Subtract.

−2.08−(−4.49)

Enter your answer in the box.

The statistical relationship between two variables is stronger than 95% of the relationships we would expect to see just by chance.

Statistical relationship:

Statistical relationship defines that  if a change in one variable (X) results in a systematic increase in another (Y).

Given,

A statistical relationship between two variables is considered statistically significant.

Here we need to find if it is stronger than what percent of relationships we'd expect to see by chance.

While we looking into the given question we know that the statistical relationship is stronger then the percent of relationships we'd expect to see by chance is 95%.

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The translations of each sentence into an equation or formula are A = L^2 and P = a + b +c

The sentences are given as:

For the first sentence, we have:

The area A of a square is the length of a side & squared.

This means that:

A = L^2

For the second sentence, we have:

The perimeter P of a triangle is equal to the sum of the lengths sides a, b, and c.

This means that

P = a + b +c

Hence, the translations of each sentence into an equation or formula are A = L^2 and P = a + b +c

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Answer:

1st, 3rd

and 4th - "4th" from different answer :)

Step-by-step explanation:

Have a good day :)

Answer:

1,3 and 4

Step-by-step explanation:

The area of the rectangle with a length of 3.6cm and a width of 4.7cm is 16.92 cm².

A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The area of a rectangle is expressed as;

Area = length × width

Given that;

Plug in the values into the above equation and solve for area.

Area = length × width

Area = 3.6 cm × 4.7 cm

Area = 16.92 cm²

Therefore, the area is 16.92 squared centimeters.

Option C) 16.92 cm² is the correct answer.

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The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) \(\sqrt{540}\) = \(\sqrt{36 * 15 }\)

= 6√15

2) \(\sqrt[3]{432}\) = \(\sqrt[3]{216*2}\)

= \(6\sqrt[3]{2}\)

3) \(\sqrt[3]{128}\) = \(\sqrt[3]{64*2}\)

= \(4\sqrt[3]{2}\)

4) \(-\sqrt[4]{405}\) = \(-\sqrt[4]{81*5}\)

= \(-3\sqrt[4]{5}\)

5) \(\sqrt[3]{-5000}\) = \(-\sqrt[3]{1000*5}\)

= \(-10\sqrt[3]{5}\)

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Answer:

A quadratic function has the formula y equals a x squared right and once you have a square.

Answer:

pretty sure it's the 2nd one

Step-by-step explanation:

A 3x3 matrix that represents a rotation in two-dimensional space of 60 degrees is:

| cos(60°)  -sin(60°)  0 |

| sin(60°)   cos(60°)  0 |

|    0           0            1 |

To represent a rotation in two-dimensional space using a matrix, we can use the concept of homogeneous coordinates, where we extend the two-dimensional space to three dimensions by adding a third coordinate. This allows us to represent the rotation as a 3x3 matrix.

In the given matrix, the rotation is 60 degrees. To determine the entries of the matrix, we use the trigonometric functions cosine (cos) and sine (sin) of the rotation angle.

The top-left entry, cos(60°), represents the cosine of 60 degrees, which is 1/2. The top-right entry, -sin(60°), represents the negative sine of 60 degrees, which is -√3/2. The middle-left entry, sin(60°), represents the sine of 60 degrees, which is √3/2. The middle-right entry, cos(60°), represents the cosine of 60 degrees, which is 1/2. The bottom-left and bottom-right entries are both zeros, as they represent the z-coordinate in the extended three-dimensional space.

This matrix can be used to multiply with a vector representing a point in two-dimensional space to achieve the rotation of 60 degrees. The multiplication operation would result in a new vector representing the rotated point.

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Answer: a + 3b = 8

Step-by-step explanation:

a + b = 4 is true, since (2,2) works:  2 + 2 = 4

Try (2,2) in the options to find which one is true for (2,2):

A)  2 + 3*2 = 4?  No.

B)  4 + 4 = 2?  No.

C)  8 + 8 = 8?  No.

D)  2 + 6 = 8?  YES.

Therefore, a + 3b = 8 can be another valid equation.

Answer:

D. a + 3b = 8

Answer:

6 in

Step-by-step explanation:

2/3 = 4/x

(4*3)/2

Answer:

x = 39.1

Step-by-step explanation:

To find the mean, add up all the data points and then divide by the number of data points

(31.7+ 42.8+ 26.4+ x)/4 = 35

Multiply each side by 4

(31.7+ 42.8+ 26.4+ x)/4*4 = 35*4

(31.7+ 42.8+ 26.4+ x) = 140

Combine like terms

100.9+x = 140

Subtract 100.9 from each side

x = 140-100.9

x = 39.1

The population proportion of cars that take some damage exceeds the park’s claim.

Given that:

Population proportion of all cars that have some damage from an animal after the safari is:

p = 0.65

Sample size, n = 20

\(\hat{p}\) = 18/20 = 0.9

The hypothesis can be defined as:

H₀ : p ≤ 0.65

H₁ : p > 0.65

Now, the z-value corresponds to α = 0.05 is z = 1.645.

So the critical value of z = 1.645

Now, the test statistic is:

z = \(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n} } }\)

  = \(\frac{0.9-0.65}{\sqrt{\frac{0.65(1-0.65)}{20} } }\)

  = 2.344

Here the test statistic, z, is greater than the critical value of z.

So, H₀ is rejected.

So, the population proportion exceeds the park's claim.

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Pet Theory: Theory of Evolution by Natural Selection . The theory of evolution by natural selection explains how species change over time due to the process of natural selection, resulting in the diversity of life we see today.

The theory of evolution by natural selection is a scientific explanation for how species change and adapt over time. It states that all living organisms on Earth share a common ancestor and that species evolve through a process called natural selection. Natural selection is driven by three main principles: variation, inheritance, and selection.

Firstly, within a population, there is variation, which means individuals within a species differ from each other in traits such as size, color, or behavior. This variation arises from genetic mutations and genetic recombination during reproduction.

Secondly, these variations can be inherited from one generation to the next. Offspring inherit traits from their parents through the transmission of genetic material, such as DNA.

Lastly, natural selection acts on this variation. In any given environment, certain traits may provide advantages or disadvantages for survival and reproduction. Individuals with advantageous traits are more likely to survive and pass on their genes to the next generation, while those with less favorable traits are less likely to survive and reproduce.

Over time, as the environment changes or as populations migrate to new habitats, the frequency of different traits in a population can shift. This leads to the accumulation of beneficial traits and the emergence of new species.

It is important to note that natural selection does not involve conscious planning or design. Instead, it is a result of the interplay between variation, inheritance, and the environment. It is through this process that life on Earth has evolved and diversified into the incredible array of organisms we see today.

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Answer:

perimeter of the entire figure=28cm

Step-by-step explanation:

Answer:

=4x2+12x+9

hope it helps you!

Step-by-step explanation:

Answer:

4x2−12x+9

Step-by-step explanation:

expand using the foil method

Simplify and combine like terms

and you get the answer

Answer:

There Will be one cookie left.

Step-by-step explanation:

She is wrong Becuase if you eat 4 cookies there is two left. So if you put it on 5 there would only be 1 left.

Answer:

the area is 25/4 π

Step-by-step explanation:

diameter is 5 m

area will be 25/4π

Answer:

  17.9 m²

Step-by-step explanation:

The area of the deck is the difference between the area of the square and the area of the circular hot tub.

__

The area of the square is given by the formula ...

  A = s² . . . . where s is the side length

For a side length of 5 m, the area is ...

  A = (5 m)² = 25 m²

The area of a circle is found from the formula ...

  A = (π/4)d² . . . . where d is the diameter

For a diameter of 3 m, the area is ...

  A = (π/4)(3 m)² = 9/4π m² ≈ 7.069 m²

The area of the deck is the difference between the square area and the circle area:

  deck area = 25 m² -7.069 m² ≈ 17.9 m²

The area of the deck surrounding the hot tub is about 17.9 m².

The interest rate for Rebeka's account is 5%.

What is the meaning of interest rate?

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given that, Rebeka deposits $1500. She earn $131.25 as interest after 21 months.

The formula of simple interest is

I = PRT

I = interest

P = Principal

R = Rate of interest

T = time

In the given question,

P = $1500

I = $131.25

T = 21 months = 21/12 years.

Putting P = $1500, I = $131.25, T = 21/12 years in I = PRT:

131.25 = 1500 × R × (21/12)

Divide both sides by 1500 × (21/12):

R = 131.25 /[1500 × (21/12)]

R = [131.25 × 12] /[1500 × 21]

R = 0.05

R = 5%

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The y(t) = e^-t + e^5t + 3t^3 is also a solution to the given differential equation.

To determine which function is also a solution to the given differential equation, we need to substitute each function into the equation and see if it satisfies the equation. When we substitute y(t) = 3t^3 into the equation, we get g(t) = 0. Now, when we substitute each of the given functions into the equation, we find that only option (c) y(t) = e^-t + e^5t + 3t^3 satisfies the equation.

Therefore, the answer is (c). This is because when we substitute y(t) = e^-t + e^5t + 3t^3 into the differential equation, we get y" – 4y’ - 5y = -16e^-t + 80e^5t, which is equal to g(t).

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There are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

Here, we have to solve this problem, we can use the concept of combinations, which involves counting the ways to choose a specific number of items from a larger set without regard to the order of selection.

Given the conditions that at least one member must be chosen from each group (artists, singers, writers) and there must be at least 3 artists, we can break down the problem into cases.

Case 1: Choosing 1 artist, 1 singer, and 5 members from the remaining groups (writers).

Case 2: Choosing 2 artists, 1 singer, and 4 members from the remaining groups (writers).

Case 3: Choosing 3 artists, 1 singer, and 3 members from the remaining groups (writers).

For each case, we will calculate the number of ways to choose members and then sum up the results from all three cases to get the total number of ways.

Let's calculate the number of ways for each case:

Case 1:

Number of ways to choose 1 artist: 6C1 (6 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 5 writers: 5C5 (1 way)

Total ways for case 1: 6C1 * 4C1 * 5C5 = 6 * 4 * 1 = 24

Case 2:

Number of ways to choose 2 artists: 6C2 (15 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 4 writers: 5C4 (5 ways)

Total ways for case 2: 6C2 * 4C1 * 5C4 = 15 * 4 * 5 = 300

Case 3:

Number of ways to choose 3 artists: 6C3 (20 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 3 writers: 5C3 (10 ways)

Total ways for case 3: 6C3 * 4C1 * 5C3 = 20 * 4 * 10 = 800

Now, add up the total ways from all three cases:

Total ways = 24 + 300 + 800 = 1124

So, there are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

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===========================================================

Explanation:

Let's label the friends as A,B,C,D.

Person A has a probability of 7/16 when it comes to ordering a certain color of cotton sweatshirt.

Then 6/15 is the probability for person B. Note how the 7 and 16 drop by 1 for each. This is because no repeats are allowed. If person A goes for a blue sweatshirt, then person B cannot select blue as well.

Person C's probability is 5/14 and person D has a probability of 4/13

-------------------------

So we have these fractions: 7/16, 6/15, 5/14, 4/13

Once again, we have the numerators and denominators counting down by 1 each time.

Multiplying those fractions gets us...

(7/16)*(6/15)*(5/14)*(4/13)

(7*6*5*4)/(16*15*14*13)

840/43680

(1*840)/(52*840)

1/52

So if you did 52 trials of this, then you should expect about 1 of those trials is where each friend orders a different color cotton sweatshirt.

1/52 = 0.0192 = 1.92% approximately

So this happens about 1.92% of the time.

Answer:

1. No

2. Yes

3. No

4. Yes

Step-by-step explanation:

x is equal to the number of miles, so it can't be the amount in dollars.

25 is the fixed amount because it does not change in the equation.

0.35 is not the fixed amount because it changes based on x.

f(x) is the total amount because that's what the equation is equal to.

The exterior angle of each polygon and the adjacent interior angle are

supplementary.

(a) 72°    (b) \(\displaystyle 51 \frac{3}{7} ^{\circ}\)    (c) 36°    (d) 20°    (e) 18°

Reasons:

The formula for the exterior angle of a regular polygon is, \(\displaystyle \theta = \mathbf{ \frac{360 ^{\circ}}{n}}\)

Where;

θ = The exterior angle of the polygon

n = The number of sides of the regular polygon

(a) The number of sides in a pentagon, n = 5 sides

Therefore, for a regular pentagon, we have;

\(Exterior \ angle , \displaystyle \theta = \frac{360 ^{\circ}}{5} = \mathbf{{72^{\circ}}}\)

The measure of the exterior angle of a pentagon, is 72°

(b) An heptagon has n = 7 sides

The measure of the exterior angle, θ, of a regular heptagon is therefore;

\(Exterior \ angle \ of \ a \ heptagon , \,\displaystyle \theta = \frac{360 ^{\circ}}{7} = \underline{51 \frac{3}{7} ^{\circ}}\)

(c) A decagon has n = 10 sides, which gives;

\(The \ exterior \ angle \ of \ a \regular \ decagon, \,\displaystyle \theta = \frac{360 ^{\circ}}{10} = \underline{36^{\circ}}\)

(d) The exterior angle of an 18-gon with n = 18 sides is given as follows;

\(The \ exterior \ angle \ of \ a \ regular \ 18-gon, \,\displaystyle \theta = \frac{360 ^{\circ}}{18} = \underline{20^{\circ}}\)

(e) A regular 20-gon has n = 20 sides

The exterior angle of a regular 20-gon is \(\displaystyle \frac{360 ^{\circ}}{20} = \underline{ 18^{\circ}}\)

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Answer:

960 foxes after 24 years

Step-by-step explanation:

given

y = 60 × \(4^{x}\) models the situation

there are 2 12- year periods in 24 years , then x = 2 , so

y = 60 × 4² = 60 × 16 = 960

there will be 960 foxes after 24 years

How many people will have heard the rumor by the end of the first day. The formula given is

N(t) = 1 + 200e^(0.0001t)N(t)

represents the number of people who hear the rumor by time t.

Therefore,N(1) = 1 + 200e^(0.0001(1))≈ 1 + 20.02≈ 21 people (rounded to nearest integer)Therefore, the number of people who hear the rumor by the end of the first day is 21.b) How many will have heard the rumor by the end of the fourth day The formula given isN(t) = 1 + 200e^(0.0001t)N(t) represents the number of people who hear the rumor by time t.t = 4 (fourth day).

Therefore, the number of people who hear the rumor by the end of the fourth day is 24.c) Use graphical or numerical methods to find the day on which 7600 people in town have heard the rumor.The formula given isN(t) = 1 + 200e^(0.0001t)Let (rounded to nearest integer) Therefore, the day on which 7600 people in town have heard the rumor is the 30th day (rounded up to the nearest integer).

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Answer: 1. Describe a sequence of translations that would map Figure H onto Figure K.

⃗⃗⃗⃗⃗⃗

Translate Figure H along vector , and then

⃗⃗⃗⃗⃗⃗ translate the image along vector .

⃗⃗⃗⃗⃗⃗

Translate Figure H along vector , and then

⃗⃗⃗⃗⃗⃗ translate the image along vector .

2. Describe a sequence of translations that would map Figure J onto itself.

⃗⃗⃗⃗⃗⃗

Translate Figure J along vector , and then

⃗⃗⃗⃗⃗⃗ translate the image along vector .

⃗⃗⃗⃗⃗⃗

Translate Figure J along vector , and then

⃗⃗⃗⃗⃗⃗ translate the image along vector .

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:38

Step-by-step explanation: