Factor the expression.
30x - 12xy =
(Factor completely.)

Answer:

x=2.5

Step-by-step explanation:

5x<12          1. /5 on both sides

x= 2.5    

Answer:

x<2.4

Step-by-step explanation:

5x < 12

x < 12/5

x < 2.4

On the number line, draw an arrow going towards left from 2.4, with an open circle at 2.4

Answer:

-26/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(16-(-10))/(-2-3)

m=(16+10)/-5

m=26/-5

m=-26/5

Answer:

0.2

Step-by-step explanation:

Answer:

The correct answer is 0.25

Convert the fraction to a decimal by dividing the numerator by the denominator.

0.25

Answer:

Step-by-step explanation:

it kind of depends on the context, but basically yes, the middle point of something is also its center

Answer:

D. sum of these edges is increased by 24 inches -- True

Step-by-step explanation:

Given a cube and its edge is increased by 2 inches.

To study the effect of this increase in the Volume, area of each face, diagonal and sum of edges.

Solution:

Let the side of original cube = a inches.

Formula for volume of cube:

\(V =side^3 = a^3\)

If the side is increased by 2 inches, the side becomes (a+2) inches.

So, new volume, \(V' = (a+2)^3\)

Using the formula:

\((x+y)^3 =x^3+y^3+3xy(x+y)\)

\(V' = (a+2)^3 = a^3+8+3\times 2 \times a(a+2)=a^3+8+6a(a+2)\)

So, \(V' = V + 8+6a(a+2)\)

Volume increased by 8+6a(a+2) [which is not equal to 8]

So, statement is false:

A. volume is increased by 8 cubic inches  -- False

Each face in a cube is a square.

Area of each face, A = \(side^2 = a^2\)

New area, A' = \((a+2)^2\)

Using the formula: \((x+y)^2 =x^2+y^2+2xy\)

\(A' = a^2+4+4a\)

Area increased by 4+4a [which is not equal to 4 sq inches]

B. area of each face is increased by 4 square inches -- False

Diagonal of each face = \(a\sqrt2\)

Increase of 2 in the edge:

New diagonal = \((a+2)\sqrt2 = a\sqrt2+2\sqrt2\)

So, increase of \(2\sqrt2\) not 2.

C. diagonals of each face is increased by 2 inches -- False

There are 12 number of edges in a square.

So sum of all 12 edges  = 12a

When edge is increased by 2, sum of all edges = 12(a+2) = 12a + 24

An increase of 24.

D. sum of these edges is increased by 24 inches -- True

we randomly select two people, drawing without replacement , the  probability of getting 2 females: a) = 1/7 ( = 0.1429) , b) = 9/49 ( = 0.1837 ).

a)  Without replacement,

2 female can be selected from 3 female by \(3C_{2}\) ways.

P(2 female) = \(3C_{2} / 7C_{2}\)

= 1/7 ( = 0.1429)

b)  With replacement,

P(female) = n(female) / total people.

= 3 / 7

P(2 female) = 3/7 * 3/7

= 9/49 ( = 0.1837 )

Probability is basically the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific outcomes — how likely they are. The investigation of occasions administered by probability is called statistics.

By and large, the probability is the proportion of the quantity of positive outcomes to the absolute outcomes in that example space. It is communicated as, Probability of an occasion P(E) = (Number of good outcomes) ÷ (Test space).

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Answer:

Step-by-step explanation:

I think is x-1

It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.

21) You most likely mean the number 0.666…. If x = 0.666…, then

10x = 6.666…

10x - x = 6.666… - 0.666…

9x = 6

x = 6/2 = 2/3

22) You either mean 1.2555… (only 5 repeats) or 1.252525… (both 2 and 5 repeat).

If x = 1.2555…, then

10x = 12.555…

100x = 125.555…

100x - 10x = 125.555… - 12.555…

90x = 113

x = 113/90

Otherwise, if x = 1.252525…, then

100x = 125.252525…

100x - x = 125.252525… - 1.252525…

99x = 124

x = 124/99

23) You either mean 0.4555… or 0.454545….

If x = 0.4555…, then

10x = 4.555…

100x = 45.555…

100x - 10x = 45.555… - 4.555…

90x = 41

x = 41/90

Otherwise, if x = 0.454545…, then

100x = 45.454545…

100x - x = 45.454545… - 0.454545…

99x = 45

x = 45/99 = 5/11

Answer:

ok you are good boyylq fjwkmdnc

The ladder would reach a distance of 6 feet up the wall.

This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:

/hyp/^2 = /opp/^2 + /adj/^2

In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.

So that, let the height of the ladder on the wall be represented by t. Then;

10^2 = t^2 + 8^2

100 = t^2 + 64

t^2 = 100 -64

     = 36

t = (36)^1/2

t = 6 feet

Thus the ladder is placed 6 feet up the vertical wall.

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Answer:

C

Step-by-step explanation:

The speed of an airplane is 208 miles per hour.

The speed of wind is 48 miles per hour.  

The distance covered by airplane against the wind = D = 640 miles

The time taken to cover D distance = T = 2.5 hours

Again

The distance covered by airplane with the wind = d = 460 miles

The time taken to cover d distance = t = 2 hours

Let The speed of the airplane = x mile per hour

and the speed of wind = y miles per hour

we know that -

∵ Speed = distance/ time

speed of airplane while moving against the wind

x - y =   D/T

Or, x - y =   640/4

Or, x - y = 160 mph        ........1

speed of airplane while moving with the wind

x + y =   d/t

Or, x + y = 640/ 2.5

Or, x + y = 256 mph        ........2

Now, Solving eq 1 and eq 2, we get,

(x - y) + (x + y) = 160mph + 256mph

Or, (x + x) + ( - y + y) = 416 mph

Or, 2 x + 0 = 416 mph

∴  x = 416/2

i,e x = 208 mph

So, The speed of airplane = x = 208 miles per hour

Now, substitute the value x = 208 in equation 1, we get,

∵  x - y = 160mph

So, 208 mph - y = 160 mph

Or, y = 208 mph - 160 mph

i.e y = 48 mph

So, The speed of wind = y = 48 miles per hour

Hence, The speed of an airplane is 208 miles per hour and the speed of wind is 48 miles per hour.

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Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

For the polygon the individual value of the interior angles.

a) 15 sides is 145°

b) 20 sides is 108°

c) 3 sides is 60°

d) 4 sides is 90°

e) 100 sides is 18°

A regular polygon is one where all sides are the same length and all interior angles are the same. The number of sides of a regular polygon can affect the value of its interior angles.

a) 15 sides: The sum of the interior angles of a regular polygon with 15 sides is equal to 2180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2180 / 15 = 145 degrees per angle.

b) 20 sides: The sum of the interior angles of a regular polygon with 20 sides is equal to 2160 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2160 / 20 = 108 degrees per angle.

c) 3 sides: The sum of the interior angles of a regular polygon with 3 sides is equal to 180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 180 / 3 = 60 degrees per angle.

d) 4 sides: The sum of the interior angles of a regular polygon with 4 sides is equal to 360 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 360 / 4 = 90 degrees per angle.

e) 100 sides: The sum of the interior angles of a regular polygon with 100 sides is equal to 1800 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 1800 / 100 = 18 degrees per angle.

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Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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Answer:

6=2/3h

Step-by-step explanation:

Answer:

29/150

Step-by-step explanation:

Probability is the number of times a certain value is obtained out of the total number of attempts.

If Carol got 6 29 times out of 150, then the probability of getting a 6 = 29/150.

This can be written as a percent or decimal too = 0.193 = 19.3%

Hope this helps.

Good Luck

The warning message "A date index has been provided, but it has no associated frequency information and so will be ignored when e.g., forecasting" is related to time series data analysis.

This message indicates that the date index provided for the data does not have any frequency information, which can be crucial for forecasting or modeling the time series data.

Time series data is characterized by observations taken at regular intervals over time. The frequency of the data could be daily, weekly, monthly, quarterly, or yearly, depending on the nature of the data. In time series analysis, the frequency of the data is an essential component that helps to determine the appropriate model to be used for forecasting or predicting future values.

When a date index is provided without any associated frequency information, it becomes difficult to determine the appropriate model for forecasting. Therefore, it is essential to ensure that the frequency information of the data is specified correctly while working with time series data. By doing so, it would enable forecasting or modeling to be done more accurately and effectively.

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Relative dating determines the order of events and the relative age of the rock, while absolute dating provides a specific numerical age. Relative dating is based on the principle of superposition and the types of fossils found, while absolute dating uses radiometric techniques to measure the decay of isotopes.

Relative dating and absolute dating are two methods used to determine the age of stratified rock.

Relative dating involves comparing the positions of rock layers and fossils in different areas to establish the relative age. It relies on the principle of superposition, which states that the older rocks are found beneath younger ones. By examining the order of rock layers and the types of fossils they contain, scientists can determine the relative age of the rock.

On the other hand, absolute dating provides a numerical age for the rock. It uses techniques such as radiometric dating, which measures the decay of radioactive isotopes in the rock to calculate its age. For example, carbon-14 dating is used to determine the age of organic material up to about 50,000 years old.

In summary, relative dating determines the order of events and the relative age of the rock, while absolute dating provides a specific numerical age. Relative dating is based on the principle of superposition and the types of fossils found, while absolute dating uses radiometric techniques to measure the decay of isotopes. Both methods are important in determining the age of stratified rock and contribute to our understanding of Earth's history

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The length of the shortest side of the triangle is 13.

We are given a triangle. One of the sides of the triangle is divided into segments of 6 and 8 units by the points of tangency of the inscribed circle. The radius of the circle is 4 units. We need to find out the length of the shortest side of the triangle. The diagram is attached below for reference.

The lengths of the corresponding tangents must be equal. Let the length of the remaining tangents be denoted by the variable "m". The area of the triangle can be calculated in two ways.

The first way is to add the sum of three triangles.

A = (1/2)×(6 + 8)×(4) + (1/2)×(6 + m)×(4) + (1/2)×(m + 8)×(4)

A = 28 + 12 + 2m + 2m + 16

A = 4m + 56

The second way is to use the formula having semi-perimeter.

A = √[s(s - a)(s - b)(s - c)]

A = √[(m + 14)(m)(8)(6)]

A = √[48m(m + 14)]

Both quantities must be equal.

4m + 56 = √[48m(m + 14)]

16(m + 14)² = 48m(m + 14)

m + 14 = 3m

2m = 14

m = 7

The lengths of the sides of the triangle are 13, 14, and 15. Hence, the length of the shortest side of the triangle is 13.

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The required probability for the students in given interval of time is answered below.

It lets you know probability  for a specific score. To utilize one, initial transform your information into an ordinary dispersion. Then, at that point, find the matching z-score to one side of the table and adjust it to the z-score at the highest point of the table. The outcome gives you the probability.

By using table,

Probability study more than 10 hours = 1 - (.01+0.5+0.2)

⇒ 0.2

According to probability distribution table, if the sample of 10 students randomly,

1 student that less than  one hour, 5 students whose study 1 to 5 hours, 2 students that study 6 to 10 hours, and 2 students that study more than 10 hours.

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Answer:

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

It is an isosceles triangle if two sides are same.

There are two possible triangles with given values.

If the 45° is between the two 8 cm sides, then as the isosceles triangle the other two angles have the measure:

So this is an acute triangle.

If the 45° angle is opposite to 8 cm side, then the other 8 cm side also has same opposite angle measure.

Then the third angle is:

It means it is a right triangle.

Answer:

2/3

Step-by-step explanation:

24students - 8 boys = 16 girls

16/24

2/3

Answer:

\(\frac{16}{24}=\frac{2}{3}\)

also

\(\frac{8}{24} =\frac{1}{3}\)

Step-by-step explanation:

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Answer: 913%

Step-by-step explanation:

Based on the concept of payday loans, Barbara's annual percentage rate is 9.125%

The Annual Percentage Rate (APR) is a term that is used to describe the cost paid each year to borrow money, such as fees, expressed as a percentage.

In this case, to get the annual percentage rate (APR) on Barbara's loan calculate the effective interest rate for the 8-day period and then annualize it.

Given that Barbara borrowed $75 and was charged a fee of $15 for an 8-day term the total amount she needs to repay is $75 + $15 = $90.

To calculate the effective interest rate we can use the following formula:

Effective Interest Rate = (Total Interest / Principal) * (365 / Loan Term)

Total Interest = $15 (fee)

Principal = $75 (loan amount)

Loan Term = 8 days

Substituting the values into the formula:

Effective Interest Rate = (15 / 75) * (365 / 8)

Effective Interest Rate = 0.2 * 45.625

Effective Interest Rate = 9.125%

Therefore, APR = Effective Interest Rate * Compounding Frequency

APR = 9.125% * 1

APR = 9.125%

Hence, in this case, it is concluded the approximate annual percentage rate (APR) on Barbara's loan is around 9.125%.

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Answer:

y = 2x -14

Step-by-step explanation:

The point-slope form is y =  mx + b

m = 2

y-intercept is located at (0, -14)

So, the equation is

y = 2x - 14

Answer:

y-6=2(x-4)

Step-by-step explanation:

point-slope form y-y1=m(x-x1)

Answer:

4.25-5 minutes

Step-by-step explanation:

Its shown in the graph and table that the speed was 0 between those times.

Answer:

other side is 12

Step-by-step explanation:

Givens

Perimeter = 64 feet

L = 20

Formula

P = 2L + 2w               Substitute Givens

64 = 2*20 + 2w         Combine

64 = 40 + 2w             Subtract 40 from both sides

64-40 = 40-40+2w    Combine

24 = 2w                      Divide both sides by 2

24/2=2w/2              

12 = w