Can someone please help me

Answer:

49

Step-by-step explanation:

discriminant,b^2-4ac

=1-4×2×(-6)=49

In this case the answer is very simple. .

Step 01:

Data

side a = 8m

side b = 15m

c = hypotenuse = ?

Step 02:

Pythagoras Theorem Formula

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

c ² = (8m)² + (15m)²

c ² = 64m² + 225m²

c ² = 289m²

The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

For the given partially decoupled system, dv/dt = -v , v(0) = -1 and dy/dt = v , y(0) = 100

The value of the constant that appears when solving for y(t) i.e, c₂ is 99..

We have given that

dv/dt = -v ; v(0) = -1

By separtion of variables ,

dv/v = - dt

=> ₋₁∫ᵛ dv/v = ₀∫ᵗ -1 dt

=> ₋₁[ ln(v) ]ᵛ = ₀[ -t]ᵗ

=> ln(v) - (-ln(-1)) = -t - 0

=> ln(v/-1) = - t

=> -v = e⁻ᵗ

=> v = - e⁻ᵗ

Now, dy/dt = v = - e⁻ᵗ

Integrating both sides y = 0 to 100 and t =0 to t

₀∫ʸ 1dy = ₀∫ᵗ - e⁻ᵗ dt

=> ₀[ y ]ʸ = - ₀[- e⁻ᵗ ]ᵗ

=> y - 100 = e⁻ᵗ - 1/e⁰ (since y(0)= 100) => y - 100 = e⁻ᵗ - 1

=> y = e⁻ᵗ - 1 + 100

=> y = e⁻ᵗ + 99

Which is general solution of dy/dt .

So, the constant that appears when solving for y(t), c₂ is 99.

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Complete question:

dy/dt =v, y(0) = 100 ; dv/dt = -v , v(0) = - 1 ..This is a partially decoupled system. Solve for v(t) first by separation of variables. Then substitute into the second equation and solve for y(t). If C1 is the constant that is in the general solution for v(t), and C2 is the constant that appears when solving for y(t), what is the value of C2?

The closure property refers to the mathematical law that states that if we perform a certain operation (addition, multiplication) on any two numbers in a set, the result is still within that set.In the expression (2x3 x2 - 4x) - (9x3 - 3x2), we are simply subtracting one polynomial from the other.

To simplify it, we'll start by combining like terms. So, we'll add all the coefficients of x3, x2, and x, separately.The given expression becomes: (2x3 x2 - 4x) - (9x3 - 3x2) = 2x3 x2 - 4x - 9x3 + 3x2We will then combine like terms as follows:2x3 x2 - 4x - 9x3 + 3x2 = 2x3 x2 - 9x3 + 3x2 - 4x= -7x3 + 5x2 - 4x

Therefore, the correct simplification of the expression is -7x3 + 5x2 - 4x. The demonstration of the closure property is shown as follows:The subtraction of two polynomials (2x3 x2 - 4x) and (9x3 - 3x2) results in a polynomial -7x3 + 5x2 - 4x. This polynomial is still a polynomial of degree 3 and thus, still belongs to the set of polynomials. Thus, the closure property holds for the subtraction of the given polynomials.

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The particular solution is a linear function with slope 6 and y-intercept 5, and the complementary solution is the sum of two exponential functions with opposite concavities. The general solution is the sum of these two curves.

We will first find the particular solution using the method of undetermined coefficients.

Since the right-hand side of the differential equation is a linear function of x, we assume that the particular solution has the form yp(x) = ax + b. We then have:

yp'(x) = a

yp''(x) = 0

Substituting these expressions into the differential equation, we get:

0 + 5a - 6(ax + b) = 22 + 18x - 18x

Simplifying and collecting like terms, we get:

(5a - 6b)x + (5a - 6b) = 22

Since this equation must hold for all values of x, we can equate the coefficients of x and the constant term separately:

5a - 6b = 0

5a - 6b = 22

Solving this system of equations, we get:

a = 6

b = 5

Therefore, the particular solution is:

yp(x) = 6x + 5

To find the general solution, we first find the complementary solution by solving the homogeneous differential equation:

y'' + 5y' - 6y = 0

The characteristic equation is:

r^2 + 5r - 6 = 0

Factoring the equation, we get:

(r + 6)(r - 1) = 0

Therefore, the roots are r = -6 and r = 1, and the complementary solution is:

yc(x) = c1e^(-6x) + c2e^x

where c1 and c2 are constants.

the general solution refers to a solution that includes all possible solutions to a given problem or equation.

The general solution is then the sum of the particular and complementary solutions:

y(x) = yp(x) + yc(x) = 6x + 5 + c1e^(-6x) + c2e^x

To solve the initial value problem, we need to use the initial conditions. However, none are given in the problem statement, so we cannot solve it completely.

what is complementary solutions?

In mathematics, the complementary solution is a solution to a linear differential equation that arises from the homogeneous part of the equation. It is also known as the "homogeneous solution."

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In general, different refrigerants should not be mixed or recovered into the same cylinder.

Different refrigerants have unique chemical compositions and properties that make them incompatible with one another. Mixing different refrigerants can lead to unpredictable reactions, loss of refrigerant performance, and potential safety hazards. Therefore, it is generally recommended to avoid recovering different refrigerants into the same cylinder.

When recovering refrigerants, it is important to use separate recovery cylinders or tanks for each specific refrigerant type. This ensures that the refrigerants can be properly identified, stored, and recycled or disposed of in accordance with regulations and environmental guidelines.

The refrigerant recovery process involves capturing and removing refrigerant from a system, storing it temporarily in dedicated containers, and then transferring it to a proper recovery or recycling facility. Proper identification and segregation of refrigerants during the recovery process help maintain the integrity of each refrigerant type and prevent contamination or cross-contamination.

To maintain the integrity and safety of different refrigerants, it is best practice to recover each refrigerant into separate cylinders. Mixing different refrigerants in the same cylinder can lead to complications and should be avoided. Following proper refrigerant recovery procedures and guidelines helps ensure the efficient and environmentally responsible management of refrigerants.

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The number of different refrigerants that may be recovered into the same cylinder is zero.

When it comes to refrigerants, it is important to understand that different refrigerants should not be mixed together. Each refrigerant has its own unique properties and should be handled and stored separately. mixing refrigerants can lead to chemical reactions and potential safety hazards.

The recovery process involves removing refrigerants from a system and storing them in a cylinder for proper disposal or reuse. During the recovery process, it is crucial to ensure that only one type of refrigerant is being recovered into a cylinder to avoid contamination or mixing.

Therefore, the number of different refrigerants that may be recovered into the same cylinder is zero. It is essential to keep different refrigerants separate to maintain their integrity and prevent any adverse reactions.

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Answer:

y = - 3x + 24

Step-by-step explanation:

Step 1:

y = mx + b         Slope Intercept Form

Step 2:

- 3x - y = - 24         Equation

Step 3:

- 3x = y - 24       Add y on both sides

Step 4:

- 3x + 24 = y        Add 24 on both sides

Answer:

y = - 3x + 24

Hope This Helps :)        

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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Answer:

12

Step-by-step explanation:

51-15=

36

36/3=12

Have a great day!

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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Answer:

Translation: Solutions to effective family education

Step-by-step explanation:

The greatest number of average students that could be in each row is 8. This is because there are an equal number of girls and boys, so the teacher can arrange them in equal rows with 4 girls and 4 boys in each row.

48 girls/8 students per row = 6 rows

32 boys/8 students per row = 4 rows

Total number of rows = 10

The teacher has 48 girls and 32 boys in the choir and wants to arrange them in equal rows. To accomplish this, the teacher needs to ensure that the same number of boys and girls are in each row. The greatest number of students that can be in each row is 8. This is because if 4 girls and 4 boys are in each row, then the total number of rows will be 6 for the girls and 4 for the boys, totaling 10 rows. This arrangement will allow the teacher to keep an equal number of boys and girls in each row, and will also ensure that the same number of students is in each row. Having 8 students in each row is the most efficient way to arrange the choir, as it will require the least amount of rows and will still keep the number of boys and girls even.

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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Answer:

Incorrect.

Step-by-step explanation:

6 + x = 19

Plug in when x = 12

6 + 12 = 19

18 = 19

It is incorrect, so 12 is not a solution.

Answer:

It is not a solution

Step-by-step explanation:

6 + x = 19

Substitute into the equation and see if it is true

6+12 = 19

18 =19

This is not true so it is not a solution

Answer: 2.5

Step-by-step explanation: 0.83333... x 3 = 2.5

Answer:

2.5

Step-by-step explanation:

(5÷6)×3=2.5

or

3/1 x 5/6 = 2 1/2 (2.5)

Vertical change meets slope constraint claim.

To test LaTisha's claim, we need to use the slope formula:

slope = (change in y) / (change in x)

For each zip line location, we need to calculate the slope of the zip line both before and after the proposed change in height. If the slope remains within the allowed range, then LaTisha's claim is correct.

For Zip line A, the initial height is 12 feet and the horizontal distance is 24 feet. The slope is:

slope = (12 - 4) / 24 = 0.333...

If the height is changed by 7 feet to a height of 9 feet, then the slope becomes:

slope = (9 - 4) / 24 = 0.208...

Since the new slope is less than the initial slope, the claim is not correct for Zip line A.

We can repeat this process for Zip line B and Zip line C to determine if LaTisha's claim holds for those locations as well.

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Answer:

\(h_t=9ft\)

Step-by-step explanation:

From the question we are told that:

Height of child \(h_c=3ft\)

Height of child's shadow  \(h_c_s=2ft\)

Height of tree's shadow \(h_t_s=6ft\)

Since position of Sun remains constant  

Generally the equation for Height of tree h_t mathematically given by

 \(h_t=f_{ts}\frac{h_c}{h_c_s}\)

 \(h_t=6*\frac{3}{2}\)

 \(h_t=9ft\)

A random variable Y has a uniform distribution over the interval (θ1, θ2). The variance of Y is (θ2 - θ1)^2 / 12.

The variance of a uniform distribution is given by:

\(Var(Y) = (θ2 - θ1)^2 / 12\)

To derive this, we can use the standard formula for variance:

\(Var(Y) = E(Y^2) - [E(Y)]^2\)

where E(Y) is the expected value of Y.

Since Y is uniformly distributed over the interval (θ1, θ2), we have:

\(E(Y) = (θ1 + θ2) / 2\)

To compute E(Y^2), we have:

\(E(Y^2) = ∫θ1^θ2 y^2 f(y) dy\)

where f(y) is the probability density function of Y, which is constant over the interval (θ1, θ2) and zero elsewhere. Therefore:

\(E(Y^2) = ∫θ1^θ2 y^2 (1 / (θ2 - θ1)) dy\)

\(= [(y^3 / 3) * (1 / (θ2 - θ1))] from θ1 to θ2\)

\(= (θ2^3 - θ1^3) / (3 (θ2 - θ1))\)

Now, we can compute the variance:

\(Var(Y) = E(Y^2) - [E(Y)]^2\)

\(= (θ2^3 - θ1^3) / (3 (θ2 - θ1)) - [(θ1 + θ2) / 2]^2\)

\(= (θ2 - θ1)^2 / 12\)

Therefore, the variance of Y is (θ2 - θ1)^2 / 12.

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Answer:

-8

Step-by-step explanation:

A= - 48

B= 6

-48/6

= 8

Negative x Negative = Positive

Negative x Positive = Negative

Positive + Positive = Positive

Answer:

\( \frac{1}{3} \times 12 \times area = 90 \\ area = 90 \div 4 = 22.5\)

Answer: 194

Step-by-step explanation:

1. Square both sides to get (b+2)=14^2=196

2. Subtract 2 from both sides to get b=194

The completed relationship is:

0.001 grams = 0.0000000551 µg

To complete the relationship, we need to convert the units of the left-hand side and simplify the right-hand side.

Starting with the left-hand side:

1 mg = 1 milligram = 0.001 grams

Now, we can substitute this into the relationship:

For the right-hand side:

1100 in binary is equal to\(12^3 + 12^2 + 02^1 + 02^0 = 8 + 4 = 12\)

10001000 in binary is equal to \(12^7 + 02^6 + 02^5 + 02^4 + 12^3 + 02^2 + 02^1 + 02^0 = 128 + 8 = 136\)

100 in binary is equal to \(12^2 + 02^1 + 0*2^0 = 4\)

Now, we can substitute these values into the relationship:

0.001 grams = 12 µg / 136 / 4

Simplifying the right-hand side:

12 µg / 136 / 4 = 12 * (1/1000000) * (1/136) * (1/4) = 0.00000005514706...

Rounding this to a reasonable number of significant digits, we get:

0.0000000551

Therefore, the completed relationship is:

0.001 grams = 0.0000000551 µg

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Answer:

c

Step-by-step explanation:

Answer:

W = 7 16/35

Step-by-step explanation:

W - 2 3/5 = 4 6/7 is the same as,

W - 2 21/35 = 4 30/35 because you tried to find like fractions,

Then, you add 2 21/35 to both sides of the equation to isolate the variable W,

(W - 2 21/35) + 2 21/35 = (4 30/35) + 2 21/35, simplify,

W = 6 51/35, simplify more,

W = 7 16/35 as the final answer

Calculating this expression will give us the probability that a random sample of 60 households in the town contains exactly 20 households that have 3 or more vehicles.

To solve this probability problem, we need to use the binomial probability formula.

The binomial probability formula calculates the probability of getting a specific number of successes in a fixed number of independent Bernoulli trials.

In this case, the probability of success is 30% (0.30), which represents the probability that a household owns 3 or more vehicles. The probability of failure is 70% (0.70), which represents the probability that a household does not own 3 or more vehicles.

Let's denote X as the number of households in the sample of 60 that have 3 or more vehicles. We want to find the probability that X = 20.

The formula for the probability mass function (PMF) of a binomial distribution is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time (n choose k),

p is the probability of success,

n is the total number of trials,

k is the number of successes.

In our case:

p = 0.30 (probability of success)

n = 60 (total number of trials)

k = 20 (number of successes)

Now, we can calculate the probability:

P(X = 20) = C(60, 20) * (0.30)^20 * (1 - 0.30)^(60 - 20)

Using the combination formula, C(n, k) = n! / (k! * (n - k)!), we can calculate:

P(X = 20) = (60! / (20! * (60 - 20)!)) * (0.30)^20 * (0.70)^40

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Number of cards made from the sheet of paper is 243.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

On the entire sheet of paper, 243 cards were created.

The sheet is described as being 324 cm 144 cm in size.

Measures 324 centimeters in length.

The sheet has a 144-cm width.

We need to determine how many cards with a 16 cm by 12 cm size can be produced from a single sheet of paper.

The paper's size is 324 144.

46656 sq. cm is the size of the paper's surface.

Now, one card is equal to 16 divided by 12.

Currently, the area of a single card is 192 square centimetres.

Hence, Number of cards made from the sheet of paper is 243.

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