Let v=⟨1,4,3⟩ - v = ⟨ 1 , 4 , 3 ⟩ - Calculate v×i,v×j,v×k

Factor the expression 25-40 x+16 x² is \((4x-5)^2\)

On rearranging the equation , we get

   \(16x^2-40x+25=0\)        ...(1)

To split the middle term of the quadratic equation, we need to look at the middle term of the quadratic equation under consideration.

Midterm is 40 x  , to split the middle term, use the sum-and-product form which is

" The sum-product form is the product of intermediate terms after splitting and must  equal a × c and the sum must equal b "

    \(f(x)=16x^2-40x+25\)

here a = 16 , b = -40 and c = 25

We need to divide into 40x  in two parts

40x = 20x + 20x

The product of the terms is \(16\times25=400\)

Now we can rewrite 40x as 20x + 20x

Putting in equation (1) , we get

      \(16x^2-(20+20)x+25=0\\\\(16x^2-20x)-(20x-25)=0\\\\4x(4x-5)-5(4x-5)=0\\\\(4x-5)(4x-5)=0\)

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Answer:

volume = 4/3 × pi × r^3

Step-by-step explanation:

Answer:

Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume.

Circumference   =   2 • π • radius   =   π • diameter

Circle Area   =       π • r²     =     ¼ • π • d²

The circumference of a circle is directly proportional to its radius. The ratio between a circle's circumference and its diameter is pi, a constant that equals approximately 3.142. The circle's diameter, in turn equals twice the radius. A regular solid that has a circle as a face is called a cylinder. Like all geometric prisms, a cylinder's volume is the product of its cross-sectional area and its length. The cross-sectional area is the area of its circle, and you can calculate it from the circle's radius. Multiply the circle's radius by 2 to calculate its diameter. For instance, if the radius equals 6 inches, compute as follows to determine the diameter: 6 x 2 = 12 inches. Multiply the diameter by pi to get the circle's circumference: 12 x 3.142 = approximately 37.7 inches. Find the square of the radius: 6 x 6 = 36 square inches. Multiply the answer determined in Step 3 by pi to get the circle's area: 36 x pi = 113 square inches. Multiply the circle's area by the cylinder's length to obtain the volume. If the length is, for instance, 10 inches, then compute as follows: 113 x 10 = 1,130 cubic inches.

Answer:

\(x=\frac{-5+\sqrt{33} }{2}\)

\(x=\frac{-5-\sqrt{33} }{2}\)

Step-by-step explanation:

Using the quadratic formula in which a=1, b=5 and c=-2

\(x_1=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\x_2=\frac{-b-\sqrt{b^{2}-4ac } }{2a}\\x_1=\frac{-5+\sqrt{5^{2}-4(1)(-2) } }{2(1)}\\x_1=\frac{-5+\sqrt{33} }{21}\\x_2=\frac{-5-\sqrt{25+8 } }{2}\\x_2=\frac{-5-\sqrt{33} }{2}\)

Answer:

I do not the answer to this question

The minimum value and median are used in the five-number summary.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

Given:

A five-number summary.

That means minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), and maximum value.

From the given choices:

The minimum value and median are the required measures.

Therefore, the minimum value and median are the required measures.

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Answer:

It would be B: $39.00!

Step-by-step explanation:

Sry can't explain now.

But the answer is correct.

$39.00

A differential equation is a mathematical equation that relates a function to its derivatives. It involves the unknown function and one or more of its derivative. The solution to the differential equation -

xy' − 2y = x^2, x > 0

is y = (1/4)x^3 + C/x.

To solve the differential equation, we will use the method of integrating factors.

The differential equation is: xy' - 2y = x^2

We can rearrange it in the standard form: y' - (2/x)y = x

The integrating factor (IF) is defined as e^∫(2/x) dx. Integrating 2/x with respect to x gives us 2ln|x|.

Therefore, the integrating factor is IF = e^(2ln|x|) = e^(ln(x^2)) = x^2.

Now, multiply the entire equation by the integrating factor x^2:

x^2(y' - (2/x)y) = x^2(x)

x^2y' - 2xy = x^3

Next, we recognize that the left-hand side is the derivative of (xy) with respect to x. Applying this, we get:

d/dx(xy) = x^3

Integrating both sides with respect to x:

∫d(xy) = ∫x^3 dx

xy = (1/4)x^4 + C

Finally, divide both sides by x:

y = (1/4)x^3 + C/x

where C is the constant of integration.

So, the solution to the given differential equation is y = (1/4)x^3 + C/x.

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Answer:

-56

Step-by-step explanation:

Equation: (4 * +1) (2 * -7)

Simplify: (4 * 1)(2 * - 7)

Multiply: (4)(-14)

Answer: -56

I hope this helps, have a nice day :D

The number of equilibrium points for the given nonlinear system is 3.

To find the equilibrium points, we need to set both equations to zero and solve for x and y:

1. x′ = y² − xy = 0
2. y′ = x³y² − x = 0

First, let's look at equation 2. We can factor x out:

x(y²x² - 1) = 0

There are two possibilities:

a. x = 0: Substitute x = 0 in equation 1:

y² - 0 = y² = 0 => y = 0

So, we have one equilibrium point (0, 0).

b. y²x² - 1 = 0: Replacing this in equation 1:

y² - (y²x² - 1)y = 0

Factor out y:

y(y²(1 - x²) - 1) = 0

There are two more possibilities:

i. y = 0: We already considered this case (0, 0).

ii. y²(1 - x²) - 1 = 0: This equation gives us two equilibrium points: (-1, 1) and (1, 1).

Thus, the system has a total of 3 equilibrium points: (0, 0), (-1, 1), and (1, 1).

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Answer:

\(21.668125\) \(or\) \(21\) \(Dollars\) \(and\) \(66\) \(Cents\)

Step-by-step explanation:

\(--------------------------------------------\)

\(9.25\%\) \(of\) \(234.25\) = \(21.668125\)

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

Answer:

\(\frac{6}{5}\)

Step-by-step explanation:

1.Turn the 9 into a fraction

\(\frac{2}{15} *\frac{9}{1}\)

2.factor the bigger numbers.

\(\frac{2}{3*5} *\frac{3*3}{1}\)

3.Cancel out the common factor(3)

\(\frac{2}{5} * \frac{3}{1}\)

4.multiply across

\(\frac{2}{5} *\frac{3}{1} =\frac{6}{5}\)

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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The answer is not one of the options listed. The closest option is (a) 9 * 8 * 7 * 5, but this does not take into account the requirement that the last digit must be odd.

To solve this problem, we can use the multiplication principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things together.

First, we need to choose the last digit of the PIN to be odd. There are 5 odd digits to choose from (1, 3, 5, 7, and 9).

Next, we need to choose the first digit of the PIN. Since it cannot be the same as the last digit, there are only 9 choices left (since 0 is allowed as the first digit).

For the second digit, we can choose from 8 digits (we can't choose the first digit or the last digit, which leaves 8 choices).

For the third digit, we can choose from 7 digits (we can't choose the first digit, the second digit, or the last digit, which leaves 7 choices).

Therefore, the total number of choices for the PIN is:

5 * 9 * 8 * 7 = 2,520

So the answer is not one of the options listed. The closest option is (a) 9 * 8 * 7 * 5, but this does not take into account the requirement that the last digit must be odd.

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Answer: 4w - 5 is in simplified form.

Step-by-step explanation:

The other expressions have like terms that can be combined.

The statement that is true is "all squares are rhombi." A quadrilateral is a four-sided polygon.

A rectangle is a quadrilateral with four right angles, but not all quadrilaterals have to be rectangles. Therefore, the statement "All quadrilaterals are rectangles" is false.

A rectangle is also a parallelogram with all right angles. A square is a special type of rectangle where all sides are congruent. However, not all rectangles have congruent sides, so the statement "All rectangles are squares" is false.

A rhombus is a quadrilateral with all sides congruent. A rectangle is a quadrilateral with two pairs of parallel sides and all right angles. While some rhombi may also be rectangles if their angles measure 90 degrees, not all rhombi are rectangles. Therefore, the statement "all rhombi are rectangles" is false.

On the other hand, a square is a special type of rectangle where all sides are congruent and all angles measure 90 degrees. Since a rhombus is a quadrilateral with all sides congruent, a square can also be classified as a rhombus. Hence, the statement "all squares are rhombi" is true.

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The type of distribution that she might use will be Poisson Distribution

We are Given that average = 24.7

Poisson Distribution, the number of occurrences in various types of defined intervals, including distance, area, or volume, can also be calculated using the Poisson distribution.

A call center gets 180 calls on average each hour, every hour of the day due to the calls being separate, the probability that you will receive the next one is unaffected by the one you just received.

To compute the probability of receiving at least 10 e-mails on such a day, the distribution that best suits will be the Poisson distribution.

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Answer:

30

Step-by-step explanation:

use calculator LOL

360 divided by 12 is 30.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Dividend=360

Divisor=12

Now

=360/12

=30

Therefore, by algebra answer will be 30.

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The probability that a randomly selected person from the group will have a systolic blood pressure below 112 is 0.0548.

To find the probability that a randomly selected person from the group will have a systolic blood pressure below 112, we need to standardize the variable using the z-score formula:

z = (x - μ) /σ

where x is the value, we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.

For this problem, we have:

z = (112 - 120) / 5 = -1.6

Now, we need to find the probability that Z (the standardized variable) is less than -1.6. We can do this by using a standard normal distribution table.

Using a standard normal distribution table, we find that the probability of Z being less than -1.6 is approximately 0.0548.

Therefore, the probability that a randomly selected person from the group will have a systolic blood pressure below 112 is approximately 0.0548 or 5.48%.

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Answer:

m∠=6, ,m∠=+20,m∠=40+3

the larger the angle, the larger the side

Answer:

No the solution is 2,12

I think

The cone has a volume of (D) 288in3.

To find the volume:

Given:

Formula:

The Pythagorean theorem is used to calculate height.

The volume of the cone:

Therefore, the volume of the cone is (D) 288in³.

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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?

A. 32

B. 96

C. 128

D. 288

E. 384

Hypothesis testing provides a systematic approach to examine data and draw conclusions about the population. By following this process, we can gain insights into predictability by evaluating the evidence against the null hypothesis and making informed statistical inferences.

To obtain a sense of predictability, Kelly suggests that we engage in hypothesis testing.

Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on sample data. It involves formulating a null hypothesis and an alternative hypothesis, collecting data, and conducting statistical tests to evaluate the evidence against the null hypothesis.

Kelly's suggestion aligns with the idea that hypothesis testing can help us understand and predict outcomes by providing a structured framework for analyzing data and making statistical inferences. Through hypothesis testing, we can assess the significance of relationships, differences, or effects in various fields of study.

Here's a brief overview of the steps involved in hypothesis testing:

Formulate the null hypothesis (H0) and the alternative hypothesis (Ha):

The null hypothesis represents the assumption of no significant difference or relationship, while the alternative hypothesis states the opposite.

Collect and analyze the data:

Gather relevant data through observation, experimentation, or sampling. Perform appropriate statistical analysis to summarize the data and calculate relevant test statistics.

Choose a significance level (α):

The significance level, denoted as α, determines the threshold for rejecting the null hypothesis. It represents the probability of rejecting the null hypothesis when it is actually true.

Calculate the test statistic:

Depending on the nature of the hypothesis and the data, select an appropriate statistical test and calculate the corresponding test statistic.

Determine the critical region and p-value:

The critical region is the range of values for the test statistic that leads to the rejection of the null hypothesis. The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.

Make a decision:

Compare the calculated test statistic with the critical value or p-value. If the test statistic falls within the critical region or the p-value is smaller than the significance level, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Draw conclusions:

Based on the results of the hypothesis test, interpret the findings in the context of the research question and the data. Provide insights into the relationship or effect being tested and assess the predictability or significance of the findings.

In summary, hypothesis testing provides a systematic approach to examine data and draw conclusions about the population. By following this process, we can gain insights into predictability by evaluating the evidence against the null hypothesis and making informed statistical inferences.

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Answer:

£ 35

Step-by-step explanation:

Ratio = 6 : 1

Gordon's share = 6x

Malachy's share = x

6x - x = 25

5x = 25

x = 25/5

x = 5

Gordon's share = 6x = 6*5 = 30

Malachy's share = x = 5

Total money they get = 30 + 5 = £35

Given:

Two triangles congruent by ASA.

To find:

The the measures of x, y, angle QPR and angle QRP.

Solution:

The triangles PQR and PSR are congruent by ASA. So,

\(\angle QPR\cong \angle SPR\)

\(PR\cong PR\)

\(\angle QRP\cong \angle SRP\)

Now,

\(m\angle QPR=m\angle SPR\)

\(2x+1=x+18\)

\(2x-x=18-1\)

\(x=17\)

And,

\(\angle QRP= \angle SRP\)

\(8y-4=4y+28\)

\(8y-4y=4+28\)

\(4y=32\)

Divide both sides by 4.

\(y=8\)

The measure of angle QPR is:

\(m\angle QPR=(2x+1)^\circ\)

\(m\angle QPR=(2(17)+1)^\circ\)

\(m\angle QPR=(35+1)^\circ\)

\(m\angle QPR=36^\circ\)

And,

\(m\angle QRP=(8y-4)^\circ\)

\(m\angle QRP=(8(8)-4)^\circ\)

\(m\angle QRP=(64-4)^\circ\)

\(m\angle QRP=60^\circ\)

Therefore, the required values are \(x=17, y=8, m\angle QPR=36^\circ ,m\angle QRP=60^\circ\).

Multiply out the things in the brackets.

3+7(x+5)=2x+16

3+7x+35=2x+16

Bring the x's over to one side and the numbers to the other side.

7x-2x=16-35-3

5x= -22

Answer:

if a= 1 and b=2 c=3 then do a4 + b4 + c4

Step-by-step explanation:

12 total

4+3=7

12-7=5

5km left

Answer:

$260

Step-by-step explanation:

20% is equal to decimal form 0.2 or fraction form 1/5

1/5 of 800 = 1/5 * 800 = 160

He earns 100$ everyday even if he made sales worth $0.

100 + 160 = 260