The sum of a first and second number is 130. If the second number is 20 less than four times the first number, find the two numbers. Let x represent the first number and y represent the second number.

Write the System of Equations used to solve this problem.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:27

Step-by-step explanation:

Answer:

100000+)9(87)238388292838

Answer:

D. Shari is standing 50 feet from a tree that is 100 feet tall. what is the distance between Shari’s foot and the top of the tree

Step-by-step explanation:

When we want to calculate the distance between Shari’s foot and the top of the tree, we apply the Pythagorean Theorem as follows.

\(h^2=50^2+100^2\\h^2=12500\\h=\pm \sqrt{12500} \\h=\pm 111.8\\h=|\pm 111.8|\\h=111.8$ feet\)

Recall, there is always a plum/minus sign before the square root symbol. This is as a result of the fact that:

\((-a)^2=a^2\\a^2=a^2\)

However, since we are looking for distance, we ignore the negative sign by making use of the absolute sign.

The correct option is D  

The system of equations we have is:

Step 1. substract the second equation from the first equation to eliminate variable x:

The minus sign changes the signs of the second equation, and now we have:

and the result of this is:

Step 2. From the result of the substraction -5y=14, solve for y:

Step 3. Substitute this value of y in the first original equation

To find the value of x.

We substitute y=-2.8

Step 4. Solve for x

Answer:

Answer:

6x + 8

Step-by-step explanation:

1.5(3x + 4) + 0.25(6x + 8)  

Distribute

4.5x + 6 + 1.5x + 2

Now, combine like terms

6x + 8

Hope this helps!

Answer:

Step-by-step explanation:

The 2 triangles are similar so corresponding sides are in the same ratio.

3/x = 6/16

6x = 48

x = 8.

9/y = 6/16 = 3/8

3y = 72

y = 24.

Answer:

using proportional equation:

\(\rightarrow \sf \dfrac{AC}{CE} = \dfrac{DB}{DE}\)

\(\hookrightarrow \sf \dfrac{9}{6} = \dfrac{y}{16}\)

\(\hookrightarrow \sf 9(16)} = {6y}\)

\(\hookrightarrow \sf y = 24\)

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

\(\rightarrow \sf \dfrac{AE}{CE} = \dfrac{EB}{DE}\)

\(\hookrightarrow \sf \dfrac{3}{6} = \dfrac{x}{16}\)

\(\hookrightarrow \sf 3(16)} = 6x\)

\(\hookrightarrow \sf x = 8\)

The measure of angle DEF is 37 degrees.

What is chord in circle

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. More specifically, a chord of a circle is a line segment whose endpoints lie on the circle.

Every circle has infinitely many chords, but some of the most commonly discussed chords are the diameter (a chord that passes through the center of the circle), and the secant (a chord that intersects the circle at two distinct points).

Chords play an important role in geometry, as they can be used to determine various properties of circles, such as their radius, diameter, and area.

Since G is the center of the circle, the angle DGE is a central angle of the circle.

Therefore, the angle DGE is equal to twice the inscribed angle DEF that subtends the same arc DE.

Let x be the measure of angle DEF. Then, we have:

2x = 74

x = 37

Hence, the measure of angle DEF is 37 degrees.

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Answer:

1. 7.3

2. 33.3

3. 21.3

4. 31.9

5. 25.6

6. 11.0

7. 42°

8. 64°

9. 13°

10. 51°

Step-by-step explanation:

make sure if you're using a math calculator that it is in degree mode.

SIN, COS, OR TAN. SOH CAH TOA. Sin is Opposite/hypotenus.

Cos is Adjacent(next to it)/hypotenus.

Tan is Opposite/Adjacent.

~~

PROBLEM 1:

So we have 63°, 16 as hypotenus, and x as one of the legs.

1. Figure out whether it is Sin, Cos, or Tan. (It's adj and hyp. of the angle degree (63° listed so it's cos.)

2. Once you set it up, it is Cos 63°= x/16 then flip it around. which makes it 16 COS 63= X.

3. Input it into your calculator as 16cos(63, then it will give you.. 7.263847996

4. Don't forget to round to the nearest tenth, which gives you

x = 7.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 2:

Given: 39°, 27 is opposite of the °, and adj is x. So this is Tan.

1. Set it up, Tan 39° = 27/x can't solve this way so fix it.

2. rewritten as X = 27/tan39

3. round ur answer.

x = 33.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 3:

Given: 49°, adj is 14, hyp is x. So this is Cos.

1. Set up according to CAH, Cos 49=(14/x).

We can't solve it this way since the X is on the bottom. So we have to fix it!

2. Turns into X Cos 49 = 14, which then turns into X= 14/cos49.

3. Put it in your calculator as 14 DIVIDED BY cos 49. ( Put image example)

4. Round.

x= 21.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 4:

Given: 15°, 33 hyp, adj x. Which is Cos.

1. Cos 15= x/33 and rewrite.

2. Input as 33 cos(15 into calculator = 31.875...

3. Round to tenth.

x = 31.9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 5:

Given: 52°, 20 adj of °, and x opp of °. Will use TAN.

1. Tan 52° = x/20

2. 20 Tan(52 into calculator

3. Round

x = 25.6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 6:

Given: 27°, opp of ° is 5, hyp is x. Will use Sin.

1. Write out as I have the last few times, Sin 27 = 5/x rewrite cause x can't be at the bottom.

2. Input into calculator as: 5/sin 27 which equals 11.01...

3. Round.

x = 11.0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 7:

Given: x°, 6 as hyp, 4 opp. now we have to solve this different since we don't know the degree. Now when we input into the calculator you will press 2nd, then sin/cos/tan so it will be negative this is depending on which one ur solving for.

We will be using SIN, x is still a °.

1. Sin X = 4/6 Rewrite.

2. X= Sin^-1 (4/6)

Make sure ur sin is negative in calculator when doing this.

3. It SHOULD give you 41.81, round.

x = 42°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 8:

Given: x°, 29 opp, 14 adj. TAN.

1. Tan x°= 29/14 or..

2. X = Tan^-1(29/14) solve..

3. gives u 64.23.... round.

x = 64°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 9:

Given: x°, hyp 54, opp 12. SIN

1. Sin x°=(12/54)

2. X= Sin^-1(12/54) solve. (dont put x= into calculator.)

3. Don't Forget to round, answer unrounded: 12.839..

x = 13°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 10:

Given: x°, adj 25, hyp 40. COS

1. Cos x°=25/40 rewrite.

2. X= Cos^-1(25/40) Solve.

3. Round.

X= 51°

Answer:

Step-by-step explanation:

log(7)6+log(7)2^3

log(7)6+log(7)8

log(7)(8*6)

log(7)48 = > D is the correct answer.

Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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Answer:

It is linear

Step-by-step explanation:

So long as the exponent on x is 1, the function is linear (doesn't form a parabola)

Answer:

the equation is linear

Step-by-step explanation:

it's in slope-intercept form, which is y = mx + b

plus, there's no exponents so the line wouldn't curve

Answer:

0.81

Step-by-step explanation:

Find the point estimate by dividing the number of respondents that thought it was a major economic concern by the total number of people in the survey:

1,620/2,000

= 0.81

So, the point estimate is 0.81

The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

The given expression is 5x²+6x+4+x²+x

Simplifying the given expression

5x²+6x+4+x²+x

Firstly, put the similar terms together

5x²+x²+6x+x+4

Adding the similar terms

6x²+7x+4

∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.

Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

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Answer:

30 = 6

45 = x

cross multiply

30x = 45*6

30x = 270

divide both sides by

30x/30 = 270/30

X = 9

9-6 = 3 days

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

Options F and G are the correct answer.

We have,

The number of students in Henderson High School.

Work = 96

College = 114

Armed forced = 48

Other = 42

The number of students in Johnson High School.

Work = 30

College = 40

Armed forced = 15

Other = 15

From the information,

The number of students in Work for Henderson High School is greater than Johnson High School.

Now,

Henderson High School:

Armed force and other = 48 + 42 = 90

Mode = college

Johnson High School.

Armed force and other = 15 + 15 = 30

Mode = college

Thus,

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

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Hence , 10 liters of a 10% acid solution and 50 liters of a 40% acid solution must be used.

Let the amount of 10 % acid solution be " x " and the amount  40 % acid solution be " y " .

The total volume of the resulting solution is 60 L which can be given by

      x + y = 60       .....(1)

The total acid in the resulting solution is 35 % acid solution which is given by     0.10 x + 0.40 y = 0.35(60)            .....(2)

Multiplying by 100 in equation (2) , we get

        10 x + 40 y = 2100          .....(3)

Putting x = 60 - y in equation (3) , we get

   10 ( 60 - y ) + 40 y = 2100

        600 - 10y + 40y = 2100

                 30y = 1500

                    y = 50

Putting y = 50 equation (1) , we get

      x = 60 - 50 = 10

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Of the 250 total shirts about, the quantity of shirts that should be red would be = 125.

The total quantity of shirts that was ordered by Mr. Torres = 250 school t-shirts

The total quantity of red shirt selected at random = 5

The total quantity of blue shirt selected at random = 13

The total quantity of grey shirt selected at random = 12

Total selected at random = 30

Now if 5 red shirts = 30

X red shirts = 250

make X the subject of formula;

X = 15× 250/30

X = 3750/30

X = 125 red shirts.

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The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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Question A is the survey that you expect to have fair results regarding attitudes about carnivals

This survey question is the most neutral and fair among the options provided. It doesn't include any leading or biased language that may influence the respondent's answer.

Option B uses the adjective "exciting," which could lead people to think positively about carnivals.

Option C brings in the unrelated factor of "traveling across town," which could negatively influence the response based on travel preference rather than attitude towards carnivals. Option D uses negative descriptors "noisy" and "overpriced," which could lead people to think negatively about carnivals.

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The correct options are -

When something is bought on credit, an initial payment is made in the form of a down payment.

Given is that Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%.

We can calculate the amount she is putting in down payment as -

{x} = 20% of 125000

{x} = 20/100 x 125000

{x} = 20 x 1250

{x} = 25000

Therefore, the correct options are -

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The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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The amount of money increases by $125,000 due to the decrease in the reserve rate. The correct answer is B. It increases the amount by $125,000.

When the Federal Reserve decreases the reserve rate, it allows banks to hold a smaller portion of their deposits as reserves and lend out a larger portion. This change stimulates lending and increases the money supply in the economy through the process of fractional-reserve banking.

In this scenario, the initial deposit of $15,000 can be multiplied by the money multiplier, which is the reciprocal of the reserve rate. Initially, with a reserve rate of 6%, the money multiplier is 1/0.06 = 16.67. Therefore, the initial deposit can lead to a maximum increase in the money supply of $15,000 x 16.67 = $250,050.

When the reserve rate is decreased to 4%, the money multiplier becomes 1/0.04 = 25. Therefore, the same initial deposit of $15,000 can now result in a maximum increase in the money supply of $15,000 x 25 = $375,000.

The difference between the two scenarios is $375,000 - $250,050 = $124,950, which is approximately $125,000. Hence, the amount of money increases by $125,000 due to the decrease in the reserve rate.

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The possible amounts Susan will spend on candy is $25 and above.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, since Susan will buy more than 6 pounds of candy, the same expression will be illustrated by x.

x > ($4 × 6)

x > $24

In this case, she'll have to spend $25 or more.

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Each expression with its equivalent expression are as followed:

(-3⁻²)⁰                  ⇒            1

3³. 3¹ . 3² .3⁻¹²     ⇒        1/729

-3⁵ ÷ -3⁸              ⇒        - 1/27

-3³ · 3³                ⇒         -729

A base number raised tο an expοnent is referred tο as a pοwer in mathematics, where base number is the factοr that is multiplied by itself and expοnent is the number οf times the same base number is multiplied.

When a base number is multiplied by an expοnent, it is said tο have been raised tο that expοnent. The base number is the factοr that is being multiplied by itself, and the expοnent represents hοw many times the base number has been multiplied.

a)  (-3⁻²)⁰

   since power of any number is 0 = 1

        (-3⁻²)⁰   =  1

b)  3³. 3¹ . 3² .3⁻¹²

    3³⁺¹⁺²⁻¹²

    =  3⁶⁻¹²

    = 3⁻⁶

    = 1/3⁶

    = 1/729

c)  -3⁵ ÷ -3⁸

    = -3⁵⁻⁸

    = -3⁻³

    = - 1/3³

    = - 1/27

d) -3³ · 3³

   = (-3 · 3)³

   = (-9)³

    = -729

Thus, we have the table as,

(-3⁻²)⁰                  ⇒            1

3³. 3¹ . 3² .3⁻¹²     ⇒        1/729

-3⁵ ÷ -3⁸              ⇒        - 1/27

-3³ · 3³                ⇒         -729

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Answer:

x<100 and look at picture

Step-by-step explanation:

x-19<81

+19  +19

x<100

+100 on number line, opened line to the left

X<100

Step-by-step explanation:

x-19<18

+19   +19

x<100

+100 on number line, opened line to the left

Answer:

Step-by-step explanation:

Wow, that’s interesting!

Is this a question?

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.

given

The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.

Calculating the sample proportion is necessary:

The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:

P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031

Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:

\(z = (0.476 - 0.34) / 0.031 = 4.39\)

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

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