1.025

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There are 8 outcomes in the sample space.

When flipping a coin 3 times, there are 2 possible outcomes for each flip: heads (H) or tails (T). Thus, the total number of outcomes in the sample space is the number of possible combinations of H and T for 3 flips, which is 2³ = 8.

These outcomes can be listed as follows: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT. Each outcome is equally likely to occur, assuming the coin is fair and the flips are independent.

The concept of sample space is an important one in probability theory, as it represents the set of all possible outcomes of an experiment.

Knowing the sample space can help us calculate probabilities for specific events within that space and inform decision-making in a wide range of fields, from finance to sports to public health.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Total number of cards is always 52 which has 4 jacks. In the given question we need to use the concept of probability.

The following steps are need to be followed:

1. First, let's identify some key information:
  - A standard deck has 52 cards, with 4 jacks (one of each suit).
  - You're drawing a card and then replacing it, which means each draw is independent and the probability remains constant.

2. Now, let's calculate the probability of drawing a jack on each draw:
  - P(Jack) = 4 jacks / 52 total cards = 1/13

3. Since you want to find the probability of drawing a jack 4 times in a row, we'll multiply the probability of drawing a jack on each draw:
  - P(All Jacks) = P(Jack) × P(Jack) × P(Jack) × P(Jack) = (1/13) × (1/13) × (1/13) × (1/13)

4. Simplify the probability:
  - P(All Jacks) = 1/28561

So the probability of drawing all 4 jacks when you pick 4 cards from a deck, replacing the card each time before picking the next card, is 1/28,561.

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Answer:

4 mg

Step-by-step explanation:

Plug in everything that they have given for the equation

since x is the number of half-lives, and iodine-131 has a half-life of 8, and the question is asking for how much there will be left after 32 days, 8 * 4 = 32, so x will be 4.

y = 64(0.5)^4

and solve

y = 4

so there will be 4 mg of iodine-131 left after 32 days.

Answer:

4 mg

Step-by-step explanation:

half- life is 8 days then 32 ÷ 8 = 4 half- lives , then

y = 64 \((0.5)^{4}\) = 64 × 0.0625 = 4 mg left