Please help. Will mark as Brainliest. ​

To show that w = u × v and v = w × u, we need to demonstrate that the cross product of vectors u and v yields the same result as the cross product of vectors w and u.

Given that u = v × w, let's calculate the cross product of w and u:

w × u = (u × v) × u

Since the cross product is not associative, we need to use the vector triple product identity:

w × u = u × (v × u) - (u · u) v

Since u is orthogonal to v, the dot product (u · v) is zero. Therefore, we can simplify the equation:

w × u = u × (v × u)

Next, let's calculate the cross product of v and u:

v × u = (u × v) × v

Using the vector triple product identity:

v × u = v × (u × v) + (v · v) u

Again, since u is orthogonal to v, the dot product (v · v) is zero:

v × u = v × (u × v)

Thus, we have shown that w = u × v and v = w × u, indicating that the cross products are equivalent in both directions.

In summary, when u, v, and w are orthogonal unit vectors, the cross product of u and v yields the same result as the cross product of w and u, as well as the cross product of v and w.

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Answer: x=5, y=7

Step-by-step explanation:

Since ΔEFG and ΔHIJ are congruent, we can set the corresponding sides equal to each other.

y+14=3y                               [subtract both sides by y]

14=2y                                   [divide both sides by 2]

y=7

------------------------------------------------------------------------------------

10x=x+45                            [subtract both sides by x]

9x=45                                 [divide both sides by 9]

x=5

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

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Answer: X=19

Step-by-step explanation:

Add up everything and set it to 180 degrees so (5x+4)+(x-2)+(3x+7)=180

next 9x+9=180

then 9x=171

x=19

If you want to check by pluggin in value for x for all angles and it should equal 180 added up

Angle POS= 99

Angle SOR= 17

Angle ROQ= 64

99+17+64=180 degrees

Answer:

i have made it in above picture

hope it helps

So the exact length of the intercepted arc is 9π.

When a circle is divided into 360 equal parts, each part is called a degree. A central angle is an angle whose vertex is at the center of the circle, and whose sides intersect the circle at two points, thereby cutting off an arc on the circle. The length of the intercepted arc is proportional to the measure of the central angle in radians.

The length of an arc intercepted by a central angle is given by the formula:

length of arc = radius × central angle in radians

Here, the radius is given as r = 12, and the central angle is given as 3π/4. Therefore, the length of the intercepted arc is:

length of arc = 12 × (3π/4) = 9π

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Answer:

3:2

Step-by-step explanation:

Answer:

666666666

Step-by-step explanation:

Given the formula

This is the formula to obtain the volume of a square pyramid, not a square prism; we will solve the question using the formula above, nonetheless.

Solve for h as shown below

The answer is h=3V/s^2.

Set V=60cm^3, and s=6cm; then,

Therefore, the answer is h=5cm.

In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.

It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.

These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.

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Answer:

it is the second one(that what I learned in school)

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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The reward of 600 points will be earned by spending the amount of $300.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, Omar earns 800 reward points for spending 300 dollars.

The amount of money spent to earn 600 reward points will be calculated as,

800 reward points = $300 spending

1 reward point = $300 / 800 spending

600 reward point = ($300 x 600) / 800

600 reward points = $225

Therefore, the reward of 600 points will be earned by spending the amount of $300.

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Answer:

g(1) = -3

Step-by-step explanation:

g(x) = 4x-7

Let x=1

g(1) = 4*1 -7

     = 4 -7

     = -3

Answer:

-3

Step-by-step explanation:

To prove that a matrix A with n linearly independent eigenvectors also has n linearly independent eigenvectors, we need to use the fact that eigenvectors corresponding to distinct eigenvalues are linearly independent.

Let λ1, λ2, ..., λn be the n distinct eigenvalues of A with corresponding eigenvectors v1, v2, ..., vn, respectively. Since these eigenvectors are linearly independent, we know that any linear combination of them that equals the zero vector must have all coefficients equal to zero.

Suppose now that there exists a linear combination of these eigenvectors that equals the zero vector, say c1v1 + c2v2 + ... + cnvn = 0, where not all ci are zero. Without loss of generality, assume that c1 is nonzero. Multiplying both sides of this equation by A, we obtain

c1λ1v1 + c2λ2v2 + ... + cnλnvn = 0.

Since λ1, λ2, ..., λn are distinct, we know that λ1 cannot be equal to λ2, λ3, ..., λn. Therefore, we can divide both sides of the above equation by λ1 and obtain

c1v1 + (c2λ2/λ1)v2 + ... + (cnλn/λ1)vn = 0.

This equation shows that we have a nontrivial linear combination of the eigenvectors that equals the zero vector, contradicting the assumption that they are linearly independent. Therefore, our original assumption must be false, and we conclude that A has n linearly independent eigenvectors.

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A 95% confidence interval compared to a 90% interval, tends to result in a wider confidence interval because of a higher level of confidence requires a larger interval to account for the increased certainty.

Based on the given information, there seems to be some inconsistency in the provided data. The number of respondents is mentioned as 2000 in one part and 1500 in another part. To provide an accurate analysis, it's important to have consistent and accurate data.

However, I can still explain the concept of confidence intervals and their widths based on general understanding.

A confidence interval is a range of values calculated from sample data that is likely to contain the true population parameter with a certain level of confidence. The width of a confidence interval depends on two main factors: the sample size and the desired level of confidence.

In general, a larger sample size tends to result in a narrower confidence interval. This is because larger sample sizes provide more precise estimates of the population parameter, reducing the uncertainty and thus narrowing the interval.

Without the specific sample data and the stated confidence levels, it is difficult to determine which confidence interval (specified by the given percentages) would be wider or why. Additionally, the inconsistency in the provided information further hinders a specific analysis.

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If 13/15 was building then that means 2/15 was land( 1-13/15 = 2/15)

Multiply the total cost by 2/15

600 million x 2/15 = 80 million

the land cost 80 million

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Step-by-step explanation:

can we become friends???

Answer:

6.17

Step-by-step explanation:

add the pepsi wich is 2.19 then do 1.99 x 2 wich would be 3.98 then add them all together

Answer:

5/6

Step-by-step explanation:

83 1/3% =

= (83 + 1/3)%      <------- the mixed numeral 83 1/3 is the same as 83 + 1/3

= (249/3 + 1/3)%    <---- to add 83 + 1/3, use the common denominator 3

= 250/3 %      <---- the sum of 83 and 1/3 is 250/3, but this is still percent

= (250/3) / 100    <---- to change percent to decimal, divide percent by 100

= 250/300    <---- now we need to reduce this fraction

= 25/30    <---- divide numerator and denominator by 10

= 5/6    <---- divide numerator and denominator by 5

Answer:

Step-by-step explanation:

This is a logical question that can be d=solved thus;

To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.

1. Using simple interest formula of ( P X R X T)/ 100

Since p  = 1500, r  = 2.5%,  T = 3

1500 x 2.5% x 3  / 100  =  1500 x 0.025 x 3 / 100

112.5 / 100 = 1.125

to find amount  = 1.125 + 1500 = 1501.25 for the three 3years.

2. Using compound interest formula of ( P ( 1 + r/n)∧nt

1 + (2%/3) ∧3(3)

1500( 0.02/3) ∧ 9

1500  x 0.006 ∧9

1500 x 2.60 = 3900

A = 3900 + 1500 = 5400

SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS

Given the data from the question, the best account to use is:

A high interest savings account, with 2.5% simple interest annually (Option 1)

I = PRT / 100

A = I + P

Where

A = P(1 + r/n)ⁿᵗ

Where

I = PRT / 100

I = (1500 × 2.5 × 3) / 100

I = $ 112.5

Thus

A = I + P

A = 112.5 + 1500

A = $ 1612.5

A = P(1 + r/n)ⁿᵗ

Since n = 1,

A = P(1 + r)ᵗ

A = 1500(1 + 0.02)³

A = $ 1591.8

SUMMARY

The amount at the end of 3 years using:

Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)

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The area of the park in square yards is: 79901 square yards

We are given that the two adjacent sides of the triangle formed will have the lengths as:

a = 503 ft

b = 516 ft

C = 38°.

Using law of cosines, we have:

c = √(503² + 516² - (2 * 503 * 516 * cos 38))

c = 332 yards

Area of a triangle with three sides given is:

A = √(s(s - a)(s - b)(s - c)

where:

s = (a + b + c)/2

s = (503 + 516 + 332)/2

s = 675.5 yards

A = √(675.5(675.5 - 503)(675.5 - 516)(675.5 - 332))

A = 79901 square yards

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The ordered pair (1, 2) is a solution to the system of inequalities

x + y > 2 and

3x + 2y ≤ 6.

To find an ordered pair that is a solution to the system of inequalities:

Start with the first inequality:

x + y > 2.

Choose a value for x and y that satisfies this inequality. For example, let's choose

x = 1 and

y = 2.

Substituting these values into the inequality:

1 + 2 > 2, which is true.

Now, let's move to the second inequality:

3x + 2y ≤ 6.

Substitute the same values, x = 1 and

y = 2, into this inequality:

3(1) + 2(2) ≤ 6.

Simplifying, we have:

3 + 4 ≤ 6, which is true.

Therefore, the ordered pair (1, 2) is a solution to the given system of inequalities.

Hence the ordered pair (1, 2) is a solution to the system of inequalities

x + y > 2 and 3x + 2y ≤ 6.

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We can construct a regression tree using the given data, we can use the rpart() function in R.

the specific instructions provided by the software or tool is used, as the steps may vary slightly depending on the platform. To construct a regression tree using the given data, follow these steps:

1. Open the data file that contains the predictor variables "XT" and "AG" and the numerical target variable "Y".

2. Check if the data is properly formatted and contains the necessary information for the regression tree.

3. If the data is in the correct format, proceed to build the regression tree.

4. Click on the provided link to access the software or tool that will help you create the regression tree.

5. Once you have access to the software, import the data file into the tool.

6. Specify the predictor variables ("XT" and "AG") and the target variable ("Y") for the regression tree.

7. Configure any additional settings or parameters as needed for your analysis.

8. Run the regression tree algorithm on the data.

9. Review the resulting regression tree, which will display the relationships between the predictor variables and the target variable.

10. Analyze the tree structure and interpret the findings to understand the impact of the predictor variables on the target variable.

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Answer:

B

-12

Step-by-step explanation:

(-4)3= (-4)+(-4)+(-4)

= - 4-4-4

=-12

Answer:

B -12

Step-by-step explanation:

(-4)3 is just -4 times 3 which is -12.

4x3=12 -4x3=-12

because only one number is negative the answer becomes negative.

if neither number was negative the answer would be positive.

Based on the information provided, I would assume that the nutritionist said Morgan had eaten as much McDonald's in 30 days as a nutritionist would say you should eat in several years, perhaps 5-10 years.

The nutritionist indicated that Morgan consumed an excessive amount of McDonald's food in just 30 days.

This amount is equivalent to what a nutritionist would recommend eating over a significantly longer period, possibly several years.

The key takeaway is to maintain a balanced diet and follow the guidance of nutritionists to ensure a healthy lifestyle.

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The nutritionist said that Morgan had eaten as much McDonald's in 30 days as a nutritionist would say you should eat in several years

The nutritionist said that Morgan had consumed as much McDonald's food in 30 days as a nutritionist would recommend eating in several years. This comparison emphasizes the excessive and unhealthy nature of Morgan's McDonald's consumption.

While the specific number of years can vary depending on individual dietary recommendations, it is typically advised to consume fast food and processed foods in moderation or as occasional treats. These foods are often high in unhealthy fats, sodium, and added sugars, which can contribute to various health issues, including obesity, cardiovascular diseases, and diabetes.

The nutritionist's statement serves as a reminder of the importance of a balanced and nutritious diet consisting of whole foods, fruits, vegetables, lean proteins, and whole grains for maintaining optimal health and well-being.

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Answer:

40 tickets

Step-by-step explanation:

Given that:

Total tickets sold = 200

Sue's chances of winning = 20% = 0.2

Number of tickets bought by Sue :

P(winning) = 20%

P(winning) = required outcome / Total possible outcomes

Required outcome = number of tickets bought by Sue

Total possible outcomes = total number of tickets sold

0.2 = x / 200

x = 0.2 * 200

x = 40

Answer:

The answer you are looking for is as x increases, y decreases then increases

Step-by-step explanation:

We know that

• 2/5 are strawberries.

• 1/4 of the strawberries are chocolate covered.

We have to find 1/4 of 2/5, let's multiply these fractions.

Given Jessica and Laura's expenditure on shirts and pants, the equation to solve for the price of each shirts and pants is:

3s + 4p = 90

4s + 2p = 70

Let

Cost of each shirts = s

Cost of each pants = p

Jessica:

3s + 4p = 90 (1)

Laura:

4s + 2p = 70 (2)

Multiply (2) by 2

8s + 4p = 140 (3)

8s + 4p = 140 (3)3s + 4p = 90 (1)

Subtract (1) from (3) to eliminate p

8s - 3s = 140 - 90

5s = 50

s = 50/5

s = $10

substitute s = 10 into (1)

3s + 4p = 90 (1)

3(10) + 4p = 90

30 + 4p = 90

4p = 90 - 30

4p = 60

p = 60/4

p = $15

Therefore, the cost of each shirts is $10 and the cost of each pants is $15

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