The three right triangles are all similar. The ratios of the sides of the triangles are AB/BC = 3/4, BC/CD = 2/3, and AD/DC = 5/6.
a) All three of the right triangles are similar.
b) Triangle ABC: AB/BC = 3/4
Triangle BCD: BC/CD = 2/3
Triangle ADC: AD/DC = 5/6
a) All three of the right triangles are similar because they all have three sides and two angles that are equal.
b) To find the ratios of the sides of the triangles, we use the Pythagorean Theorem.
Triangle ABC: AB^2 + BC^2 = AC^2. Therefore, AB/BC = (3/4)^2/(5/4)^2 = 3/4.
Triangle BCD: BC^2 + CD^2 = BD^2. Therefore, BC/CD = (2/3)^2/(4/3)^2 =2/3.
Triangle ADC: AD^2 + DC^2 = AC^2. Therefore, AD/DC = (5/6)^2/(7/6)^2 = 5/6.
The three right triangles are all similar. The ratios of the sides of the triangles are AB/BC = 3/4, BC/CD = 2/3, and AD/DC = 5/6.
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What’s the difference between these two
A right triangle A B C. Angle A C B is a right angle. Angle B A C is unknown. Side A C is six units. Side B C is three units.
The picture explains it all. We use tangent rule to find out the measure of angle A.
The measure of angle unknown angle is 30°.
Use the concept of the triangle defined as:
A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
Given that,
Side AC = 6 units
Side BC = 3 units
Let ∠BAC = θ
Since we know that,
Sin θ = opposite/Hypotenuse
Sin θ = BC/AC
Put the values,
Sin θ = 3/6
Sin θ = 1/2
Since we know that,
sin(π/6) = 1/2
Therefore,
Sin θ = sin(π/6)
Take the inverse of sin on both sides we get,
θ = π/6 or 30°
Hence,
The measure of angle unknown angle is 30°.
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at a local veterinary office, 48% of dogs get their teeth cleaned, while 35% of cats get their teeth cleaned. let p hat subscript upper d and p hat subscript upper c be the sample proportions of dogs and cats at this veterinary office, respectively, who get their teeth cleaned. suppose 25 dogs and 32 cats from this veterinary office are selected at random to collect data on their teeth-cleaning history. which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of p hat subscript upper d baseline minus p hat subscript c ?
The difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.
The third option is correct.
What is the standard deviation?
Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.
Percentage of Dogs getting their teeth cleaned = 48% = pD
Percentage of Cats getting their teeth cleaned = 35% = pC
Number of Dogs selected = nD = 25
Number of Cats selected = nc = 32
As the sample sizes are large enough, we can apply Central Limit Theorem
According to Central Limit Theorem for proportions –
pD-hat ~ Normal(pD, {pD*(1-pD)}/nD)
Thus, pD-hat ~ Normal(0.48, 0.009984)
Similarly,
pC-hat ~ Normal(pC, {pC*(1-pC)}/nC)
Thus, pC-hat ~ Normal(0.35, 0.0071094)
Now if X ~ N(E(X), Var(X)) and Y ~ N(E(Y), Var(Y))
then X -Y ~ N(E(X)-E(Y), Var(X)-Var(Y)) (If X and Y are Independent)
Thus,
pD-hat - pC-hat ~ Normal(0.48-0.35, 0.009984 – 0.0071094)
pD-hat - pC-hat ~ Normal(0.13, 0.0028746)
Thus, Standard Deviation of pD-hat - pC-hat = (0.0028746^0.5) = 0.0536 that is 0.054 approximately
Hence, the difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.
Third Option is correct.
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Work out 194.55 divided by 1.5
Answer:129.7
Step-by-step explanation:
Literally just used a calculator but if you need explanation lmk
through: (-2, 3), slope = -1
Slope is y is -1x + 1.
Find slope?To enter data and find the equation's solution, we can utilize the equation's point-slope form.
use the point ( 2, 3) and the slope of 1.
m \s= \s− \s1
x \s1 \s= \s− \s2
y \s1 \s= \s3
In the point-slope formula,
y \s− \sy \s1 \s= \sm \s( \sx \s− \sx \s1 \s)
the values into the plug
y \s− \s3 \s= \s− \s1 \s( \sx \s− \s( \s− \s2 \s) \s)
symbol reduction
Distribute the 1 according to y 3 = 1 (x + 2).
Use additive inverse to find the y in the equation y = 3 = 1 x 2
y \s− \s3 \s+ \s3 \s= \s− \s1 \sx \s− \s2 \s+ \s3
simplify
y \s= \s− \s1 \sx \s+ \s1.
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1(x-3)^2-2/(x^2-9)+1/(x+3)^2
Answer:
Here is your answer. Hope this helps.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
2, 6, 10,..
Find the 41st term.
The given sequence appears to be an arithmetic sequence, as the common difference between consecutive terms is 4.
The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference and n is the nth term.
Given that the first term of the sequence is 2, the common difference is 4.
To find the 41st term of the sequence, we can use the formula:
a_41 = 2 + (41-1) * 4 = 2 + 40 * 4 = 2 + 160 = 162
Therefore, the 41st term of the sequence is 162.
a computer that normally cost 500 dolars was on sale for 200 dollars. what is the percent decrease. please show work for brainlist
Answer:
(100/500) *200 =40%
Step-by-step explanation:
Solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form M(x, y) dx + N(x, y) dy = 0, where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions y = vx and dy = x dv + v dx.
(x^3 + y^3) dx − xy^2 dy = 0
The solution to the differential equation (x^3 + y^3) dx − xy^2 dy = 0 is y/x^3 = Ce^(−(y/x)^3), where C is an arbitrary constant.
Substituting y = vx and dy = x dv + v dx, we get:
(x^3 + (vx)^3)dx − x(vx)^2(x dv + v dx) = 0
Simplifying and rearranging, we get:
x^2v dx + (x^3 + 3xv^2 − v^3x^2)dv = 0
Dividing both sides by x^2v and rearranging, we get:
dx/x + (1/v)dv + (3/xv - v^2)dv = 0
Integrating both sides, we get:
ln|x| + ln|v| + 3ln|v/x| − v^3 = C
Where C is an arbitrary constant. Simplifying, we get:
ln|vx/x^3| = C − v^3
Rearranging, we get:
vx/x^3 = Ce^(−v^3)
Finally, we can express this in terms of x and y as:
y/x^3 = Ce^(−(y/x)^3)
The solution to the differential equation (x^3 + y^3) dx − xy^2 dy = 0 is y/x^3 = Ce^(−(y/x)^3), where C is an arbitrary constant.
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(c) use the answers to parts (a) and (b) to estimate by how much the average monthly cell phone bill changed between 1990 and 2008. (round your answer to two decimal places.)
The area above x axis is 12.6 sq units while the area under the y-axis is 42.443 sq units. The change in the average phone bill is 29.843 units.
a) Here we see that the graph is in the shape of a right-angled triangle above the x-axis
The area of a triangle = 1/2 X Base X Height
Here the base will be the measure of the distance of co-ordinates on the x-axis
The height is the distance between the coordinates on the axis for that triangle
= 1/2 X (16 - 8) X (3.15 - 0)
= 1/2 X 8 X 3.15
= 12.60 sq units
b)
Below the x-axis, the graph is a rectangle and a triangle
The area of the rectangle = length X width
Here length is the distance of the co-ordinates of the y-axis and width is the distance between the coordinates for the x-axis
Hence we get
(0 - (-5.14))(8 - 0)
= 5.14 X 8
= 41.12 sq units for the rectangle.
The area of the triangle will be
1/2 X (18 - 15.48) X (0 - (-1.05))
1/2 X 2.52 X 1.05
= 1.323 sq unit
Hence, the total area is
41.12 + 1.323
= 42.443 sq unit
c)
Since the area under the graph represents change,
Here we see that the change in the average cell phone bill will be
42.443 + 12.6
= 55.043
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Complete Question
(Image Attached)
What is the degree of the polynomial
Answer:
A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients).
For example: 6x4 + 2x3+ 3 is a polynomial. Here 6x4, 2x3, 3 are the terms where 6x4 is a leading term and 3 is a constant term. The coefficients of the polynomial are 6 and 2.
The degree of the polynomial 6x4 + 2x3+ 3 is 4.
if trace of a matrix is postive and determinant is positive does it mean eigen values are all positive?
To have the determinant negative, at least one Eigenvalue has to be negative but the reverse of this statement may or may not be true.
If we add all the diagonal elements of the square matrix, we get the trace of the given matrix.
Eigenvalues is a scalar that associates with a set linear equation described as -
(A - λ I) X = 0
If we take the product of all the eigenvalues of a matrix, we'll get the determinant of the matrix. If we consider a case in which the trace of the matrix is +ve, and its determinant is -ve, then at least one or an odd no. of Eigenvalues must be negative, since their product has to be positive when we solve for the determinant of the matrix
Therefore, to have the determinant negative, at least one Eigenvalue has to be negative but reverse may or may not be true.
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A number is between 26 and 31. It has prime factors of 2 and 7. What is the number?
Answer:28
Step-by-step explanation:
Trick: just check if it's divisible by both numbers
The scale factor is _______________ the original figure
Answer: A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller). Therefore, The scale factor would be 1/2
C
Salida 7-8: Comprobacion rapida
What is the missing number in the following equation
33 +52 = 9/1/20
10
A 3
B.5
С. 6
D 8
The numbers that have been omitted from the given series of a number with comparable discrepancies between them are known as missing numbers.
What is the missing number?Finding similarities between those numbers and filling in the missing phrases in the designated series and locations is the strategy indicated for writing the missing numbers.We can solve one-step equations in four different ways: by adding, subtracting, multiplying, and dividing. Both sides of an equation will stay equal if we add the same amount to each side.The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."Two expressions joined by an equal sign form a mathematical statement known as an equation.To learn more about missing number refer to:
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A radio station plays tree commercials between two songs. The commercials play for two minutes altogether. The first commercial is 1/2 minute and the second commercial is 1 1/4 minutes how long is the third commercial
find a set r of representatives such that every power of x is equal to exactly one element of r (and prove it.)
Consequently, x∈R denotes that x belongs to the set of Real numbers. This means that x is a real number.
What is meant by Real numbers?Any number that can be used to quantify a continuous, one-dimensional quantity, such as time, temperature, or distance, is referred to as a real number. Continuous in this context suggests that values may vary by arbitrary little amounts.An endless decimal expansion allows for a nearly universal representation of every real number. Rational numbers like positive and negative integers, fractions, and irrational numbers are all examples of real numbers. In other words, every number we can come up with aside from complicated numbers is a real number. Examples of real numbers include 3, 0, 1.5, 3/2, √5, and so forth.Real numbers are all entire numbers. Irrational numbers are integers. Natural numbers are numbers that make sense.Hence, As a result, the symbol x∈R indicates that x is a member of the Real number set. Thus, x must be a real number.
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g write a method odd sum that accepts an array of numbers. the method should return the total sum of all odd numbers of the array. odd sum([5, 4, 6, 13, 1])
The odd_sum method accepts an array of numbers and returns the total sum of all odd numbers found in the array.
def odd_sum(numbers)
sum = 0
numbers.each do |num|
if num.odd?
sum += num
end
end
sum
end
1. We define a method called odd_sum that accepts an array of numbers as an argument.
2. We set a variable called sum and set it to 0.
3. We iterate through the array using the each method.
4. We check if the number is odd using the odd? method.
5. If the number is odd we add it to the sum variable.
6. We return the sum variable at the end of the method.
The odd_sum method accepts an array of numbers and returns the total sum of all odd numbers found in the array
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.
prove mr. greedy that it is enough to work on 2 edges to find your circumcenter by providing a 2 columns proof of the circumcenter theorem
The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC.
Column 1:
1. Given three points A, B and C, draw lines AB and AC.
2. A bisector of angle BAC is the perpendicular bisector of segment AC.
3. The perpendicular bisector of segment AC intersects line AB at the circumcenter of triangle ABC.
Column 2:
1. Given three points A, B and C, draw lines AB and BC.
2. A bisector of angle ABC is the perpendicular bisector of segment BC.
3. The perpendicular bisector of segment BC intersects line AB at the circumcenter of triangle ABC.
The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC. Therefore, it is enough to work on two edges to find the circumcenter.
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Pls help me with questions, I will give brainliest
Cotangent is the inverse of tangent:
cotΘ = 1/tanΘ
cotΘ = [tex]1/\frac{\sqrt{6} }{2}[/tex]
=[tex]\frac{2}{\sqrt{6}}[/tex]
=[tex]\frac{2}{\sqrt{6}}*\frac{\sqrt{6}}{\sqrt{6}}=\frac{2\sqrt{6}}{6}[/tex] Rationalize the denominator
cotΘ = [tex]\frac{\sqrt{6}}{3}[/tex]
Plug and solve.
[tex]\frac{\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{3} }{\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{3}}[/tex]
We'll break the problem into 2, simplify the denominator, then simplify the numerator.
Simplify the denominator with the common denominator 6, of 2 and 3:
[tex]{\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{3} = {\frac{3\sqrt{6}}{6}-\frac{2\sqrt{6}}{6} = {\frac{3\sqrt{6}-2\sqrt{6}}{6} = {\frac{\sqrt{6}}{6}[/tex]
Simplify the Numerator with the common denominator 6, of 2 and 3:
[tex]{\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{3} = {\frac{3\sqrt{6}}{6}+\frac{2\sqrt{6}}{6} = {\frac{3\sqrt{6}+2\sqrt{6}}{6} = {\frac{5\sqrt{6}}{6}[/tex]
Back in original equation with simplified numerator and denominator:
[tex]\frac{\frac{5\sqrt{6}}{6}}{\frac{\sqrt{6}}{6}}[/tex]
Multiply by reciprocal and simplify:
[tex]\frac{5\sqrt{6}}{6}*\frac{6}{\sqrt{6}} = \frac{5\sqrt{6} * 6}{6\sqrt{6}} = 5*\frac{6\sqrt{6}}{6\sqrt{6}} = 5*1 = 5[/tex]
A car dealership pays a wholesale price of $14,000 to purchase a vehicle. They sell the car for $16,100. If the dealership decided to use a 20% markup instead, how much MORE would they make?
If the dealership decided to use a 20% markup instead, then they earn $700 more.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that A car dealership pays a wholesale price of $14,000 to purchase a vehicle.
They sell the car for $16,100
If the dealership decided to use a 20% markup instead, we have to find the hu=ow much more would they make.
Let us find 20% of 14000
20/100×14000
0.2×14000
2800
So with 20% the price will become $16800.
As they sell the car for $16100.
The difference between $16800-$16100 is $700
Hence, If the dealership decided to use a 20% markup instead, then they earn $700 more.
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Find a general solution to the differential equation -6y = 1+x+y+xy by solving the equation and then applying the initial condition y(-1) = C.
The general solution with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.
The general solution to the differential equation -6y = 1+x+y+xy is y = -(1+x)/(6+x). To apply the initial condition, we can substitute x=-1 and y=C into the above equation and solve for C. We get C=-(2/7). Therefore, the general solution to the differential equation with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.
Substituting x=-1 and y=C into the equation:
-6C = 1-1+C+(-1)C
-7C = 1
C = -1/7
Therefore, the general solution with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.
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Use the result of Example 6 to compute arctan 0.2 correct to five decimal places.
The value of [tex]tan^{-1}(0.2)[/tex] = -0.19739 + ... i.e. [tex]tan^{-1} (0.2)= (0.2) - \frac{(0.2)^{3} }{3} +\frac{(0.2)^{5} }{5} -\frac{(0.2)^{7} }{7}+...[/tex]
The power series of [tex]tan^{-1}(x)[/tex] obtained in example 6 is called the Gregory's series. The Gregory series is an infinite series of fractions or rational numbers
After the Scottish mathematician James Gregory (1638-1675) who had anticipated some of Newton's discoveries we have shown that the Gregory's series is valid when -1 < x < 1.
But it turns out (although it isn't easy to prove) that it is also valid when:
x = 1 or ≠ 1.
According to Example 6, The radius of convergence of the series for
[tex]1/(1 +x^{2} )[/tex] is 1, the radius of convergence of this series for [tex]tan^{-1}(x)[/tex] is also 1.
[tex]tan^{-1} x = x - \frac{x^{3} }{3} +\frac{x^{5} }{y} -\frac{x^{7} }{y} +....[/tex]
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A client who weighs 70 kg is receiving a dopamine solution of 800 mg/500 ml normal saline at 5 ml/hour. How many mcg/kg/minute is the client receiving? (Enter the numeric value only. If rounding is required, round to the nearest tenth.)
To calculate the mcg/kg/minute, first divide 800 mg by 500 ml to get 1.6 mg/ml. Then, multiply 1.6 mg/ml by 5 ml/hour to get 8 mg/hour. Finally, divide 8 mg/hour by 70 kg to get 0.114 mcg/kg/minute.
To calculate the mcg/kg/minute, first divide 800 mg by 500 ml to get 1.6 mg/ml, which is the concentration of dopamine in the solution. Next, multiply 1.6 mg/ml by 5 ml/hour to get 8 mg/hour, which is the rate of infusion. Finally, divide 8 mg/hour by 70 kg to get 0.114 mcg/kg/minute, which is the mcg/kg/minute the client is receiving. This calculation can also be done by dividing 800 mg by 500 ml to get 1.6 mg/ml, then multiplying 1.6 mg/ml by 5 ml/hour to get 8 mg/hour, and finally dividing 8 mg/hour by 70 kg to get 0.114 mcg/kg/minute. By doing this calculation, the client is receiving 0.114 mcg/kg/minute of dopamine solution.
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FILL IN THE BLANK When multiplying matrices, multiply the elements in each ____ of the first matrix time the corresponding elements in each column of the second matrix.
The answer to the problem is: row
what is the volume of the figure below, which is composed of two cubes with side lengths of 5 units?
Answer:
250u2
Step-by-step explanation:
The volume of a cube is found by multiplying LxWxH. 5x5x5-125, 125x2-250
Hope this helped :)
how many minutes are in 3 years
Answer:
1,576,800 minutes
write the equation of an ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)
An ellipse is defined as the set of all points such that the sum of the distances between the point and the two foci is constant. The equation of an ellipse can be represented in the standard form as:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where (h, k) is the center of the ellipse, a is the distance from the center to a vertex, and b is the distance from the center to the focus.
Given that the center of the ellipse is at (2, 1), one vertex is at (2, -4), and one focus is at (2, -2), we can use this information to find the values of a and b, and represent the equation of the ellipse:
a = distance from center to vertex = |1 - (-4)|/2 = 2.5
b = distance from center to focus = |1 - (-2)|/2 = 1.5
The equation of the ellipse is:
(x-2)^2/2.5^2 + (y-1)^2/1.5^2 = 1
which can also be written as:
(x-2)^2/6.25 + (y-1)^2/2.25 = 1
This equation represents the ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)
Which sign makes the following statement true?
1/4 _____ 5/16
Answer:
2. <
Step-by-step explanation:
To compare these two fractions we can first find them a common denominator. A common denominator between 4 and 16 is 16.
To get from 16 from 4 we multiply by 4 so we do the same to the numerator, changing 1/4 to 4/16.
5/16 already has a denominator of 16 so we can leave that one as is.
4/16___5/16
In this form it is obvious that 5/16 is the larger fraction because 5 is larger than 4, meaning that 5/16 is larger than 1/4.
Gabriel is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $250 equipment fee. Company B charges $55 per hour and a $200 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the interval of hours, t,t, for which Company A is cheaper than Company B.
The linear functions for each situation are given as follows:
Company A: 45x + 250.Company B: 55x + 200.The interval of hours for which Company A is cheaper than Company B is given as follows:
x > 5.
How to model the linear functions?The linear functions are modeled in slope-intercept format, as follows:
y = mx + b.
In which:
The slope m represents the cost per hour.The intercept b represents the equipment fee.Hence the functions are defined as follows:
Company A: 45x + 250.Company B: 55x + 200.Company A will be cheaper when:
45x + 250 < 55x + 200
10x > 50
x > 5.
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