Need help on multiple choice question

As a result, y = 200 + 160[tex]e^{(0.4t)}[/tex] is the answer to the provided differential equation with starting conditions of y = 40 and t = 0.

A mathematical statement that shows the equivalence of a couple of equations is what an equation at algebra means. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

The given differential equation is:

dy/dt = 0.4(y - 200)

To solve this differential equation, we need to separate the variables and integrate:

dy/(y - 200) = 0.4 dt

Integrating both sides, we get:

ln|y - 200| = 0.4t + C

where C is the constant of integration.

To determine the value of C, we use the initial condition that y = 40 when t = 0:

ln|40 - 200| = 0.4(0) + C

ln|-160| = C

C = ln(160)

Thus, the equation becomes:

ln|y - 200| = 0.4t + ln(160)

Taking the exponential of both sides, we get:

|y - 200| = [tex]e^{(0.4t+ln(160))}[/tex] = 160[tex]e^{(0.4t)}[/tex]

Simplifying, we get:

y - 200 = ±160[tex]e^{(0.4t)}[/tex]

y = 200 ± 160[tex]e^{(0.4t)}[/tex]

Using the initial condition that y = 40 when t = 0, we can determine the value of the constant of integration:

40 = 200 ± 160[tex]e^{(0.4(0))}[/tex]

40 = 200 ± 160

Solving for the two possible values of y, we get:

y = 360 or y = 40

Therefore, the solution to the given differential equation with the initial condition y = 40 and t = 0 is:

y = 200 + 160[tex]e^{(0.4t)}[/tex]

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The value of 2(s + t)^{3} - 6 is 244.

What is an equation?

In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=).

For example, the equation 3x + 5 = 11 asserts that the expression 3x + 5 is equal to the expression 11. An equation can have one or more variables, which are typically represented by letters. In the example above, x is the variable.

To evaluate 2(s + t)^{3} - 6 when s = 3 and t = 2, we can substitute 3 for s and 2 for t in the expression and simplify.

So we have:

2(s + t)^{3} - 6 = 2(3 + 2)^{3} - 6 (substituting s = 3 and t = 2)

= 2(5)^{3} - 6 (evaluating the expression inside the parentheses)

= 250 - 6 (cubing 5 and multiplying by 2, and then subtracting 6)

= 244 (subtracting 6 from 250)

Therefore, when s = 3 and t = 2, the value of 2(s + t)^{3} - 6 is 244.

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Answer:    -2(x-1)(4x-3)

Step-by-step explanation:   because im just that guy

Answer:80

Step-by-step explanation:

if 79.9 Is 99% of the unknown number the other 1% would be 80

The GCF (Greatest Common Factor) of 2.4x and 12 is 2.4. Therefore, we can write: 2.4x - 12 = 2.4(x - 5)

What is expression ?

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. It can be a simple numerical value or a more complex arrangement of terms and operations.

To generate an expression equivalent to 2.4x - 12 using the GCF, we need to find the largest common factor between the terms 2.4x and 12.

First, we can simplify 2.4x by dividing both the numerator and denominator by 0.4, which gives us:

2.4x = 6x

Now, we can find the GCF between 6x and 12, which is 6. We can factor out this GCF from both terms to get:

2.4x - 12 = 6(x - 2)

So, the expression equivalent to 2.4x - 12 using the GCF is 6(x - 2). This expression represents the same quantity as 2.4x - 12, but is simplified and factored.

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The fοrmula fοr t in terms οf 2kπ is: t = kπ + π/2, where k is an integer.

Tο draw a unit circle fοr the given cοοrdinates, we first draw the hοrizοntal and vertical axes intersecting at the οrigin (0,0):

Next, we draw a circle with radius 1 centered at the οrigin:

Tο find pοints οn the circle with y-cοοrdinate 1, we lοοk at the pοint where the circle intersects the vertical axis. This οccurs when x = 0, sο the pοint οn the circle with y-cοοrdinate 1 is (0,1):

(0,1)

Tο find οther pοints οn the circle, we can use the Pythagοrean identity:

sin²(t) + cοs²(t) = 1

Since we want y = sin(t) tο be 1, we can sοlve fοr x = cοs(t)

cοs(t) = sqrt(1 - sin²(t))

Using this fοrmula, we can find several pοsitive and negative real numbers t that determine pοints Q οn the circle with y-cοοrdinate 1:

t = 0 radians (0 degrees): Q = (1,0)

t = π/6 radians (30 degrees): Q = (√3/2, 1/2)

t = π/4 radians (45 degrees): Q = (√2/2, √2/2)

t = π/3 radians (60 degrees): Q = (1/2, √3/2)

t = π/2 radians (90 degrees): Q = (0,1)

t = 7π/6 radians (-150 degrees): Q = (-√3/2, 1/2)

t = 3π/4 radians (-135 degrees): Q = (-√2/2, √2/2)

t = 5π/6 radians (-120 degrees): Q = (-1/2, √3/2)

t = π radians (-180 degrees): Q = (-1,0)

Tο write a fοrmula fοr t in terms οf 2kπ, we can use the inverse sine functiοn:

sin(t) = 1

t = sin⁻¹(1) + 2kπ

Since sin(π/2) = 1, we have:

t = π/2 + 2kπ

Sο the fοrmula fοr t in terms οf 2kπ is:

t = kπ + π/2, where k is an integer.

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Hope this helps.

Answer:

Pls mark as brainliest

Step-by-step explanation:

To solve this problem, we can use the concept of present value of money. We want to find the equal payments that will settle the obligations in 5 and 11 months, respectively, and we know the amounts and due dates of the obligations.

Using a 6% interest rate, we can find the present value of each obligation on each comparison date, and then solve for the unknown equal payments.

Comparison date is 11 months hence:

The present value of $10,000 due in 3 months at a 6% interest rate is:

PV1 = $10,000/(1 + 0.06 * 3/12) = $9,703.70

The present value of $20,000 due in 7 months at a 6% interest rate is:

PV2 = $20,000/(1 + 0.06 * 7/12) = $19,003.22

To settle these obligations with two equal payments, we can set up the equation:

PV1/(1 + 0.06 * 8/12) + PV2/(1 + 0.06 * 4/12) = x + x/(1 + 0.06 * 6/12)

where x is the size of each payment.

Simplifying the equation, we get:

9703.70/1.04 + 19003.22/1.02 = 2.5x

Solving for x, we get:

x = $8,102.67

Therefore, each payment should be $8,102.67.

Comparison date is now:

The present value of $10,000 due in 3 months at a 6% interest rate is:

PV1 = $10,000/(1 + 0.06 * 3/12) = $9,703.70

The present value of $20,000 due in 7 months at a 6% interest rate is:

PV2 = $20,000/(1 + 0.06 * 7/12) = $19,003.22

To settle these obligations with two equal payments, we can set up the equation:

PV1 + PV2/(1 + 0.06 * 4/12) = x + x/(1 + 0.06 * 6/12)

where x is the size of each payment.

Simplifying the equation, we get:

9703.70 + 19003.22/1.02 = 2.5x

Solving for x, we get:

x = $8,556.54

Therefore, each payment should be $8,556.54.

Comparison date is 3 months:

The present value of $10,000 due in 3 months at a 6% interest rate is:

PV1 = $10,000

The present value of $20,000 due in 7 months at a 6% interest rate is:

PV2 = $20,000/(1 + 0.06 * 4/12) = $19,508.67

To settle these obligations with two equal payments, we can set up the equation:

PV1/(1 + 0.06 * 8/12) + PV2 = x + x/(1 + 0.06 * 6/12)

where x is the size of each payment.

Simplifying the equation, we get:

10000/1.04 + 19508.67 = 2.5x

Solving for x, we get:

x = $8,433.13

Therefore, each payment should be $8,433.13.

The correct answer is Option B, The amount Jonathan is paid for each hour over 10.

The expression { 7 . 5 x ; 0 ≤ x ≤ 10 75 + 9 ( x − 10 ); x > 10 } gives the amount of money Jonathan is paid each week based on the number of hours he works, x. The first part of the expression, 7.5x, applies when x is between 0 and 10, inclusive. The second part of the expression, 75 + 9(x - 10), applies when x is greater than 10.

So, the term 9(x - 10) represents the amount he is paid for each hour over 10. When Jonathan works more than 10 hours, he is paid a flat rate of $75 for the first 10 hours, and then an additional $9 for each hour over 10. Therefore, if Jonathan works x hours and x is greater than 10, then he is paid 9(x - 10) dollars for each hour over 10.

Therefore, the correct answer is B. the amount he is paid for each hour over 10.

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Answer:

x=43.85

Step-by-step explanation:

solution Given.

let the given angle be θ: 20 degree.

It's opposite side is 12.

It's hypotenuse is x.

Since

We have

Sin θ= opposite/hypotenuse

Sin20 degree=12/x

0.34202014332=12/x

doing criss cross multiplication

x=12/0.34202014332

therefore x=43.8570660032

in two decimal form x=43.85

Answer:31/36

Step-by-step explanation:

we should find greatest common divisor(GCD) ,

GCD(12,18)=36

7/12=7*3/36=21/36

5/18=5*2/36=10/36

21/36+10/36=31/36

Answer:

31/36

Step-by-step explanation:

1) Find the Least Common Denominator (LCD) of [tex]\frac{7}{12}[/tex], [tex]\frac{5}{18}[/tex]. In other words, find the Least Common Multiple (LCM) of 12, 18.

1) List the multiples of each number

Multiples of 12: 12, 24, 36, ...

Multiples of 18: 18, 36, ...

2) Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 36

1) List the prime factors of each number.

Prime Factors of 12: 2, 2, 3

Prime Factors of 18: 2, 3, 3

2) Find the union of these primes.

2, 2, 3, 3

3) Multiply these number: 2 x 2 x 3 x 3 = 36. This is the LCM.

LCM = 36

STEP 2: Make the denominators the same as the LCD.

[tex]\frac{7\times3}{12\times3} +\frac{5\times2}{18\times2}[/tex]

3) Simplify. Denominators are now the same.

[tex]\frac{21}{36} +\frac{10}{36}[/tex]

4) Join the denominators.

[tex]\frac{21+10}{36}[/tex]

5) Simplify.

[tex]\frac{31}{36}[/tex]

Thank you,

Eddie.

The value equivalent tο the expressiοn "4 times 3 cubed" is 108.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants. An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

It is a cοmbinatiοn οf numbers, variables, and symbοls arranged in a meaningful way tο represent a mathematical statement οr relatiοnship.

The expressiοn "Fοur times Three cubed" means that we shοuld first cube the number 3, and then multiply the result by 4.

Tο cube 3, we multiply it by itself three times :

[tex]3^3 = 3 * 3 * 3 = 27[/tex]

Next, we multiply this result by 4:

4 * 27 = 108

Therefοre, the value equivalent tο the expressiοn "4 times 3 cubed" is 108.

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the answer is "EF = 3.16". According to condition of Similar triangles.

How to solve these problem?

To solve this problem, we will use the property of similar triangles, which states that corresponding angles of similar triangles are equal, and their corresponding sides are proportional.

First, we need to find the ratio of the sides of the two triangles. We can do this by dividing the length of one side of triangle ABC by the corresponding side of triangle DEF. Let x be the length of EF, then:

AB/DE = BC/EF = CA/DF

Substituting the given values, we get:

11/4.4 = 7.9/x = 7.6/(DE + x)

Solving for x, we get:

x = 3.16

Therefore, EF = 3.16.

Hence, the answer is "EF = 3.16".

Note that we can also check our answer by verifying that the corresponding sides of the two triangles are proportional using the ratios we found:

AB/DE = 11/4.4 = 2.5

BC/EF = 7.9/3.16 = 2.5

CA/DF = 7.6/(4.4+3.16) = 2.5

Since the ratios are all equal, we can conclude that the triangles are similar.

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Answer:

224 more adults than children

Step-by-step explanation:

150+192=342 adults together

460-342=118 children

342-118= 224

sooo there were 224 more adults than children

The length of the AG in the cuboid is 7.56 cm.

To find the Length of the diagonal AG, we need to find the length of AC. Use the Pythagorean formula to find the length of AC. Now use the trigonometric ratios formulas to find the length of AG.  

Here we have a cuboid

Where AD = 23 cm, DC = 18 cm and ∠GAC = 75°  

From the right angle triangle, ADC

=> AC² = AD² + DC²    [ Using the Pythagorean formula ]

=> AC² = (23)² + (18)²

=> AC² = 529 + 324

=> AC = √853 = 29.20    

Hence, the length of AC = 29.20

From the right angle triangle, AGC

=> Cos B = AC/AG

=> Cos 75° = 29.20/AG

=> AG = Cos 75° (29.20)

=> AG = (0.26)(29.20)

=> AG = 7.56

Therefore

The length of the AG in the cuboid is 7.56 cm.

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Answer:

Step-by-step explanation:

Awnser=48

Answer:

Step-by-step explanation:

6

Answer:

To calculate the percent error, we need to find the absolute difference between the correct value and the measured value, divide that by the correct value, and then multiply by 100 to get a percentage.

The absolute difference between the correct value and the measured value is:

$38.07 - $38.06 = $0.01

Dividing this by the correct value ($38.07) gives:

$0.01 / $38.07 ≈ 0.0002626

Multiplying by 100 gives the percent error:

0.0002626 x 100% ≈ 0.02626%

Therefore, the percent error in the student's calculation is approximately 0.02626%.

The percent error in the student's calculation is 2.63%.

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Answer: We can use the formula for the future value of an annuity with monthly compounding to determine how much money should be deposited:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

FV = future value (the amount we want to accumulate, which is $13,000 in this case)

P = periodic payment (the amount we need to deposit each month)

r = annual interest rate (2.5% in this case)

n = number of compounding periods per year (12 for monthly compounding)

t = number of years (4 in this case)

We want to solve for P, so we can rearrange the formula as follows:

P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)

Substituting the given values, we get:

P = 13000 * (0.025/12) / ((1 + 0.025/12)^(12*4) - 1)

Calculating this expression gives us:

P = $279.27 (rounded to the nearest cent)

Therefore, we need to deposit $279.27 each month for 4 years in an account that earns 2.5% compounded monthly in order to accumulate $13,000. Alternatively, if we want to make a single deposit today, we can multiply this monthly amount by 12 and then by 4, which gives us:

P = $13,414.08 (rounded to the nearest cent)

Therefore, we need to deposit $13,414.08 today in an account that earns 2.5% compounded monthly in order to accumulate $13,000 after 4 years.

Step-by-step explanation:

Sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval is 2sin3x

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle.

Y= A sin( B( X-C))+ D Or  Y= A cos( B( X-C))+ D

where,

A is the value of the amplitude

B is the number of cycles between 0 and 2 pi since B is the graph's period, or (2π).

C is the graph's horizontal movement.

D is the graph's vertical movement.

amplitude=2

number of cycle in the interval=3

Example:

Y= 2 sin 3X

it has an amplitude of 2

There are three cycles of sin between 0 and 2 π

Hence, y=2sin3x  is the sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval.

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The answer of the given question based on the scatterplot for determining  when she will reach 10,000 songs the answer is Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

Slope is  measure of  steepness or incline of  line. In geometry and mathematics, slope is defined as  ratio of the change in  y-coordinates to  change in  x-coordinates between two distinct points on  line. This is often represented by  letter "m".

To determine when Maria will reach 10,000 songs, we need to find the point on the line of best fit where the y-value is 10,000.

From the scatterplot, we can estimate that the line of best fit intersects the y-axis at approximately 2000. This means that the initial number of songs downloaded was 2000.

Next, we need to find the slope of the line of best fit. Let's choose the points (5, 6500) and (10, 9500).

The slope of the line passing through these two points is:

slope = (y2 - y1)/(x2 - x1) = (9500 - 6500)/(10 - 5) = 600 songs per month

This means that Maria is downloading 600 songs per month on average.

Finally, we can use the slope-intercept form of a line to find the x-value when the y-value is 10,000:

y = mx + b

10,000 = 600x + 2000

8000 = 600x

x = 13.33

Therefore, Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

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The function in vertex form is f(x) = 10(x + 2)² - 8.

In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic function is given by:

y = a(x - h)² + k

y = 10(x - (-2))² + (-8)

y = f(x) = 10(x + 2)² - 8

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The probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.

Statistics and probability theory both make substantial use of probability, which is a measure of the possibility or chance of an event occurring. A number between 0 and 1, where 0 denotes an event that is impossible and 1 denotes an event that is certain, is used to indicate the likelihood of an occurrence.

We must count the number of favourable possibilities—those that match the event of interest—and divide that number by the total number of potential outcomes in order to calculate the probability of an occurrence.

There are 8 letters in the word, so the total number of arrangements is 8! = 40,320.

For O and E to be together we consider it as a sing letter, thus:

There are 7! ways to arrange the letters of new word.

Now, OE can be written as OE or EO thus:

2 x 7! = 10,080

Now, the probability of O and E together is:

Probability = 10,080 / 40,320

Probability = 0.25

Hence, the probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.

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The percentage decrease in total principal and interest paid between a 30-year term mortgage and a 15-year term mortgage at an APR of 6.5% and principal of $242,300.00 is about 31.1%

A mortgage is a loan used to purchase property.

The principal balance = $242,300.00

The Annual Percentage Rate, APR = 6.5%

The term of the loan = 30-year and 15-year

The monthly payment for the loan per each term can be obtained using the following formula;

M = P·[r·(1 + r)^n]/[(1 + r)^n - 1]

Where;

M = The monthly payment

P = The principal amount of the loan = $242,300.00

r = The monthly interest rate = APR/12 = 0.065/12

n = The the number of periods of payment = 12 × 30 = 360

The monthly payment for the 30-year loan term is therefore;

M₃₀ = 242,300 × [(0.065/12)·(1 + (0.065/12))^360]/[(1 + (0.065/12))^360 - 1] ≈ 1531.5

The total payment for the 30-year term ≈ 360 × 1531.5 = 551,340.3

The monthly payment for the 15-year loan term is found as follows;

n = 12 × 15 = 180

M₁₅ = 242,300 × [(0.065/12)·(1 + (0.065/12))^180]/[(1 + (0.065/12))^180 - 1] ≈ 2110.7

The total payment in 15 years ≈ 15 × 12 × 2110.7 = 379962

The percentage decrease, is therefore;

((551,340.3 - 379,962)/551,340.3) × 100 ≈ 31.1%

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The factored representation of the quadratic function 2x² - 10x - 48 is given as follows:

2(x - 8)(x + 3).

The quadratic function for this problem is defined as follows:

2x² - 10x - 48

The leading coefficient of 2 is common to all the terms of the expression, hence the expression can be simplified as follows:

2x² - 10x - 48 = 2(x² - 5x - 24).

The term with the square of x can be simplified as follows:

x² - 5x - 24 = (x - 8)(x + 3).

Meaning that x = 8 and x = -3 are the roots of the quadratic function, hence, considering the leading coefficients and the linear factors, the simplified expression is given as follows:

2x² - 10x - 48 = 2(x - 8)(x + 3).

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The factorization of the quadratic equation is:

y = 2*(x + 3)*(x - 8)

Here we have the quadratic equation:

2x^2 - 10x - 48

To factorize it, we need to find the roots of the quadratic, to do so we need to solve the equation:

y = 2*x^2 - 10*x - 48 = 0

2x^2 -10x - 48 = 0

Dividing by 2 in both sides we will get:

(2x^2 - 10x - 48)/2 = 0/2

x^2 - 5x - 24 = 0

Now we can use the quadratic formula to get the roots:

[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*-24} }{2} \\\\x = \frac{5 \pm 11}{2}[/tex]

The roots are:

x = (5 + 11)/2 =8

x = (5 - 11)/2 = -3

Then the factorization will be:

y = 2*(x - (-3))*(x - 8)

y = 2*(x + 3)*(x - 8)

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Answer:

4

Step-by-step explanation:

The cardinality of a set is the number of elements in the set.

Therefore, the cardinal number for the set A={Pacific, Indian, Atlantic, Gulf of Mexico} is 4, since it has four elements.

The names of the column headers in the table indicates that the function c(x) = q(x) ÷ m(x), where q(x) and m(x) are whole numbers, indicates that the function c(x) is a rational function.

Rational functions are functions that consists of a ratio of polynomial functions. A rational function, f(x), consists of the functions g(x) and h(x), such that f(x) = g(x)/h(x), where h(x) ≠ 0.

The input variable of the functions is; x

The functions in the question are; q(x) and m(x)

The function c(x) is; c(x) = q(x) ÷ m(x)

The function c(x) is composed of two functions q(x) and m(x), that are together presented as a fraction, which indicates that c(x) is a rational function.

The type of function represented by the function c(x) is therefore;

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