Consider the initial value problem y⃗ ′=[33????23????4]y⃗ +????⃗ (????),y⃗ (1)=[20]. Suppose we know that y⃗ (????)=[−2????+????2????2+????] is the unique solution to this initial value problem. Find ????⃗ (????) and the constants ???? and ????.

Answer:

The value = 54

Step-by-step explanation:

–2n(5+n–8–3n) = –2(3)(5+3-8-3(3)) = –6(5+3-8-9)=–30–18+48+54=54

I hope I helped you^_^

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Therefore, the population of seabirds 6 years ago was approximately 11,745.5.

Percent is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". For example, if there are 25 students in a class and 20 of them passed the test, the percentage of students who passed the test is 80%. This is calculated by taking the number of students who passed (20) and dividing it by the total number of students (25), then multiplying by 100.

Here,

3. The amount of the radioactive element can be modeled by the equation:

\(A(t) = A(0) *e^{rt}\)

where A(t) is the amount of the element at time t, A(0) is the initial amount at time t=0, r is the continuous rate of decrease, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we know that the initial amount A(0) is 4500 nanograms, the continuous rate of decrease r is 15% per hour, and we want to find the amount of the element at 6 p.m., which is 6 hours after noon.

First, we need to convert the continuous rate of decrease from hourly to continuous, using the formula:

r = ln(1 - p)

where p is the hourly rate of decrease, expressed as a decimal. In this case, p = 0.15, so:

r = ln(1 - 0.15)

≈ -0.1707

Substituting the given values into the equation for A(t), we get:

\(A(t) = 4500*e^{-0.1707t}\)

where t is the time in hours since noon. To find the amount of the element at 6 p.m. (t = 6), we plug in t = 6 and evaluate:

\(A(6) = 4500*e^{-0.1707*6}\)

≈ 2595.5

Therefore, there will be approximately 2595.5 nanograms of the element at 6 p.m.

4a. The population of seabirds can be modeled by the equation:

\(P(t) = P(0)*e^{rt}\)

where P(t) is the population at time t, P(0) is the initial population at time t=0, r is the continuous rate of growth, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we know that the initial population P(0) is 16,000, the continuous rate of growth r is 4% per year, and we want to find the population 6 years from now.

We need to convert the continuous rate of growth from years to continuous, using the formula:

r = ln(1 + p)

where p is the annual rate of growth, expressed as a decimal. In this case, p = 0.04, so:

r = ln(1 + 0.04)

≈ 0.0392

Substituting the given values into the equation for P(t), we get:

\(P(t) = 16000*e^{0.0392t}\)

where t is the time in years since the initial time. To find the population 6 years from now (t = 6), we plug in t = 6 and evaluate:

\(P(6) = 16000*e^{0.0392*6}\)

≈ 20661.7

Therefore, the population of seabirds will be approximately 20,661.7 in 6 years.

4b. To find the population 6 years ago, we can use the same equation but with t = -6 (since we are going back in time):

\(P(6) = 16000*e^{0.0392*-6}\)

≈ 11745.5

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Answer:

if your proportion is  \(\frac{2}{x}\) = \(\frac{18}{15y}\)  then your answer would be 1.667 or 1 \(\frac{2}{3}\)

edit: your answer could also be \(\frac{5}{3}\)

Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

Answer:

i dont know what exactly the question was asking but all i now is student 2 was doing it right sorry if this didn't help.

Step-by-step explanation:

The correct radical form of b^1/5 is 5^√b.

Square root and nth roots are represented by the symbol "radical," which. a square root is a component of a radical expression, which is an expression.

A number's or an algebraic expression's simplest radical form is referred to as this. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

Explanation:

Convert to radical form using the formula

a^x/n=n^√a^x

5^√b.

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Answer:

\(Solution,\\Volume(V)=72cm^{3} \\Radius(r)=3cm\\Height(h)=?\\As ,\\V=\pi r^{2} h\\72cm^{3} =\pi *(3cm)^{2} *h\\\frac{72cm^{3} }{9\pi cm^{2} }=h\\ h=2.5464cm\)

Step-by-step explanation:

Hence the height ≈ 2.5464cm

Answer:

D. The actual price is 12.5% higher than the expected price.

Step-by-step explanation:

hope i helped :)

Answer:

5 1/2- 1 2/7

11/2-9/7

(11×7-9×2)/14

59/14

4 3/14

Answer:

False

Step-by-step explanation:

Because 10 - 4 = -6

Not 3

Answer:

true

Step-by-step explanation:

first you do the division

10-4+9/3

10-4+3

then you do addition or subtraction in left-to-right order

6+3

9

so it's true

Answer:

The p-value of the test is 0.5028>0.05, which means that there is sufficient evidence to determine that 68% represents the state in question.

Step-by-step explanation:

Test if 68% represents the state in question.

This means that at the null hypothesis, we test if the proportion is 68%, that is:

\(H_0: p = 0.68\)

At the alternate hypothesis, we test if the proportion is different of 68%, that is:

\(H_a: p \neq 0.68\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.68 is tested at the null hypothesis:

This means that \(\mu = 0.68, \sigma = \sqrt{0.68*0.32}\)

32 of the 44 online courses at this particular community college were taught by full-time faculty.

This means that \(n = 44, X = \frac{32}{44} = 0.7273\)

Test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.7273 - 0.68}{\frac{\sqrt{0.68*0.32}}{\sqrt{44}}}\)

\(z = 0.67\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion differing by the population proportion by at least 0.7273 - 0.68 = 0.0473, which is P(|z| > 0.67), which is 2 multiplied by the p-value of z = -0.67.

Looking at the z-table, z = -0.67 has a p-value of 0.2514

2*0.2514 = 0.5028

The p-value of the test is 0.5028>0.05, which means that there is sufficient evidence to determine that 68% represents the state in question.

Answer:find the distance between the co ordinate of the points A(2,3) and B(10,-3)

Distance formula,

━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore the distance is 10 units

Step-by-step explanation:

Answer:

x = -19

Step-by-step explanation:

first isolate x by subtracting 8 on both sides:

179 = -9x + 8

-8              -8

=> 171 = -9x

then divide -9 on both sides to solve for x:

=> x = 171 ÷ -9 = -19

hope it helps ;)

The regression equation is Y = −12.201 + 2.195x.

In the given question,

A regression analysis shows the following results.

                                    Coefficients       Standard Error       t-Stat      p-value

Intercept                        −12.201                     6.560            −1.860       0.100

Number of contacts         2.195                      0.176             12.505      0.000

We have to find the regression equation.

Given that,

Coefficient of Intercept(a) = −12.201

Coefficient of Number of contacts(b) = 2.195

The regression equation is,

Y = a + bx

Y = −12.201 + 2.195x

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The right question is:

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results.

                                    Coefficients       Standard Error       t-Stat      p-value

Intercept                        −12.201                     6.560            −1.860       0.100

Number of contacts         2.195                      0.176             12.505      0.000

What is the regression equation?

Answer:

Step-by-step explanation:

If the sum of the two given angles is 5 + 10 = 15 then the third side cannot be larger than 15. If it is, the two given angles will fall flat on the third angle.

If the third angle is less than 5 then the sum will be less than 10 and the same thing will happen as described above.

So the correct answer is B

The addition of the given fraction expression is 7/8.

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. It can be a simple combination of numbers or a more complex combination involving variables, functions, or other mathematical constructs.

When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same.

In this case, both fractions have a denominator of 8, so we can add their numerators:

5/8 + 2/8 = (5 + 2)/8 = 7/8

Thus, the sum of 5/8 and 2/8 is 7/8.

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Answer:

Two functions which satisfies the H(x) are f(x) = 2x - 4, (x)    = x⁵  and

f(x)  = 2x,  g(x)  = x⁵ - 2

Step-by-step explanation:

The given question is based on the decomposition of a given function into two functions

Decomposition of a function :- functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition

so the function given in the question is H(x) = 2x⁵ - 4

now by using the concept of decomposition of a function we can find two functions f and g

therefore,

f(x) = 2x - 4

and    g(x)    = x⁵

similarly we can find another pair which satisfies the function H(x)

f(x)  = 2x

and g(x)  = x⁵ - 2

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Answer:

n = the first

n + 1 = the 2nd

n + 2 = the 3rd

n(n + 2) - (n + 1) = 10(n + 2) + 1

n2 + 2n - n - 1 = 10n + 20 + 1

n2 - 9n - 22 = 0

(n - 11)(n + 2) = 0

If two factors = 0, at least one must = 0.

n - 11 = 0

n = 11

11,12,13

n + 2 = 0

n = -2

-2,-1,0

Answer:

19.99%

Step-by-step explanation:

hope this helps

here you go

Answer:

x intercept: (-8,0)

y intercept: (0,2)

The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."

According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.

The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:

Sum = (7/2)(x + (x + 6))

Simplifying the equation:

(7/2)(2x + 6) = (21/4)(x + 6)

Multiplying both sides by 4 to eliminate the fractions:

14x + 42 = 21x + 126

Subtracting 14x from both sides:

42 = 7x + 126

Subtracting 126 from both sides:

-84 = 7x

Dividing both sides by 7:

-12 = x.

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(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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9514 1404 393

Answer:

  90

Step-by-step explanation:

1 dekameter is 10 meters, so each of Glenn's 9 pieces of ribbon can be cut to make 10 1-meter pieces.

  9 × 10 m = 90 m . . . . length of available ribbon

  (90 m)/(1 m/piece) = 90 pieces

Glenn can cut 90 1-meter pieces from the ribbon he has.

Answer:

x=

Step-by-step explanation:

⅔x= 7x-1

2/3x=6

multiply both sides by 3/2

(3/2)(2/3x)= 6×3/2

x=

The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).

The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.

We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .

Factorization by grouping:

We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.

This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)

Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).

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Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

\(\dfrac{AD}{AB} = \dfrac{DE}{BC}\)

\(\dfrac{8}{12} = \dfrac{2}{y}\)

8y = 24

y = 24/8

y = 3 meters

Let take an integral look  at the distance of the man from the building as x, therefore the distance from the spotlight to the man is  12 - x

∴

\(\dfrac{12-x}{12}=\dfrac{2}{y}\)

\(1- \dfrac{1}{12}x = 2* \dfrac{1}{y}\)

To find the derivatives of both sides ;we have:

\(- \dfrac{1}{12}dx = 2* \dfrac{1}{y^2}dy\)

\(- \dfrac{1}{12} \dfrac{dx}{dt} = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}\)

During that time ;

\(\dfrac{dx}{dt }= 1.4 \ m/s\)   and y = 3

So; replacing the value into above ; we have:

\(-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}\)

\(\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 } }{ \dfrac{2}{9}}\)

\(\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 } }*{ \dfrac{9}{2}}\)

\(\dfrac{dy}{dt} =0.525 \ m/s\)

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Solving a system of equations we wll see that there are  are 24 women, and the other 15 students are men in foruth grade.

We know that there are 39 students in fourth grade, we know that:

3/4 of the women went

2/3 of the men went

And this leaves 11 students at the school, then we can write the equation:

(3/4)*W + (2/3)*M + 11 = 39

Where W and M are the number of women and men respectively.

(3/4)*W + (2/3)*M = 39 - 11  = 28

(3/4)*W + (2/3)*M = 28

And we also know that the total number is 39, then:

M + W = 39

So we can write the system of equations:

(3/4)*W + (2/3)*M = 28

M + W = 39

M = 39 - W

REplacing that on the other equation we get:

(3/4)*W + (2/3)*(39 - W) = 28

(3/4)*W - (2/3)*w + 26 = 28

(3/4)*W - (2/3)*W = 28 - 26 = 2

(9/12)*W - (8/12)*W = 2

(1/12)*W = 2

W = 2*12 = 24

There are 24 women, and the other 15 students are men.

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Answer:

0.75

Step-by-step explanation:

this is easy no offense

Answer:

\(\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}\)

Step-by-step explanation:

Given the expression \(\frac{5x-4}{x(x^2+7)^2}\), we are to re-write the expression in form of a partial fraction.

Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.

Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.

\(\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}\)

From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are  both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.