Which expressions are a factor of -48xyz – 24xy + 40xyz?
A) 4
B) 24
C) 3x
D) 8y
E) 2xy
F) 6xy
G) xyz

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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If the intended margin of error equals 4 less than with a 0.95 probability, the sample size is 126.

The \(\alpha\) level is calculated by subtracting 1 from the confidence interval and dividing by 2.

\(\alpha\) = (1 - 0.95) ÷ 2

\(\alpha\) = 0.025

Find z inside the Z-table because it has a p-value of 1 - \(\alpha\).

So, z = 1.96 with a p-value = 1 - 0.025 = 0.975.

Now, consider that margin of error M.

M = z × (σ ÷ √n)

The standard deviation is determined as the square root of variance.

σ = √522 = 22.84

With a 0.95 probability, the sample size that requires to be accepted if the expected margin of error is 4 or less is,

The sample size of at least n, in which n is encountered when M = 4. So,

M = z × (σ ÷ √n)

4 = 1.96 × (22.84 ÷ √n)

4√n = 1.96 × 22.84

√n = (1.96 × 22.84) ÷ 4

√n = 11.1916

n = (11.1916)²

n = 125.25 ≈ 126

A sample size of at minimum 126 people is required.

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Answer:

25x^2 - 1

Step-by-step explanation:

khan

Answer:

15 hours

Step-by-step explanation:

10 guests - 1.5 hours

1 guest - 1.5 / 10 = 0.15 hours

100 guests - 0.15 x 100 = 15 hours

Answer:

y=0

Step-by-step explanation:

branliest

Answer:

2. Y=O

Step-by-step explanation:

I really don't have a good explanation but that's it

Answer: He did not both sides by 100. He did not look for the common denominator before solving.

x is actlly equal to 64

Answer:

53 cupcakes

Step-by-step explanation:

Take the amount of frosting and divide by the amount needed per cupcake

431/8

53.875

We round down since we cannot frost part of a cupcake

53 cupcakes

Answer:

53 cupcakes

Step-by-step explanation:

He has a total of 431 ounces and each cupcake needs 8 ounces of frosting. Therefore can divide the total amount of frosting (431 ounces) by the amount per cupcake (8 ounces)

total amount/ amount per cupcake

431 ounces/8 ounces

431/8

53.875

0.875, or a fraction/part of a cupcake can’t be frosted, so we should round down to the nearest whole number.

53

He can frost 53 cupcakes.

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

$13,450

Step-by-step explanation:

The fixed costs of production, are the costs incurred that are independent from the production volume, that is, regardless of how many spinners the company produces, those costs will remain the same. If 'x' is the number of spinners produced, interpreting the cost function, we can see that it costs $1.28 to produce each spinner and that there is a cost that does not rely on production of $13,450. Therefore, the fixed cost of production is $13,450.

There are 86 treats did Sidney buy in all.

We have to given that;

Sidney bought some treats for her puppy.

And, She bought 5 packs of crunchy treats and 7 bags of soft treats.

Since, There were 6 crunchy treats in each pack and 8 soft treats in each bag.

Hence, Total crunchy treats in 5 packs are,

= 5 x 6

= 30

And, Total soft treats in 7 bags are,

= 8 x 7

= 56

Therefore, Total number of treats did Sidney buy in all is,

⇒ 56 + 30

⇒ 86

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The commute times are shorter for City A but more predictable for City B. Thus, option c is correct.

In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded.

The interval [1, 5] represents a set of real numbers that includes all the numbers between 1 and 5, including 1 and 5 themselves. The square brackets indicate that the endpoints of the interval are included in the set. The left bracket "[" indicates that the interval includes the number 1, and the right bracket "]" indicates that the interval includes the number 5.

In interval notation, we can write this interval as:

[1, 5] = {x | 1 ≤ x ≤ 5}

This means that the set of all real numbers x, such that x is greater than or equal to 1 and less than or equal to 5, is equal to the interval [1, 5].

Graphically, we can represent this interval on a number line as follows:

 |-----|-----|-----|-----|-----|

 0     1     2     3     4     5

The interval [1, 5] is the closed interval between 1 and 5, including both endpoints, so we use closed circles to indicate that the endpoints are included in the interval:

 |-----|-----|-----|-----|-----|

 0     1     2     3     4     5

       [     ○-----○     ]

            1         5

The interval includes all the numbers on the number line between 1 and 5, including 1 and 5 themselves, but no other numbers outside of that range.

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Answer:

(3,-2)

Step-by-step explanation:

See image

The function is increasing on \($(-\infty, -2)$\) and \($(2, \infty)$\), decreasing on \($(-2, 0)$\) and \($(0, 2)$\), has a local maximum at \($x = 0$\), and is concave up on its entire domain.

The first derivative of the function is given by \(f'(x) = \frac{2x}{(x^2-4)^2}\). Setting this equal to zero, we find that \($x = 0$\) is the only critical point.

To determine the intervals of increase and decrease, we can test the sign of \($f'(x)$\) in the intervals \((-\infty, -2)$, $(-2, 0)$, $(0, 2)$,\) and \((2, \infty)\). We find that \($f'(x) > 0$\) in the intervals \($(-\infty, -2)$\), \($(2, \infty)$\) and \($f'(x) < 0$\) in the intervals \($(-2, 0)$\) and \($(0, 2)$\). Thus, the function is increasing on \($(-\infty, -2)$\), \($(2, \infty)$\) and decreasing on \($(-2, 0)$\) and \($(0, 2)$\).

Since the first derivative changes sign from positive to negative at \($x = 0$\), this point is a local maximum. The second derivative of the function is given by \($f''(x) = \frac{6x^2+8}{(x^2-4)^3}$\). This is positive for all \($x \neq \pm 2$\), so the function is concave up on its entire domain. There are no points of inflection or intervals of downward concavity.

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There are no real solutions.

Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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Step-by-step explanation:

again option D x = 10, y= 3

is the correct answer of this question.

plz mark my answer as brainlist.if you find it useful.

hope this will be helpful to you.

Answer:

x = 10

y = 7

Step-by-step explanation:

4x-2 = x+28

4x-x = 28+2

3x = 30

x = 30÷3

x = 10

4y-7 = y+14

4y-y = 14+7

3y = 21

y = 21÷3

y = 7

Answer:

n = 7/2

Step-by-step explanation:

We are given the equation:-

\( \displaystyle \large{8 \times \sqrt{2} = {2}^{n} }\)

To solve an exponential equation, first, we convert the whole equation with same base.

Let our main base is 2 for whole equation, the following number must be:-

From √2 = 2^(1/2) comes from:-

\( \displaystyle \large{ {a}^{ \frac{m}{ n } } = \sqrt[n]{ {a}^{m} } }\)

\( \displaystyle \large{ {2}^{ \frac{1}{ 2 } } = \sqrt{2} }\)

Rewrite the equation with base 2.

\( \displaystyle \large{ {2}^{3} \times {2}^{ \frac{1}{2} } = {2}^{n} }\)

Recall the law of exponent:-

\( \displaystyle \large{ {a}^{m} \times {a}^{n} = {a}^{m + n} }\)

Therefore:-

\( \displaystyle \large{ {2}^{3 + \frac{1}{2} } = {2}^{n} } \\ \displaystyle \large{ {2}^{ \frac{6}{2} + \frac{1}{2} } = {2}^{n} } \\ \displaystyle \large{ {2}^{ \frac{7}{2} } = {2}^{n} }\)

Compare the exponent and thus:-

n = 7/2.

Answer:

92.5

Step-by-step explanation:

\(\frac{18.5}{100} = \frac{x}{500}\)

cross multiply:

18.5 · 500 = 9250

100 · x = 100x

isolate x by dividing 100 from both sides:

x = 92.5

hope this helps!

Given statement solution is :- If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability.

If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability. However, the psychic claims to have the ability to sense the outcome of each flip, which would suggest that he believes he can accurately predict the results.

To put the psychic to the test, you can proceed with flipping the coin six times and ask the psychic to guess the outcome of each flip. After the coin has been flipped, compare the psychic's guesses with the actual outcomes to evaluate the accuracy of their predictions.

Keep in mind that even if the psychic does make correct predictions, it does not necessarily prove their psychic abilities. Random chance can occasionally lead to a streak of correct guesses, even if there is no true psychic ability involved. To draw any meaningful conclusions, a larger sample size or repeated testing would be required.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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The p-value for this hypothesis test for a proportion p is 0.039.

What is a random sample?

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals is chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left-tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where,

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail is 0.039

Thus,

p = 0.039

Hence, the p-value for this hypothesis test for a proportion p is 0.039.

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The height of the antenna with the help of the trigonometric function is  8.06 feet.

The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.

When solving difficulties involving the right-angle triangle in everyday life, the trigonometric function is excellent and highly helpful.

The given situation is making right-angle triangles.

tan22° = x/25

x = 10.1 feet

tan36° = (x + h)/25

10.1 + h = 18.163

h = 8.06 feet

Hence "Using the trigonometric function, the antenna's height comes out to 8.06 feet".

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Answer:

n = -1

Step-by-step explanation:

you've accidently substracted 6n from 12n when you were supposed to be adding them. (-6n becomes +6n when brought to the otherside of the equal sign)

Answer:

58.6 degrees

Step-by-step explanation:

Answer: Congruence essentially means that two figures or objects are of the same shape and size. ... Similarity means that two figures or objects are of the same shape, though usually not of the same size. Two circles will always be similar, for example, because by definition they have the same shape.

Hope this helps :)

Tell me if it’s wrong :0

I hope this helps you

If R measures 18°,q equals 9.5 ,p equals 6.0 then we can find the length of PQ which is r using the law of cosines.

In trigonometric ratios law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Law of cosines is as under:

\(c^{2} =a^{2} +b^{2} -2ab cos d\)

where c is the side opposite to the angle given, a,b are the other sides and d is the angle given.

We have been given ∠R=18°, q equals 9.5 , p equals 6.0 then the length r can be calculated as under:

\(r^{2} =p^{2} +q^{2} -2pq cos 18\)

r=\(\sqrt{p^{2} +q^{2} -2pq cos 18}\)

Hence the length of r is equal to \(\sqrt{p^{2} +q^{2} -2pq cos 18}\).

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Answer:

solution here

<M=62

add 30+32

Answer:

D. not enough information

Step-by-step explanation: