The three sides of a triangular lot are represented by x , 2 x , and 3 x + 2. Find each side if the perimeter of the triangular lot is 362 feet. The lengths of the sides of the triangle are :

For part A, the student has 13 colleges to choose from that are not expensive and near home. For part B, the total possible selections of two colleges is 156, considering the student won't attend the same college before and after the transfer.

The subject of this question pertains to probability and set theory, a branch of mathematics. We use the principle of inclusion and exclusion to solve the problem.

For part A. there are total 24 colleges, 8 are expensive which means 24 - 8 = 16 are not expensive. Among 24 colleges, 8 are far from home which means 24 - 8 = 16 are near. But remember, there are 5 colleges that are both expensive and far, hence these 5 colleges got subtracted twice. So, we need to add them back. The number of colleges that are not expensive and near home are 16 + 16 + 5 = 37. However, this goes beyond the total number of colleges, so we subtract 24 from it to get the correct count of 13.

For part B, the number of ways before transferring are the same as in part A, 13. The number of ways after transferring, there are total 24 colleges, 8 are expensive which means 24 - 8 = 16 are not expensive. Among 24 colleges, 8 are near which means 24 - 8 = 16 are far. Adding the count of not expensive and far gets us 16 + 16 = 32. Subtract the total number of colleges to get the correct figure 32 - 24 = 8. Nothing the student can't attend the same college before and after the transfer, so the count of total selections is 13 choices for the first selection multiplied by 12 choices for the second selection, getting us a total of 156 possible selections.

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Answer:

B is the correct answer

Step-by-step explanation:

A. is wrong because 3/8 would shrink the circle, not expand it.

B. is correct because 8/3 means the circle will expand, not shrink.

C. is wrong because those coordinates only reposition and move the circle, not dilate.

D. is wrong because those coordinates only reposition and move the circle, not dilate.

Final answer:

The amplitude of a wave is its maximum displacement from equilibrium and can be directly read from the equation as A, while the period is the time for one complete cycle, inversely related to frequency as T = 1/f. Given a frequency of 2.0 MHz, the period is 5.0 x 10⁻⁷ seconds, with the amplitude being 30 V/m.

Explanation:

The period and amplitude of a sinusoidal function can be determined from its formula or graph. For example, in the given context, if we are presented with a wave with an amplitude of 30 V/m and a frequency of 2.0 MHz, we can calculate the period. We know that the period (T) of a wave is the inverse of the frequency (f), so T = 1/f. Given the frequency of 2.0 MHz, or 2.0 x 106 Hz, the period T is 5.0 x 10-7 seconds (since 1 Hz = 1/s). The amplitude is the maximum displacement from the equilibrium position, in this case, 30 V/m. The amplitude is typically denoted by A in the wave equation y(x, t) = A sin(kx - wt + p), and the period can be derived from the angular frequency with T = 2π/ω.

For a physical representation, observing a wave plotted on a graph such as in Figure 24.8(b) or a given wave function, the amplitude is seen as the distance from the equilibrium position (center line) to the peak, and the period is the time it takes for one complete cycle of the wave. Understanding these concepts is crucial for analyzing waves whether in physics or mathematics.

Answer:

x=7

y=8

Step-by-step explanation:

-Given that the mean and median is the same.

-Let b=mean =median

#Given that the set is arranged in order and is even:

[tex]median=\frac{n+1}{2}\\\\Median=3^{rd} \ term\\\\=x[/tex]

Hence:

[tex]b=median=mean\\\\b=x\\\\\therefore mean=median=x[/tex]

-Applying the mean formula:

[tex]\bar x=\frac{1}{n}\sum{x_i}\\\\\therefore 5x=4+6+x+y+10\\\\4x=20+y\\\\x=5+0.25y[/tex]

#Since the number are in order:

[tex]6<x<y<10\\\\\#let\ x=7,y=8\\\#Substitute\\\\7=5+0.25(8)\\7=7\\\\[/tex]

Hence, x=7 and y=8

Answer:

1

Step-by-step explanation:

[tex]x_0=\dfrac{-b}{2a} =\dfrac{-4}{2\times(-2)}=1\\y_0=-2\times1^2+4\times1+1=-2+4+1=3\\Answer: The\: vertex\: is \:(1;3). It's\:maximum\:point \:because \:a=-2<0[/tex]

Answer:

centered at (5,-3)

radius of 14 units

Step-by-step explanation:

A linear transformation will be the opposite of what contained in the parentheses( (x-5)^2 will be a regular line x but +5 units along the axis.

Therefore the variables contained in the parentheses will then correspond to the transformation, so it will be shifted +5 units along the x and -3 units along the y.

The radius is simply the answer square rooted which is 14 units in this case.

Answer:

False

Step-by-step explanation:

Correct statement would be:

A tangent line is a line that insersects a circle at exactly one point.

Step-by-step explanation:

Your mistake is here: cos(-45°) = +½√2, not -½√2.

±√((1 + ½√2) / 2)

= ±√((2 + √2) / 4)

Given:

The time required for a box to slide down an inclined plane is

[tex]T = \sqrt{\frac{2a}{g(sin\theta cos\theta)} }[/tex]

where,

g be the,acceleration due to gravity.

[tex]\theta[/tex] be the inclined plane.

To find the value of [tex]\theta[/tex] for which the given expression is undefined.

Now,

T will be undefined if the denominator is 0.

⇒ [tex]g(sin \theta cos \theta) = 0[/tex]

or, [tex]sin\theta cos\theta = 0[/tex] [ g ≠ 0 it is a constant]

either [tex]sin\theta = 0[/tex] or [tex]cos\theta = 0[/tex]

For, [tex]sin\theta = 0[/tex] ⇒ [tex]\theta = 0^\circ[/tex]

Again,

For, [tex]cos\theta = 0[/tex] ⇒ [tex]\theta = 90^\circ[/tex]

Hence,

The expression will be undefined for the value of 0° and 90° of θ.

Option C.

Option(C). In the formula √(2a/g•sin(theta)•cos(theta)), the expression is undefined when theta=0° or 90°, since in these cases, sin(theta) or cos(theta) equal to zero respectively.

Consider the formula √(2a/g•sin(theta)•cos(theta)).

The expression in the root (√) is undefined when we divide by zero. Looking at the formula, we divide by the product of sin(theta) and cos(theta). For the expression to be undefined, one or both must be zero.

The values of theta that would cause this to happen are when theta=0°, sin(theta)=0 and when theta=90°, cos(theta)=0.

Therefore, the expression is undefined when theta is either 0° or 90°.

So, the answer is C. Both A and B.

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Answer:

DEFCON= MEANS DEFense readiness CONdition

Step-by-step explanation:

HI THERE: IT IS AN CALL OF ALERT STATE OF EMERGENCY WHICH IS SOMETIMES USED BY THE USAF (UNITED STATES AIR FORCE)

Answer:

Step-by-step explanation:

The alternate hypothesis use the sumbol for the population value

Let p be the proportion , Mean be [tex]\mu[/tex] and stadard deviation be [tex]\sigma[/tex]

The null hypothesis states that population value is equal to the value mentioned in the given claim.

[tex]H_0:\mu=18[/tex] (by given).

The alternate hypothesis for the significance test states that the opposite of the null hypothesis(based on the claim )

∴ [tex]H_a:\mu<18[/tex]

The symbol "<" because we want to test if the maze is completed faster and thus if the time has decreased.

Answer:

the the scale of the drawing is 1/4

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

As we know that, the formula to find the are of a triangle is:

A = 1/2 b*h where:

From the photo, we can see that, the height is 3 units and the base is 6 units. So the area of the shaded triangle is:

A = 1/2 6*3 = 9 square units

Given that the triangle depicted by the drawing has an actual area of 36 square units. So the the scale of the drawing is:

area of the shaded triangle / the actual area

9 /36 = 1/4

Hope it will find you well.

Answer:

C ( 6 units

Step-by-step explanation:

just took the quiz

Answer:

$18.90

Step-by-step explanation:

Lets break this question down into smaller sections to make it easier:

There are 3 bottles

Each bottle can hold 0.75 liters

For every 25 milliliters she pays $0.21

With that information in mind, we notice that we need to convert liters to milliliters in order to get an accurate answer.

For every 1 liter = 1000 milliliters

So, we need to take 0.75 * 1000 = 750 milliliters per bottle

Next, we take 750 milliliters / 25 milliliters to find how many times we have to fill one bottle

Each bottle will take 30 times of 25 milliliters to fill the whole bottle

Now take 30 * $0.21 to find the cost of one bottle

One bottle = $6.30 to fill

Take $6.30 * 3 to find the total cost to fill ALL the bottles.

For a final result, we get $18.90 to fill all three bottles completely

Hope this Helps!

Answer:

it's 18.90

Step-by-step explanation

my friend told me it was 5.67 and for some reason i believed her but no i took the test and it's 18.90

Answer:

35 People

Step-by-step explanation:

From the given information

Let the number of people attending the banquet=x

Therefore:

Cost of Hall Rental + Total Meal Cost = Total Bill

125+12x=545

12x=545-125

12x=420

x=420/12=35

Since x=35, we conclude that 35 People attended the banquet.

Answer: 121/1024

Step-by-step explanation:

If 5 burglaries were reported in 2003,

16 in 2004, this means that were addition of more (16 - 5) = 11

and 32 in 2005

Total outcome will be 32 windows

 The probability that both will have occurred in 2004 will be

11/ 32 × 11/32 = 121/1024

The probability that both will have occurred in 2004 is 121/1024

Given that:

In 2003, 5 burglaries were reported

16 in 2004

Hence, the total outcome is 32

The probability that both will have occurred in 2004 will be

[tex]11/ 32 * 11/32 \\= 121/1024[/tex]

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Answer:

star a; 5.7 units

Step-by-step explanation:

Answer:

B. $0.72

Step-by-step explanation:

Here is the stock listing for Enam Telecom

52 wk high is 122.86

52 wk low is 64.77

Div. is 3.45

Close is 99.14

Net change is 4.74

From the question the lowest price which was 64.77 was 48 days ago.

therefore net change in value is:

Close - lowest price:

99.14 - 64.77 = 34.37

Since change is in 48 days,

the average change per day is:

Total change / number of days = 34.37/48 = 0.716

This answer is approximately 0.72

Therefore average change per day is 0.72

Answer:

B

Step-by-step explanation:

Answer is: 16x8 = 128

Answer:

D. 21,386

Step-by-step explanation:

The question is incomplete. Here is the complete question.

"The number of trees in a forest follows the logistic growth function,

f(t) = 32000/1+12.8e^-0.065t where t is the time in years. According to the growth model, how many trees will there be after 50 years?"

Given the logistics growth function,

f(t) = 32000/1+12.8e^-0.065t

To calculate the number of trees that will be there after 50years, we will substitute the value of t = 50 into the function

f(50) = 32000/1+12.8e^-0.065(50)

f(50) = 32000/1+0.496

f(50) = 32000/1.496

f(50) = 21,385.94

f(50) = 21,386

Number of trees that will be there after 50years is 21,386years

Answer:

12

Step-by-step explanation:

3x =12 whn x=4

Answer:

the answer is 4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:

64, 81, 100, 121 there are 4

Step-by-step explanation:

Answer:

heyyy there

Step-by-step explanation:64, 81, 100, 121, are the perfect square numbers between 50 and 140..

64=8*8

81=9*9

100=10*10

121=11*11

................12 *12 bcoms 144 so its not between 144

hope it helps

Answer:

[tex]x-8[/tex],  smaller integer is 8.

Step-by-step explanation:

Given:

The product of two consecutive integers is 72.

The equation x(x+1)=72 represents the situation, where x represents the smaller integer.

Question asked:

Which equation can be factored and solved for the smaller integer ?

Solution:

[tex]x(x+1)=72\\\\ x^{2} +x=72\\ \\ By\ subtracting\ both\ sides\ by\ 72\\ \\ x^{2} +x-72=72-72\\ \\ x^{2} +x-72=0\\ \\ x^{2} +9x-8x-72=0\\ \\ Taking\ x+9\ as\ common \\ \\ x(x+9)-8(x+9)=0\\ \\ x+9=0,x-8=0\\ \\ x=-9,x=8[/tex]

[tex]x-8[/tex]  can be factored and solved for the smaller integer, and that is 8.

Two consecutive integers are 8 and  9 and their product is 8 [tex]\times[/tex] 9 = 72

Final answer:

To determine the number of problems the student answered correctly, calculate 75% of 20. The student correctly answered 15 out of 20 problems on the math test.

Explanation:

A student earned a grade of 75% on a math test that had 20 problems.

To find out how many problems the student answered correctly, we can simply calculate 75% of 20.

Step 1: Convert the percentage to a decimal: 75% = 0.75

Step 2: Multiply the decimal by the total number of problems: 0.75 × 20 = 15

Therefore, the student answered 15 problems correctly on the math test.

Answer:

149,730 strawberries

Step-by-step explanation:

Answer:

149,730 strawberries

Step-by-step explanation:

The equation [tex]\( K = C + 237.15 \)[/tex]) provides a way to convert temperatures from degrees Celsius to Kelvin. It reflects the fact that the Kelvin scale starts from absolute zero and is offset from the Celsius scale by 273.15 degrees.

K as the temperature in Kelvin,

C as the temperature in Celsius.

We're given that a temperature in Kelvin is 237.15 greater than the temperature in degrees Celsius. So, we can express this relationship as an equation:

[tex]\[ K = C + 237.15 \][/tex]

This equation shows that to convert from Celsius to Kelvin, you add 237.15 to the Celsius temperature. Similarly, to convert from Kelvin to Celsius, you subtract 237.15.

Here's the equation:

[tex]\[ K = C + 237.15 \][/tex]

1. **Definition of Kelvin and Celsius Scales**:

  - Kelvin (K): Kelvin is an absolute temperature scale where 0 Kelvin represents absolute zero, the lowest possible temperature where particles cease to move. One Kelvin is equal in magnitude to one degree Celsius.

  - Celsius (C): Celsius is a temperature scale based on the freezing and boiling points of water, where 0 degrees Celsius represents the freezing point of water and 100 degrees Celsius represents the boiling point of water at standard atmospheric pressure

2. **Relationship between Kelvin and Celsius**:

  - To convert from Celsius to Kelvin, you add 273.15 to the Celsius temperature. This adjustment is made because the Kelvin scale starts from absolute zero, which is -273.15 degrees Celsius.

3. **Given Relationship**:

  - The given information states that a temperature in Kelvin is 237.15 greater than the temperature in degrees Celsius. This means that to convert from Celsius to Kelvin, you add 237.15 to the Celsius temperature.

  - We can express this relationship mathematically as [tex]\( K = C + 237.15 \).[/tex]

    - Here, [tex]\( K \)[/tex] represents the temperature in Kelvin, and  [tex]\( C \)[/tex]represents the temperature in degrees Celsius.

    - Adding 237.15 to the Celsius temperature converts it to Kelvin.

  - The equation [tex]\( K = C + 237.15 \)[/tex]) provides a way to convert temperatures from degrees Celsius to Kelvin. It reflects the fact that the Kelvin scale starts from absolute zero and is offset from the Celsius scale by 273.15 degrees.