The side of a triangle are in the ratio 2:3:4. triangle is 18cm. find its lenght

Answer:

ASA

Step-by-step explanation:

We can see that the triangle has at least one similar side and one similar angle. We can also see that the triangles meet at a point, so they must have the same angle at that point where they connect. So that leads us to our answer being ASA since they have two similar angles and one similar side. This is the answer that I think is correct just by looking at the image. I haven't take this class since last year, so this is simply from memory. Correct me if I am wrong!

Answer:

x = 55

Explanation:

In a parallelogram, the sum of each two consecutive angles is 180°.

In the given parallelogram ABCD, we can note that angles A and B are consecutive angles. This means that their summation is 180°

Therefore:

∠A + ∠B = 180

2x + 15 + x = 180

3x + 15 = 180

3x = 180 - 15

3x = 165

x = 165 / 3

x = 55

Now we can check:

angle A = 2(55) + 15 = 125°

angle B = 55°

angle A + angle B = 125 + 55 = 180°

Hope this helps :)

The values of p and q are 3 and 2.

Given:

The equation of the graph is y = pq^x where p and q are positive constants.

From the graph:

curve linear course points are:

(0,3) and (1,6)

substitute points in y = pq^x

3 = pq^0

3 = p*1

p = 3

y = pq^x

6 = pq^1

6 = p*q

6 = 3*q

divide by 3 on both sides

6/3 = 1

q = 2

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she worked 3 hours a week

Answer:

13 vertices. In geometry, the augmented hexagonal prism is one of the Johnson solids (J54). As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid (J1) to one of its equatorial faces. When two or three such pyramids are attached, the result may be a parabiaugmented hexagonal prism, a metabiaugmented hexagonal prism or a triaugmented hexagonal prism. Augmented hexagonal prism.

Type: Johnson J53 - J54 - J55

Faces: 2x2 triangles 1+2x2 squares 2 hexagons

Edges: 22

Vertices: 13

The $130,000 would be considered as Statistic.

In statistics, a population refers to the entire group of individuals or items of interest, while a sample is a subset of the population. A parameter is a numerical value that describes a characteristic of a population.

In this scenario, the survey results are based on a sample of 10,000 graduates out of a total population of 200,000 graduates. The average salary of $130,000 is calculated from the data collected within this sample. Since it is derived from the sample, it is considered a statistic.

A parameter would be used to describe the average salary of the entire population of 200,000 graduates if data were collected from all of them. However, in this case, the given information only pertains to the subset of the sample.

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The Gauss-Markov assumptions associated with the Classical Linear Regression Model (CLRM) are important for obtaining unbiased and efficient estimates of the regression coefficients.

a) These assumptions include linearity, strict exogeneity, no perfect multicollinearity, zero conditional mean, homoscedasticity, and no autocorrelation. Violations of these assumptions can lead to biased and inefficient parameter estimates, affecting the validity and reliability of the regression results. In addition, the Normality assumption is required for hypothesis testing, assuming that the error term follows a normal distribution.

b) To estimate the Cobb-Douglas production function Qt = BIL PR B2 B3, it is appropriate to take the natural logarithm of both sides of the equation to transform it into a linear equation. By doing so, the model becomes ln(Qt) = ln(B) + α ln(L) + β ln(PR) + γ ln(B2) + δ ln(B3), where ln represents the natural logarithm.

To test the hypothesis of constant returns to scale, the sum of the coefficients α, β, γ, and δ is examined. If α + β + γ + δ = 1, it indicates constant returns to scale in the production function. This hypothesis can be tested using a t-test to assess the significance of the sum of the coefficients. The null hypothesis is that α + β + γ + δ = 1, while the alternative hypothesis is that α + β + γ + δ ≠ 1. If the estimated sum significantly deviates from 1, it suggests that the production function does not exhibit constant returns to scale.

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In the equation\(`x = sin^-1(1/u)`,\) the letter x represents the angle while the letter u represents the value of the trigonometric function.

The inverse sine function is defined as the arc or angle whose sine is equivalent to the value of the input argument.

It's also known as the arcsine function. In trigonometry, it is commonly represented as \(sin^-1\) or arcsin.

In trigonometry, the sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse of a right-angled triangle.

It is often abbreviated as sin.

The sine of an angle x is denoted by

sin(x) = Opposite side / Hypotenuse.

For any angle x, the sine function returns a value between -1 and 1.

In summary, x represents the angle in the equation \(x = sin^-1(1/u)\)while u represents the value of the trigonometric function, which is equal to 1/sin(x).

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We can find the marginal densities as follows: f_X(x) = integral from 0 to 1 of f(x,y) dy = integral from 0 to 1 of (2/3)(x + y) dy

To find the value of C, we need to use the fact that the total probability over the region must be 1. That is,

integral from 0 to 1 of (integral from 0 to 1 of C(x + y) dy) dx = 1

We can simplify this integral as follows:

integral from 0 to 1 of (integral from 0 to 1 of C(x + y) dy) dx = integral from 0 to 1 of [Cx + C/2] dx

= (C/2)x^2 + Cx evaluated from 0 to 1 = (3C/2)

Setting this equal to 1 and solving for C, we get:

C = 2/3

To compute the covariance, we need to first find the means of X and Y:

E(X) = integral from 0 to 1 of (integral from 0 to 1 of x f(x,y) dy) dx = integral from 0 to 1 of [(x/2) + (1/4)] dx = 5/8

E(Y) = integral from 0 to 1 of (integral from 0 to 1 of y f(x,y) dx) dy = integral from 0 to 1 of [(y/2) + (1/4)] dy = 5/8

Now, we can use the definition of covariance to find Cov(X,Y):

Cov(X,Y) = E(XY) - E(X)E(Y)

To find E(XY), we need to compute the following integral:

E(XY) = integral from 0 to 1 of (integral from 0 to 1 of xy f(x,y) dy) dx = integral from 0 to 1 of [(x/2 + 1/4)y^2] from 0 to 1 dx

= integral from 0 to 1 of [(x/2 + 1/4)] dx = 7/24

Therefore, Cov(X,Y) = E(XY) - E(X)E(Y) = 7/24 - (5/8)(5/8) = -1/192

To compute the correlation, we need to first find the standard deviations of X and Y:

Var(X) = E(X^2) - [E(X)]^2

E(X^2) = integral from 0 to 1 of (integral from 0 to 1 of x^2 f(x,y) dy) dx = integral from 0 to 1 of [(x/3) + (1/6)] dx = 7/18

Var(X) = 7/18 - (5/8)^2 = 31/144

Similarly, we can find Var(Y) = 31/144

Now, we can use the definition of correlation to find p(X,Y):

p(X,Y) = Cov(X,Y) / [sqrt(Var(X)) sqrt(Var(Y))]

= (-1/192) / [sqrt(31/144) sqrt(31/144)]

= -1/31

Finally, to determine if X and Y are independent, we need to check if their joint distribution can be expressed as the product of their marginal distributions. That is, we need to check if:

f(x,y) = f_X(x) f_Y(y)

where f_X(x) and f_Y(y) are the marginal probability densities of X and Y, respectively.

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Here, I made a graph through MS Paint.

If the mean of a set of data is 4.11 and its standard deviation is 3.03. the z score for a value of 10.86 is: 2.23.

Using this formula to find the z-score

z-score  =  Value - Mean / Standard deviation

Where:

Value = 10.86

Mean = 4.11

Standard deviation = 3.03

Let plug in the formula

z-score  =  10. 86 - 4.11 / 3.03

z-score  =  6.75 /3.03

z-score = 2.227

z- score = 2.23

Therefore the z-score is 2.23.

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The average speed for the entire trip rounded to the nearest tenth is 17.5 mi/h.

Average speed is defined as the total distance divided by time. Average speed can be determined by this equation :

v = d/t

where v is average speed, d is distance and t is time.

From the question above, we know that :

the distance which Lisa traveled is the same so we can conclude that Lisa's average speed is

v = (v1 + v2) / 2

where v1 is average speed going to school and v2 is average speed on the return.

v1 = 15 mi/h

v2 = 20 mi/h

v = (v1 + v2)/2

v = (15 + 20)/2

v = 35 / 2

v = 17.5 mi/h

Hence, the average speed for the entire trip rounded to the nearest tenth is 17.5 mi/h

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To determine the number of loan applicants that fall within a credit score range, we can use the concept of the normal distribution and the given mean and standard deviation. Assuming a bell-shaped curve, we need to calculate the percentage of loan applicants within the given credit score range and then convert it to the actual number of applicants.

Given:
Mean credit score: 635
Standard deviation: 17
To find the number of loan applicants within a credit score range of 601 and 669, we need to calculate the percentage of applicants within this range.
First, we need to calculate the z-scores for the lower and upper bounds of the credit score range:
Z1 = (601 - 635) / 17
Z2 = (669 - 635) / 17
Next, we use a standard normal distribution table or calculator to find the corresponding probabilities:
P1 = P(Z ≤ Z1)
P2 = P(Z ≤ Z2)
To find the percentage of loan applicants within the credit score range, we subtract the lower probability from the higher probability:
Percentage = (P2 - P1) * 100
Finally, we can calculate the number of loan applicants within the range by multiplying the percentage with the total number of applicants:
Number of applicants = Percentage * 335 / 100
By applying these calculations, we can determine the approximate number of loan applicants that fall within the given credit score range.

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The percent of the regular price is 81.5%.

From the information, the shirt that normally costs $40 is on sale for 32.60.

The percent of the regular price that the sale price is will be gotten thus:

= Sale price / Regular price × 100

= 32.60 / 40 × 100

= 81.5%

The percentage is 81.5%.

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Answer:

147

Step-by-step explanation:

you just add both angles

Answer:

990

Step-by-step explanation:

M/J = 2/7

J = 3/4 L

L = M + 396

7M = 2J

J = 3.5M

3.5M = 3/4 L

L = 4/3(3.5M)

L = 14/3 M

14/3 M = M + 396

11/3 M = 396

M = 3/11 × 396

M = 108

L = M + 396

L = 108 + 396

L = 504

J = 3/4 L

J = 3/4 × 504

J = 378

M + L + J = 108 + 504 + 378 = 990

Comparison of Enrollments in Vocational and Theoretical Courses in India

States: Uttar Pradesh and Maharashtra

In Uttar Pradesh, there were more male enrollments in vocational courses than female enrollments in all years. The difference was more pronounced in the early years, but it has narrowed over time. In 2010, there were 2.5 times more male enrollments in vocational courses than female enrollments. By 2020, the ratio had decreased to 1.75.

In Maharashtra, the difference between male and female enrollments in vocational courses was smaller than in Uttar Pradesh. In 2010, there were 1.5 times more male enrollments in vocational courses than female enrollments. By 2020, the ratio had decreased to 1.25.

Age

In Uttar Pradesh, the majority of enrollments in vocational courses were from the 15-29 age group. In Maharashtra, the majority of enrollments in vocational courses were also from the 15-29 age group.

The data also shows that there are some differences in the enrollment patterns between the two states. In Uttar Pradesh, the majority of enrollments are from the 15-29 age group, and the most popular vocational courses are in the areas of IT, engineering, and healthcare. In Maharashtra, the majority of enrollments are also from the 15-29 age group, but the most popular vocational courses are in the areas of IT, hospitality, and manufacturing.

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Answer:

2:2:2

1:1:1

2 to 2 to 2

1 to 1 to 1

Step-by-step explanation:

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:56

Step-by-step explanation:

Answer:

Rosie is 10 years old

Step-by-step explanation:

A)

Rosie is x years old

Rosie's age (R) = x

R = x

Eva is 2 years older

Eva's age (E) = x + 2

E = x + 2

Jack is twice Rosie’s age

Jack's age (J) = 2x

J = 2x

B)

R + E + J = 42

x + (x + 2) + (2x) = 42

x + x + 2 + 2x = 42

4x + 2 = 42

4x = 42 - 2

4x = 40

\(x = \frac{40}{4} \\\\x = 10\)

Rosie is 10 years old

By using substitution method the values of x and y are, x = -1/7 and y = -32/7.

What is substitution method?

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Consider, the given equations

-8x = 5y + 24       ..(1)

-9y = 40 - 8x        ..(2)

From equation (1),

x = -(5y + 24)/8

x = -5/8y - 3            ..(3)

Plug value of x in equation (2),

-9y = 40 - 8(-5/8y - 3)

-9y = 40 + 5y + 24

-14y = 64

y = -64/14

y = -32/7

Plug y = -32/7 in equation (3)

x = -5/8(-32/7) - 3

x = -1/7

Hence, by using substitution method the values of x and y are, x = -1/7 and y = -32/7.

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sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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Consider the following matrix equation:

Applying the additive property, this is equation is equivalent to:

This is equivalent to the following linear system of equations:

Equation 1:

Equation 2:

Equation 3:

Equation 4:

From equation 1, we get:

From equation 2, we get:

From equation 3, we get:

From equation 4, we get:

we can conclude that the correct answer is:

and

Answer:

27,648

-110,592

442,368

Step-by-step explanation:

each term is multiplied by -4

The cost to hire a tent consists of a fixed cost of $17.50 and a variable cost of $2.40 per day.

Let's call the total cost of hiring a tent for 4 days as T4, and the total cost of hiring a tent for 7 days as T7.

The first equation is the cost for 4 days:

T4 = c + 4d

The second equation is the cost for 7 days:

T7 = c + 7d

We know the values of T4 and T7 from the problem statement:

T4 = $27.10 and T7 = $34.30

We can now use these two equations and their corresponding values to solve for c and d:

Substitute the value of T4 into the first equation:

$27.10 = c + 4d

Substitute the value of T7 into the second equation:

$34.30 = c + 7d

Now we have a system of two equations with two variables (c and d).

Subtract 4d from both sides of the first equation:

$27.10 - 4d = c

Subtract c from both sides of the second equation:

$34.30 - c = 7d

Now we can substitute the value from step 4 into step 5:

$34.30 - $27.10 + 4d = 7d

7d = $34.30 - $27.10 + 4d

3d = $7.20

d = $7.20 / 3 = $2.40

Now we have the value of d, we can substitute it back into the first equation to find the value of c:

$27.10 = c + 4d

$27.10 = c + 4($2.40)

$27.10 = c + $9.60

c = $27.10 - $9.60

c = $17.50

Therefore, c= $17.50 and d= $2.40

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There are 30240  different id cards can be made if there are five digits on a card and no digit can be used more than once.

a) If repetition is allowed, then there are 10 ways to choose each of 5 digits. Hence, by the multiplication rule, we obtain that the total number of possible different ID cards is:

10⋅10⋅10⋅10⋅10 = 10⁵= 100000.

b) If repeats are not allowed, there are 10 ways to choose the first number, 9 ways to choose the second number (because we chose 1 digit as the first number), and 9 ways to choose the third number. There are 8 ways, 7 ways, and 7 ways to choose the 4th number. 6 ways to select the digit to select and the 5th digit.

So according to the multiplication rule the answer is:

10 × 9× 8×7×6 = 30240.

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Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.

An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.

An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"

2x + y = 4

now, putting the values in the equation (6,-8)

2(6) + (-8) = 4

or, 12 - 8 = 4

or, 4 ≡ 4

This equation, point IS a solution to the system.

x + 3y = - 20

or, 6 + 3(-8) = -20

or, 6 - 24 = -20

or, - 18 ≠ - 20

So, for this equation the result is not identity.

Thus, option A is the correct answer.

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