Factor the polynomial by its greatest common monomial factor.

Answer:

2.5

Step-by-step explanation:

15-10=5

5/2=2.5

Answer:

5°

Step-by-step explanation:

because: -5°+5°=0° I think

Answer:

5 degrees

Step-by-step explanation:

-5+5=0

Each pound of bananas costs $1.49 when buying 10 pounds, and $1.51 when buying 8 pounds.

The standard unit of money in the United Kingdom, equivalent to 16 ounces (or 0.454 kilograms), is used in most English-speaking countries. For more information, see measure. also known as the pound sterling.

Let the cost per pound of bananas be represented by x. Then we can set up the following system of equations:

\(10x &= 14.90 \\8x &= 12.08\)

Solving for $x$ in each equation, we get:

x = 14.9/10 =  1.49

x = 12.08/8 = 1.51

Therefore, each pound of bananas costs $1.49 when buying 10 pounds, and $1.51 when buying 8 pounds.

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Answer:

It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

Step-by-step explanation:

Answer:

The answer is "\(116 \ ft^2\) "

Step-by-step explanation:

Please find the complete question in the attachment file.

Calculating the sides of the room:

\(8\times 8=64\\\\12\times 2=24 \\\\2\times 6=12 \\\\4 \times 4=16\\\\\)

adding the value of the side area:

\(\to 64+24+12+16=116\)

Answer:

21.5 square units

Step-by-step explanation:

The 4 circles touching eachother have a total combined length of 20.

There are 4 circles. 20/4 = 5. The diameter of each circle is 5 units.

The length ofthe rectangle is 20 units. the width of the rectangle is 5 units.

The area of the shaded region is the area of the rectangle minus the ares of 4 circles.

A = area of rectangle - area of 4 circles

A = LW - 4 × πr²

The radius of each ciorcle is d/2 = 5/2 = 2.5

A = 20 × 5 - 4 × 3.14 × 2.5²

A = 100 - 78.5

A = 21.5

The symbol for population mean is μ  and the symbol for population variance is σ².

In statistics, the mean and variance are two of the most commonly used measures of central tendency and dispersion, respectively. The mean is the average value of a set of data, and the variance is a measure of how spread out the data is.

When dealing with a population, the mean and variance are denoted by different symbols than when dealing with a sample. The population mean is denoted by the   (μ), and the population variance is denoted by  (σ²).

The population mean is calculated by summing up all the values in a population and dividing by the total number of values in the population. The population variance is calculated by finding the difference between each value in the population and the population mean, squaring each difference, and then averaging the squared differences.

It's important to note that when dealing with a sample, the mean and variance are denoted by different symbols. The sample mean is denoted by x-bar and the sample variance is denoted by s².

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Answer:

Nope

Step-by-step explanation:

It doesnt. Functions look like that

Among the given options, option D, where the clerk completed the transaction without giving Susan a receipt or informing her of the due date, invalidates the contract.

To determine which event invalidates the contract Susan signed with Super Video, we need to identify the event that goes against the terms and conditions of the contract.

A contract typically includes specific terms and conditions that both parties must adhere to. Option D states that the clerk completed the transaction without giving Susan a receipt or otherwise informing her of the due date. This event violates the terms of the contract. The contract should have specified that Susan is entitled to receive a receipt and be informed of the due date to fulfill her obligations and protect her rights as a customer. As a result, this event invalidates the contract Susan signed with Super Video.


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Answer:

Step-by-step explanation:

This "subtraction problem" involves: "one value" minus "another value":
The first value is:  " 10m³n²σ⁵ " ;

The second value is:  25m⁴nσ " ;
_________________________
The problem to be solved is:
  " 10m³n²σ⁵ − 25m⁴nσ = ?? ;  

 Let us "factor out" what we can—considering the two (2) values:
  1)  " 10m³n²σ⁵ " ; and:
  2) " 25m⁴nσ " ;

The GCF ["Greatest Common Factor"] of:
 "10" and "25" :
______________________
List the factors for Both "10" and for "25"—as follows:

 10: 1, 2, 5, 10.
25: 1,  5, 25.
        → The GCF for "10 and 25" is "5".
→ Note that the GCF for " m³ and m⁴ " is "m³ ."

→ Note that the GCF for: " n²  and n" is "n".   {Note:  " n  =  n¹ ".}

→ Note that the GCF for: " σ⁵  and "σ" is "σ".  {Note:  " σ =  σ¹ ".}

So, the GCF for entire problem:

Factor out:  " 5m³nσ"

________________________

The first expression:
 10m³n²σ⁵  ;

 Factor out:  (5m³nσ} ;

   (5m³nσ} (2*1*nσ⁴}
  =   (5m³nσ} (2nσ⁴}

______________________

The second expression:
 25m⁴nσ ;

Factor out:
  (5m³nσ} (5m*1*1} ;

 = {5m³nσ} (5m} .

________________________
So:

  (5m³nσ} (2nσ⁴} − (5m³nσ}  (5m} ;

  =    {5m³nσ} * (2nσ⁴ − 5m) ;   {Note:  {" ax − ay  =  a(x − y) "}.

Now, simplify:
 

{5m³nσ} * (2nσ⁴ − 5m) =

 {5m³nσ} * 1(2nσ⁴ − 5m) ;

   →  1 (2nσ⁴ − 5m) ;   Note:  a(b+c) = ab + ac ;  

                                               a(b−c) = ab − ac ;

  1 (2nσ⁴ − 5m) = 2nσ⁴ + (-5m)

                          = 2nσ⁴ − 5m ;
Now bring down the:

 {5m³nσ} ; and rewrite:
     ⇒  {5m³nσ}*(2nσ⁴ − 5m);  Note: a(b+c) = ab + ac ;  ==> again:
 in which:  a = 5m³nσ ;  b = 2nσ⁴ ; c = -5m ;
      →   {5m³nσ}*(2nσ⁴ - 5m} =
             [5m³nσ}*(2nσ⁴} +  {5m³nσ}{-5m) ;

Start with the "left-hand side" of the problem; ^directly above:
[5m³nσ}*(2no⁴} = 5*2*m³*n²σ⁵  = 10m³*n²σ⁵ ;

Then: We shall examine the "right-hand side" of the above:
   "{5m³nσ}{-5m)" ;

        →   {-25m⁴nσ);

________________
Then, we shall add these values together:
 10m³*n²σ⁵  +  (-25m⁴nσ);

   = 10m³*n²σ⁵  − 25m⁴nσ);

Answer:

and i

Step-by-step explanation:

oop.

The probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to .  The odds that it will not rain tomorrow are to 0.8.

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability that it will rain tomorrow is 0.2

i.e.

P(it will rain tomorrow )=0.2

Now probability that it won't rain tomorrow is,

P(it won't rain tomorrow )=1- P(it will rain tomorrow)=1-0.2=0.8

Thus

P(it won't rain tomorrow)=0.8.

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(q ∨ (¬r ∧ ¬q)) → ¬p is the propositions and create logic sentences.

What is propositions ?

An axiom is a mathematical assertion that is predicated on a proposition, such as "3 is greater than 4," "an infinite set exists," or "7 is prime."

If you are more than  18 years old or if you are above 18 but lack identification proving your age, you are not permitted to to watch cartoon.

Prepositions -

p = You are allowed to watch cartoon.

q = your age is more  than 18 years old

r = you have age proof

(q ∨ (¬r ∧ ¬q)) → ¬p

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Answer:

2 hours

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

32>25

it will be 7 inches

The resulting reflection will be (4,-5) and will be followed by (-4,-5).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. A series of data indicating a precise position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is 12 units long and 5 units high.

Here,

given coordinates=(4,5)

Firstly, reflecting across x axis, point (x,y) turns to (x, -y).

=(4,-5)

Secondly, reflecting (x,-y) across y-axis, point (x,-y) turns to (-x,-y).

=(-4,-5)

The resultant reflection will lead (4,-5) followed by (-4,-5).

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The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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Possible answers to the expression 2x - 15 are given as follows:

An expression is solved isolating the variable of which we want to find the value.

In this problem, the expression is given as follows:

2x - 15 = c.

In which c is a constant that is not given in the incomplete problem here, hence we will attribute values to it.

With c = -35, we have that the solution is found as follows:

2x - 15 = -35

2x = -20 (-35 + 15)

x = -20/2

x = -10.

Now, if c = 3, the solution is calculated as follows:

2x - 15 = 3

2x = 18

x = 18/2

x = 9.

In your problem, a value for c(the right-handed side of the equality) will be given, and you will solve it applying the same procedure I applied in the answer here.

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Answer:

x = 5/6

Step-by-step explanation:

Cross multiply.

18(x - 2) = 3(-7)

Divide both sides by 3.

6(x - 2) = -7

Distribute the 6.

6x - 12 = -7

Add 12 to both sides.

6x = 5

Divide both sides by 6.

x = 5/6

Answer: x = 5/6

\(\dashrightarrow\:\:\sf \dfrac{x - 2}{3} = \dfrac{-7}{18} \\ \\ \\ \)

\(\dashrightarrow\:\:\sf (x - 2) \times 18= -7 \times 3 \\ \\ \\ \)

\(\dashrightarrow\:\:\sf 18x - 36 = -21 \\ \\ \\ \)

\(\dashrightarrow\:\:\sf 18x = -21 + 36\\ \\ \\ \)

\(\dashrightarrow\:\:\sf 18x = 15\\ \\ \\ \)

\(\dashrightarrow\:\:\sf x = \dfrac{15}{18} \\ \\ \\ \)

\(\dashrightarrow\:\:\sf x = \dfrac{5}{6} \\ \\ \\ \)

\(\dashrightarrow\:\: \underline{ \boxed{\textsf{\textbf{x $\approx$ 0.84}}}}\\ \\ \\ \)

Answer:

whole number is the answer

Mean is 27 and SD is 2 then the normal curve ​with highest range would be at domain 27.

The mean is the average of a set of numbers. It is calculated by adding all the numbers in the set together, and then dividing by the number of values in the set.  It is calculated by adding up all the numbers in the set, dividing by how many values there are in the set, and then multiplying by that number. The average of a group of numbers is called the mean.

Mean is 27 and SD is 2

a) P(23<x<27)= P((23-27)/2<z<(27-27)/2)=P(-2<z<0)=P(z<0)-P(z<-2) or P(z<0)-(1-P(z<2))

From normal distribution table we get 0.5-(1-0.9772)=0.4772

b) P(x>31)=P(z>(31-27)/2)=P(z>2) or 1-P(z<2)=1-0.9772=0.0228

c) P(x<29)= P(z<(29-27)/2)=P(z<1)=0.8413

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The least number of 6th graders who want to take part in both classes is 145.

The intersection of sets A and B is the set of all the elements which are common to both A and B. The intersection of sets is denoted by the symbol '∩'. Hence, we can write the intersection of A and B as A ∩ B.

The number of graders that want to take geometry is 170.

The number of graders that want to take algebra is 175.

A ∩ G= n(A) + n(G) -( AUB)

=175+170-200

= 345-200

= 145

Therefore, the least number of 6th graders who want to take part in both classes is 145.

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Answer:

16

Step-by-step explanation:

Base: 2x2=4

The 4 Triangles: 2x3x1/2 (for each triangle), each triangle equals 3

3x4=12

12+4=16

16 is the final answer

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

Given:

The right triangular prism.

Height of prism = 28 in.

Hypotenuse of base = 25 in.

leg of base = 24 in.

To find:

The lateral surface area of the prism.

Solution:

Pythagoras theorem:

\(Hypotenuse^2=Perpendicular^2+Base^2\)

Using Pythagoras theorem in the base triangle, we get

\(25^2=24^2+Base^2\)

\(625-576=Base^2\)

\(\sqrt{49}=Base\)

\(7=Base\)

The perimeter of the triangular base is:

\(P=7+25+24\)

\(P=56\)

Lateral area of a triangular prism is:

\(A=Ph\)

Where, P is the perimeter of the triangular base and h is the height of the prism.

Putting \(P=56,h=28\) in the above formula, we get

\(A=56(28)\)

\(A=1568\)

Therefore, the lateral area of the prism is 1568 in².

The degree of freedom would be 36.

What is the degree of freedom in statistics?

It is a mathematical equation that tells how many values can vary and can aid in determining whether or not the results are statistically significant. In statistics, the most commonly encountered equation for determining degrees of freedom is df = N-1.

Que.16)

It is a statistic. Because it gives information about the sample.

Que.17)

Because 35 is close to 36.

Que.18)

degrees of freedom = n -1 = 37-1 = 36

Que .19)

\(C.I. = \bar{X} \ \pm \ t_{\alpha/2, n-1} \ \frac{s}{\sqrt{n}} \\ \\ \\ C.I. = 5.2 \pm 2.160 \ \frac{1.9}{\sqrt{14}} \\\\\\ C.I. = (4.1032, 6.2968)\)

\(t_{\alpha/2, n-1} = t_{0.05/2, 14-1} = 2.16\) it is obtained using t table.

Que. 20)

\(\\ C.I. = \bar{X} \pm z_{\alpha /2} \ \frac{\sigma }{\sqrt{n}} \\ \\ \\ C.I. = 93.2 \pm 2.58 \frac{16.9}{\sqrt{110}} \\\\\\ C.I. = (89.0427, 97.3573)\)

Hence, the degree of freedom would be 36.

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1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.

In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:

ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,

where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.

To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:

-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.

If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:

-c^2*dt^2 + dx^2 = k^2.

This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.

Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.

(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)

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Answer:

Since the Bank of Peace will pay Marco more in interest over the 3-year period, Marco should choose the Bank of Peace to get the most interest

Step-by-step explanation:

To determine which bank will give Marco the most interest over the 3-year period, we need to calculate the total amount of interest that each bank will pay Marco over the 3 years.

First, let's consider the Bank of Peace. Since the interest rate is 2.5% per year and is compounded annually, Marco will earn 2.5/100 * £15000 = £375 in interest in the first year. In the second year, the interest will be calculated on the original £15000 plus the £375 of interest earned in the first year, for a total of £15000 + £375 = £15375. So Marco will earn 2.5/100 * £15375 = £383.44 in interest in the second year. In the third year, the interest will be calculated on the original £15000 plus the £375 of interest earned in the first year and the £383.44 of interest earned in the second year, for a total of £15000 + £375 + £383.44 = £15728.44. So Marco will earn 2.5/100 * £15728.44 = £391.71 in interest in the third year.

Therefore, the total amount of interest that Marco will earn from the Bank of Peace over the 3-year period is £375 + £383.44 + £391.71 = £1150.15.

Now let's consider the Bank of Trust. In the first year, Marco will earn 3.8/100 * £15000 = £570 in interest. In the second year, the interest rate is 1%, so Marco will earn 1/100 * £15000 = £150 in interest. In the third year, Marco will also earn £150 in interest.

Therefore, the total amount of interest that Marco will earn from the Bank of Trust over the 3-year period is £570 + £150 + £150 = £870.