Find the height of a cuboid if it's length is 15cm, it's breath is 12cm and it's total surface are is 900cm

Answer:

Discount =40\%

Selling price of headphone =\$36

Solution --

we know that,

MP=SP * 100/(100-D\%)

putting values now we get,

MP = 36 * 100 / 60=60$

so, initial price of Headphone was =$60

The correlation between variables x and y is 0.50 . The true option is option (c) .

that's the regression coefficient is positive for given bivariata.

Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The

sample correlation coefficient r quantifies the strength of the relationship.

Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.

Here:

Pearson's correlation coefficient is denoted by "r" and is

r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)

We have given that correlation between x and y is 0.50.

cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2

=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)

Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.

Symbolically it can be expressed as:

bₓᵧ= r σ ₓ /σ ᵧ

where x and y are correlated

σ ₓ --> standard deviation of X

σᵧ ---> standard deviation of y

We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.

Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.

Hence, Regression cofficient is positive.

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The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

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There is a lower limit but no upper limit for a random variable that follows the exponential probability distribution.

We know that, an exponential distribution is a type of continuous distributions.

This probability distribution times the occurrence of events.

In exponential probability distribution, events happen continuously and independently at a constant average rate.

The continuous random variable, say X is said to have an exponential distribution, if it has the following probability density function:

\(f_X(x)=\left \{ {{\lambda e^{-\lambda x~~~x > 0}} \atop {0~~~~~~~x\leq 0}} \right.\)

The exponential distribution is memoryless.

We know that, for exponential the lower limit is 0, but the upper limit is infinity, meaning there is no upper limit.

Therefore, There is a lower limit but no upper limit for a random variable that follows the exponential probability distribution.

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Answer:

Fraction: 3/5
Decimal: 0.006

Step-by-step explanation:

The perimeter of the rectangle created in this problem is given as follows:

20 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The points for the rectangle in this problem are given as follows:

(-1, 3), (3,3), (-1, -3) and (3,-3).

Hence the side lengths of the rectangle are given as follows:

Hence the perimeter of the rectangle is given as follows:

P = 2(4 + 6)

P = 20 units.

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The equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) is 27.6% and its worth (rounded to the nearest ten dollars) after 1 year is $138,000.

Devaluation rate:

Basically, the devaluation rate refers the deliberate downward adjustment of the value of a country's money relative to another currency, group of currencies, or currency standard.

Given,

In a recent stock market downturn, the value of a $5,000 stock is decreasing at 2. 3% per month. This situation can be modeled by the equation A(t) = 5,000(0. 977)^12t, where A(t) is the final amount and t is time in years.

Here we need to find the equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest ten dollars) after 1 year.

While we looking into the given question,

We have identified that, the decreasing percent per month is 2.3%.

So, for 1 year, the decreasing percent is,

=> 12 x 2.3 = 27.6%

Similarly, devaluation rate after one is year calculated by applying the value of t as 1, in the given equation, then we get,

=> A(1) = 5,000(0.977)¹²ˣ¹

=> A(1) = 5,000(0.977)¹²

=> A(1) = 5000 x 276

=> A(1) = 138000

Therefore, the annual devaluation rate is 138,000.

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the original number Juan started with was 6.

Let "x" represent the original number. Juan first adds 2 to the original number, which can be expressed as (x + 2). He then multiplies this by 2, resulting in 2(x + 2). Next, he subtracts 2 from this product: 2(x + 2) - 2. Finally, he divides the resulting number by 2, giving us the equation [(2(x + 2) - 2) / 2] = 7.
Now, let's solve for the original number, x:
1. Simplify the equation by distributing the 2: [2x + 4 - 2] / 2 = 7
2. Combine the constants: (2x + 2) / 2 = 7
3. Multiply both sides by 2 to remove the denominator: 2x + 2 = 14
4. Subtract 2 from both sides: 2x = 12
5. Divide both sides by 2: x = 6

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Answer:

360

Step-by-step explanation:

50x4=200

200x0.9=180

180x2=360

Answer:

5x+3y-1475=0

Step-by-step explanation:

if this helps please mark brainliest <3

Answer:

288

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

To find a percent you just need to divide

48 ÷ 600 is 0.08

Next you move the decimal over by too places to get 8%

The x-intercept of the line is: -4.

The y-intercept is: -8

The y-intercept of a line is the point where the line cuts across the y-axis (vertical axis), which is the value of y when x is zero.

The x-intercept of a line is the point where the line cuts across the x-axis (horizontal axis), which is the value of y when x is zero.

Given that a line passes through (-4, 0) and (0, -8), it means that:

The line cuts the y-axis at y = -8

The line cuts the x-axis at x = -4.

Therefore, we can state that the y-intercept of the line is -8, while the x-intercept of the line is -4.

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Answer:

area of the floor = 540*840.

=453600 cm sq.

area of the marbal piece = 1/2 * 40* 30 = 600 cm sq.

now,

no. of marble piece reqd. = 453600 / 600 = 756 marbal piece.

hope it helps u.

Answer:

c

Step-by-step explanation:

they get a flat out $500 either way and a steady $50 for every hour which will increase their pay by 50 each hour.

Answer:

n = 3 x m

Step-by-step explanation:

n will represent the total movies he will watch in m month according to your plan of watching three movies each month.

It took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

Let L(t) be the amount of undeveloped land in acres at time t, where t is measured in years since 2002. Then, we can write:

L(t) = 30 * (7/8)^t

We know that the amount of undeveloped land we are interested in is approximately 15.39 acres. Therefore, we can set up the following equation:

15.39 = 30 * (7/8)^t

To solve for t, we can first divide both sides by 30:

0.513 = (7/8)^t

Next, we can take the natural logarithm of both sides:

ln(0.513) = ln[(7/8)^t]

ln(0.513) = t * ln(7/8)

t = ln(0.513) / ln(7/8)

t ≈ 5.3

Therefore, it took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

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a. The population of interest in this case is the general public of the United States who have knowledge about the criminal trial and its verdict. b. It is likely that the proportion of people unhappy with the verdict in the sample is similar to the proportion of individuals unhappy with the verdict in the population.

a. The population of interest in this case is the general public of the United States who have knowledge about the criminal trial and its verdict.

b. It is likely that the proportion of people unhappy with the verdict in the sample is similar to the proportion of individuals unhappy with the verdict in the population. This is because the television news program invited viewers to go to their website and indicate their opinion, which means that only a certain segment of the population who watched that particular news program and had access to the internet were able to participate in the poll. Additionally, people who feel strongly about the verdict may be more likely to participate in the poll, leading to potential bias in the sample. Therefore, it is important to acknowledge that the poll results may not be entirely representative of the entire population and should be interpreted with caution. In order to obtain a more accurate estimate of the proportion of people unhappy with the verdict in the population, a larger, more diverse and random sample should be used.

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Answer:

7 1/2

Step-by-step explanation:

Answer:

7.5, 0.42857142857, 0.41666666666, .4, .375

Step-by-step explanation:

3/.4

3/7

3/7.2

3/7.5

3/8

The relationship will be a solid line .

How to find the relationship between the given amounts?

Given:

The amount of one lunch =$4

The amount of the school lunch card=$100

Let, the amount remaining on the card= b

Let the number of lunches to buy  = a

The equation is given by,

b = 100 - 4a

When 1 lunch is bought ,a= 1 ;

b= 100 - 4(1) = 96

When 2 lunches are bought ,a= 2;

b= 100 - 4 (2)= 92

When 3 lunches are bought ,a= 3;

b= 100 - 4 (3)= 88

When 4 lunches are bought ,a= 4;

b= 100 - 4 (4)= 84

Since ,the decrease is gradual and same, the relationship will be a solid line.

The complete question is:

What is the relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card. Is the relationship a solid line or a set on unconnected points?

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Answer:

b>1

Step-by-step explanation:

\(3(3b-4)> 8b-11\\9b-12> 8b-11\\9b-8b> -11+12\\b> -11+12\\b>1\)

Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

Step-by-step explanation:

6/√3×√3/√3=6√3\√3

because √3×√3=3 hope you are not confused pls follow

Answer:

2√3

Step-by-step explanation:

because yes

Answer:

Option C

Step-by-step explanation:

Given the following question:

Total cost is $725
15% Marcus makes in commission.

In order to find the answer, we have to find 15% of $725 and that number will be the total in commissions he earned that week.

\(\frac{15\times725}{100} =15\times725=10875\div100=108.75\)

Marcus makes "$108.75" or option C in commissions last week.

Hope this helps.

Answer:

its b

Step-by-step explanation:

hope this helps

Meg can get 1 and 3/4 servings of 1/2 jug from her 7/8 jug of orange juice.

Meg has a 7/8 jug of orange juice, and she wants to know how many 1/2 jug servings she can get from it. To solve this problem, we need to divide the total amount of orange juice by the amount of orange juice in each serving.

First, we need to convert the 7/8 jug to an equivalent fraction with a denominator of 2. To do this, we can multiply both the numerator and denominator of 7/8 by 2, which gives us 14/16.

Next, we can divide 14/16 by 1/2 to find out how many 1/2 jug servings Meg can get from the jug. To divide fractions, we invert the second fraction and multiply. So we have:

14/16 ÷ 1/2 = 14/16 x 2/1 = 28/16

Now, we need to simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 4. So we have:

28/16 = (28 ÷ 4) / (16 ÷ 4) = 7/4

Therefore, Meg can get 7/4 or 1 and 3/4 servings of 1/2 jug from her 7/8 jug of orange juice.

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Answer:

look at the explanation below

Step-by-step explanation:

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing the same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number

i hope this helps

Answer:

5

Step-by-step explanation:

double 5 is 10

10+3=13

13 multiplied by 4=52