Construct a quadrilateral PQRS with PQ= 5cm, QR = 5.5cm, RS = 5.5cm, SP= 6.5cm & angle PQR = 75°.Also construct a Triangle QRM whose area is equal to quadrilateral PQRS.​

Answer:

c should be the answer

Step-by-step explanation:

Answer:

140 is total length.

Step-by-step explanation:

If it is square, the formula for the area of the land would equal \(x^{2}\).

Or, side times side.

So, you would have to find the square root of 1225, which is 35.

Since there is four sides, 35*4 = 140

140 is the total length of the wire.

The length of each piece is 150/3 which is 46.(6)

The value of the constant of variation is 130

Constant of variation can be defined as the ratio between two variables in  an inverse variation on a direct variation.

From the information given, we have that;

The number of hours is x

The temperature is y

x α 1/ y

x = k/y

k = xy

Substitute the values

k = 2 × 65

k= 130

Thus, the value of the constant of variation is 130

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The complete question:

the number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65 degrees find the constant of variation

The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

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The sample's data values ought to be unrelated to one another. The sample data need to be consistent. Data from the quantitative ordered pair sample should be gathered at random or in a way that is representative of the overall population. The sample's data values ought to be unrelated to one another.

A confidence interval is a much better tool to use if we wish to communicate the level of uncertainty surrounding our point estimate (CI). A confidence interval (CI) is a symmetrical range of values where the results of repeated, related experiments are likely to fall. The middle of this range corresponds to our point estimate.

Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications.

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1. There are 120 ways to arrange the months of birth for the five friends.2. There are 95,040 ways to assign the months of birth so that each friend has a different birth month. 3. The probability that all five friends have different birth months is 792/1.4. The probability that at least two of the friends have the same birth month is 0.43. 5. The probability that three of the friends are born in March and two are born in July is 0.57.

1. The number of ways in which five different things can be arranged is 5! or 120, therefore there are 120 ways to arrange the months of birth for the five friends.

2. One way to think about this is to think about the first person choosing from all twelve months, the second person from the remaining eleven months, the third person from the remaining ten months, etc.

This can be expressed as:

12 x 11 x 10 x 9 x 8 = 95,040

Therefore, there are 95,040 ways to assign the months of birth so that each friend has a different birth month.

3. Using the answer from the previous question, we can plug it into the formula for probability:

Probability = number of favorable outcomes / total number of outcomes

Probability = 95,040 / 120 = 792

Therefore, the probability that all five friends have different birth months is 792/1.

4. This is a bit tricky to calculate directly, so it's often easier to calculate the probability that none of the friends have the same birth month, and then subtract that from 1 (the total probability).

To calculate the probability that none of the friends have the same birth month, we can think about the first person choosing from all twelve months, the second person choosing from the remaining eleven months, the third person choosing from the remaining ten months, etc.

This can be expressed as:

12 x 11 x 10 x 9 x 8 = 95,040

But now we need to divide by the number of ways to arrange five people (since we don't care about the order of the people, only the order of the months). This is 5! or 120.

So the probability that none of the friends have the same birth month is:

95,040 / 120 = 792

And the probability that at least two of the friends have the same birth month is:

1 - 792/120 = 1 - 6.6 = 0.434.

Therefore, the probability that at least two of the friends have the same birth month is 0.43.

5. This is a bit tricky to calculate directly, so it's often easier to calculate the probability that each friend has a specific birth month, and then multiply those probabilities together.

To calculate the probability that one friend is born in March, we can think about the first person choosing March and the other four people choosing from the remaining 11 months.

This can be expressed as:

1 x 11 x 10 x 9 x 8 = 7,920

But now we need to multiply by the number of ways to choose which friend is born in March (since any of the five friends could be the one born in March). This is 5.

So the probability that exactly one friend is born in March is:

5 x 7,920 / 120 = 330

And the probability that three friends are born in March is:

330 x 7,920 / 120 x 11 x 10 = 0.0476

Similarly, the probability that two friends are born in July is:

2 x 1 x 10 x 9 x 8 / 120 = 12

And the probability that three friends are born in March and two are born in July is:

0.0476 x 12 = 0.5712

Therefore, the probability that three of the friends are born in March and two are born in July is 0.57.

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Answer:9/40

Step-by-step explanation:

there is no use of hupotenuse as tanA = p/b

Answer:

B. y = sinx

Step-by-step explanation:

kasi yan ang "Tamang Sagot"

Students no longer have to visit a physical store to buy course books because most course books can now be obtained online.

What should you try first if an online course is having technical issues?

What drawbacks exist with online learning?

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This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.

Here's an example Python function called count_characters that counts the number of times each character appears in a user-supplied string s:

def count_characters(s):

Given a string s, returns a dictionary containing the count of each character in the string.

char_count = {}

for char in s:

if char in char_count:

char_count[char] += 1

else

char_count[char] = 1

return char_count

This function creates an empty dictionary called char_count to store the counts of each character. It then loops through each character in the string s and checks if it's already in the char_count dictionary. If it is, it increments the count for that character. If it's not, it adds the character to the dictionary with a count of 1. Finally, the function returns the char_count dictionary.

You can call this function like this:

string = "hello world"

char_count = count_characters(string)

print(char_count)

Output:

python

{'h': 1, 'e': 1, 'l': 3, 'o': 2, ' ': 1, 'w': 1, 'r': 1, 'd': 1}

This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.

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There are 28 numbers in total that are odd numbers greater than 500 with no digit being repeated.

First, there are 18 odd numbers with four digits, and all of them are greater than 500. To see that, starting from the end of the number, there are 3 options for the last digit, 3 for the second last, 2 for the second digit, and 1 for the first digit. Multiplying one gets 3*3*2*1=18.

Second, for numbers with 3 digits, in order to be greater than 500, it must start either with 5 or with 6. If it starts with 5, there are 2 options for the last digit and 2 options for the second digit.

Thus, there are 4 different numbers in this case. Finally, if it starts with 6, then there are 3 options for the last digit and 2 options for the second digit. Thus, there are 6 different numbers in this case.

Complete question: How many different odd numbers greater than 500 can be made using some or all of the digits 1,3,5 and 6 with no digit being repeated?

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As per the permutations, there as 36 three digit numbers that are greater than 500 and which are odd one also.

The term permutation in math is defined as the way of arranging objects or numbers in order.

Here we have given that we have to identify the 3 digit numbers greater than 500 are odd

Let us make three digit numbers 1st

Here we know that if we want odd number at end then one number from three numbers can come there so

=> 3P1

Then the rest of the two numbers don't matter so

Then it can be written as

=> 3P2

Then the overall combination is written as

=> 3P1 * 3P2=18

Here now let us make four digit numbers

Then the digit odd again and it can be written as

=> 3P1

Here also the rest of the order Doesn't matter so

then it can be written as

=> 3P3 =6

Then the four digit value is

=> 3p1 * 3p3= 18

Therefore, the overall count is written as

=> Overall = 18+18= 36

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The equation in slope-intercept form of the line passing through (-5, -2) and (4, 6) is  \(y = \frac{8}{9}x + \frac{22}{9}\).

The equation of line in slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given that the line passes through (-5,-2) and (4,6).

First, we determine the slope:

\(m = \frac{y_2 - y_1}{x_2 - x_1 } \\\\m = \frac{6-(-2)}{4-(-5)} \\\\m = \frac{6+2}{4+5} \\\\m = \frac{8}{9}\)

Now, plug the slope m = 8/9 and point (-5,-2) into the point-slope form and simplify:

( y - y₁ ) = m( x - x₁ )

\(y - (-2) = \frac{8}{9}(x - (-5)) \\\\y + 2 = \frac{8}{9}(x + 5)\\\\y + 2 = \frac{8}{9}x + \frac{40}{9} \\\\y = \frac{8}{9}x + \frac{40}{9} - 2\\\\y = \frac{8}{9}x + \frac{22}{9}\)

Therefore, the equation of the line is \(y = \frac{8}{9}x + \frac{22}{9}\).

The complete question is:

Find the equation of the line passing through the given pair of points.

Write the equation in slope-intercept form of the line that passes through (-5,-2) and (4,6).

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Answer:

0.01 %  

Step-by-step explanation:

Answer:

l9-7l is the answer

Step-by-step explanation:

Answer:

I and j I believe

Step-by-step explanation:

Answer:

Step-by-step explanation:

70+59+55+25+30+17=276

The probability that the person selected at random doesn't use any facility is 0.25

The probability of an event can be mathematically said to be the number of required outcome divided by the number of possible outcomes.

From the question:

Total number of people who used at least any of the three facilities=26+21+14+11+19+24+6=121

The number of persons that doesn't use any of the facility=125-121=4

Hence, the number of possible outcomes=4 and the probability that the person selected at random doesn't use any facility is 1/4 or 0.25

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The charge on the K+ ion is 1.6 × 10⁻¹⁹ C. This can be calculated using the force and electric field strength, which are related to the mass and acceleration of the ion.

The mass and acceleration of a K+ ion are given as 6.5 × 10⁻²³ kg and 1.7 × 10⁶ m/s², respectively.

To calculate the charge on the K+ ion, we need to use the formula:

F = ma

Where F is the force, m is the mass, and a is the acceleration.

We can rearrange the formula to solve for the force:

F = ma

F = (6.5 × 10⁻²³ kg) × (1.7 × 10⁶ m/s²)

F = 1.105 × 10⁻¹⁶ N

Next, we can use another formula to calculate the charge on the K+ ion:

F = qE

Where F is the force, q is the charge, and E is the electric field strength. We can rearrange the formula to solve for the charge:

q = F/E

We are given the acceleration of the K+ ion, which we can use to find the electric field strength:

E = a/q

We can substitute the value of acceleration a = 1.7 × 10⁶ m/s² and solve for the electric field strength:

E = a/q

q = a/E

Mass of K+ ion m = 6.5 × 10⁻²³ kg

Acceleration a = 1.7 × 10⁶ m/s²

Charge on K+ ion q = 1.6 × 10⁻¹⁹ C

The charge on the K+ ion is 1.6 × 10⁻¹⁹ C. This can be calculated using the force and electric field strength, which are related to the mass and acceleration of the ion.

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f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor is \((x-2)^2(x-8)\).

What is factor?

In mathematics, an integer m that can be multiplied by another integer to produce n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.

Knowing that (x−2) is a factor you can divide the polynomial:

2.....|.......1.........-12.........+36.........-32

........|...................2..........-20.........+32

........|.......1.........-10..........+16...........0

and find:

\(x^3-12 x^2+36 x-32=(x-2)\left(x^2-10 x+16\right)\)

We could use the quadratic formula to find the factors of \($q(x)=\left(x^2-10 x+16\right)$\)

or go simply by inspection:

1) q(x) has two changes in sign, so it has two positive real roots.

2) The product of the roots is 16

3) the sum of the roots is 10

It's easy to see that x=2 and x=8 are such roots, and thus:

\(x^3-12 x^2+36 x-32=(x-2)^2(x-8)\)

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The algebraic equation have the value of c equal to 4.

An algebraic equation is a mathematical statement that involves two equated algebraic expressions.

The unknown value c can be evaluated for the agebraic equation 2(c + 1) = 10 as follows:

open brackets

2c + 2 = 10

subtract 2 from both sides of the equation

2c + 2 - 2 = 10 - 2

2c = 8

divide through by the coefficient of c

2c/2 = 8/2

x = 4

Therefore, the value of c that makes the algebraic equation true is 4.

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Answer:

a. After the first bounce, the ball will be at 85% of 8 ft. After 2 bounces, it'll be at 85% of 85% of 8 feet. After 3 bounces, it'll be at (85% of) (85% of) (85% of 8 feet).  You can see where this is going. After n bounces the ball will be at

\(h(n) = (85\%)^n 6ft = (\frac{17}{20})^n(6ft\times 12\frac{in}{ft}) = (\frac{17}{20})^n\times72'\)

b. After 8 bounces we can apply the previous formula with n = 8 to get

\(h(8)=(\frac{17}{20})^8\times 72' = 19.62'\)

c. The solution to this point requires using exponential and logarithm equations; a more basic way would be trial and error using the previous \(h(n)\)increasing the value of n until we find a good value. I recommend using a spreadsheet for that; the condition will lead to the following inequality:

\(1>(\frac{17}{20})^n\times 72\) Let's first isolate the fraction by dividing by 72.

\((\frac{17}{20})^n<\frac1{72}\)  Now, to get numbers we can plug in a calculator, let's take the natural logarithm of both sides:

\(ln ((\frac{17}{20})^n) < ln \frac 1{72} \rightarrow n\times ln (\frac{17}{20}) < -ln72\). Now the two quantities are known - or easy to get with any calculator, replacing them and solving for n we get:

\(-(0.16)n < - 4.27 \rightarrow n>26.31\) Now, since n is an integer - you can't have a fraction of a bounce after all, you pick the integer right after that, or n>27.

Answer:

b - 1/4 = 3 1/2

Step-by-step explanation:

b - 1/4 = 3 1/2

b - 1/4 = (3 + 1/2)

4b = 15

b = 15/

4

= 3.75

Answer:

24

Step-by-step explanation:

253727737273762663552636626636277463726373782883847772

Answer:

if two angles are supplementary angles, then the sum of their angle measures is equal to 180°.

Step-by-step explanation:

the if p statement is called the hypothesis of the conditional statement.

the then q statement of the conditional statement is called the conclusion.

The probability she will get a package of cupcakes is none of the above.

There is a chance of receiving a box is

The likelihood of receiving a box of cupcakes is 14/15

The probability  of missing out on the cupcake package

1/14+1 = 1/15

Receiving a box of cupcakes is likely to happen

1 - 1/15

= 15-1 / 15

=14 / 15

Simply put, probability is the likelihood that something will occur. We can discuss the likelihood of several outcomes or the potential of one outcome when we are unsure of how something will turn out.

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Answer:

B).

Step-by-step explanation:

Unit rate = 720/60

= 72/6

= 12.

- and sore hands!!!!

Answer:

3. 200ft
4. 21ft
5. 37.5m
6. 4.2ft

Step-by-step explanation:

3. use proportions:
\(\frac{h}{50} = \frac{50}{12.5}\)
50(50) = 12.5h
h = 200ft

4.
\(\frac{h}{6} =\frac{7}{2}\)
6(7) = 2h
h = 21ft

5.
\(\frac{25}{8} =\frac{x}{12}\)
25(12) = 8x
x = 37.5m

6.
\(\frac{9}{15} =\frac{h}{7}\)
9(7) = 15h
h = 4.2ft

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

From the question, we have the following parameters that can be used in our computation:

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:

[see below]

Step-by-step explanation:

Assuming that we need to see if the point is a solution:

\(y=3x+4\\\\2=3(3)+4\\\\2=9+4\\\\2\neq 11\)

The point is not a solution to the equation.

Hope this helps.

To determine the solution y(t) for the given system, we will apply the superposition property of linear time-invariant (LTI) systems. The superposition property states that the response of a system to a sum of input signals is equal to the sum of the individual responses to each input signal.

The differential equation for the system is:

(4 x 10^-3) dy/dt + 3y = 5cos(1000t) - 10cos(2000t)

Step 1: Solve for the response to the input signal 5cos(1000t).

Let's assume y1(t) represents the response to the input signal 5cos(1000t). We can rewrite the differential equation as:

(4 x 10^-3) dy1/dt + 3y1 = 5cos(1000t)

First, solve the homogeneous part of the equation:

(4 x 10^-3) dy1/dt + 3y1 = 0

The homogeneous solution is given by:

y1_h(t) = Ae^(-3t/(4 x 10^-3))

Now, consider the particular solution yp1(t) for the non-homogeneous part:

yp1(t) = Acos(1000t)

Differentiating yp1(t) and substituting into the differential equation, we get:

(4 x 10^-3)(-1000Asin(1000t)) + 3(Acos(1000t)) = 5cos(1000t)

Simplifying, we find:

-4000Asin(1000t) + 3000Acos(1000t) = 5cos(1000t)

Comparing coefficients, we have:

-4000A = 0 and 3000A = 5

Solving for A, we find A = 5/3000 = 1/600.

Therefore, the particular solution yp1(t) is:

yp1(t) = (1/600)cos(1000t)

The complete solution for the input signal 5cos(1000t) is given by:

y1(t) = y1_h(t) + yp1(t)

      = Ae^(-3t/(4 x 10^-3)) + (1/600)cos(1000t)

Step 2: Solve for the response to the input signal -10cos(2000t).

Let's assume y2(t) represents the response to the input signal -10cos(2000t). Similar to Step 1, we can find the particular solution and the homogeneous solution for this input signal.

The particular solution yp2(t) is:

yp2(t) = Bcos(2000t)

The homogeneous solution is given by:

y2_h(t) = Ce^(-3t/(4 x 10^-3))

The complete solution for the input signal -10cos(2000t) is given by:

y2(t) = y2_h(t) + yp2(t)

      = Ce^(-3t/(4 x 10^-3)) + Bcos(2000t)

Step 3: Apply the superposition principle.

Since the system is linear, the total response y(t) is the sum of the responses to each input signal:

y(t) = y1(t) + y2(t)

    = Ae^(-3t/(4 x 10^-3)) + (1/600)cos(1000t) + Ce^(-3t/(4 x 10^-3)) + Bcos(2000t)

This is the general solution for y(t).

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