According to the statement the ratio of the corresponding sides of both triangles is equal.i.e., δWXY ~ δWVZ.
Given: δWXY is isosceles with legs WX and WY; δWVZ is isosceles with legs WV and WZ.To prove: δWXY ~ δWVZProof:In δWXY and δWVZ;WX = WY (Legs of isosceles triangle)WV = WZ (Legs of isosceles triangle)We have to prove δWXY ~ δWVZWe know that two triangles are similar when their corresponding sides are in the same ratio i.e., when they have the same shape.So, we have to prove that the ratio of the corresponding sides of both triangles is equal.(i) Corresponding sides WX and WVIn δWXY and δWVZ;WX/WV = WX/WZ (WZ is the corresponding side of WV)WX/WV = WY/WZ (WX is the corresponding side of WY)WX.WZ = WY.WV (Cross Multiplication).....(1)(ii) Corresponding sides WY and WZIn δWXY and δWVZ;WY/WZ = WX/WZ (WX is the corresponding side of WY)WY/WZ = WX/WV (WV is the corresponding side of WZ)WX.WZ = WY.WV (Cross Multiplication).....(2)From (1) and (2), we getWX.WZ = WY.WVHence, the ratio of the corresponding sides of both triangles is equal.i.e., δWXY ~ δWVZHence, Proved.
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Solve the system by elimination or you can also use substitution. No matrices. Show all work clearly and neatly!
Given the system of equations:
\(\begin{gathered} \begin{cases}{8-y+3z=8} \\ {3x+y_-2z{2x+4y+z=0}\end{cases}}\end{cases} \\ \\ \end{gathered}\)x - y + 3z = 8
3x + y - 2z = -2
2x + 4y + z = 0
Let's solve the system of equations using elimination method.
Take the first two equations:
x - y + 3z = 8
3x + y - 2z = -2
Since the y variables are opposite of each other, let's eliminate y by adding both equations:
x - y + 3z = 8
+ 3x + y - 2z = -2
__________________
4x + z = 6
Rewrite the equation for z.
Subtract 4x from both sides:
4x - 4x + z = 6 - 4x
z = 6 - 4x
Also, eliminate y in the second and third equations:
3x + y - 2z = -2
2x + 4y + z = 0
Multiply the equation 2 by -4:
-4(3x + y - 2z = -2)
2x + 4y + z = 0
-12x - 4y + 8z = 8
2x + 4y + z = 0
______________
-10x + 9z = 8
We now have the results:
4x + z = 6
-10x + 9z = 8
Multiply the top equation by -9:
-36x - 9z = -54
-10x + 9z = 8
____________
-46x = -46
x = 1
Substitute 1 for x into any of the equations:
4x + z = 6
4(1) + z = 6
z = 6 - 4
z = 2
Substitute 2 for z, and 1 for x in any equation and solve for y:
2x + 4y + z = 0
2(1) + 4y + 2 = 0
4 + 4y = 0
4y = -4
y = -1
Therefore, we have the solutions:
x = 1, y = -1, z = 2
Lily's favorite show is Captain's Cove. Lily watched all 30 episodes last season. Altogether, she spent 15 hours watching it! This season, there will only be 24 episodes. How many hours will Lily spend watching this season of Captain's Cove?.
Lily will spend 12 hours for watching this season's 24 episodes of Captain's Cove.
What is the division means?For division, we need two values, one get divided by other. let a is divided by b i.e., \(\frac{a}{b}\) . It means a is divided in b parts.
In our case, given that
30 episodes watching time is 15 hours for Lily.
So we can divide 15 hours in 30 parts to get one episode watching time.
30 episodes watching time ⇔ 15 hours
1 episode watching time ⇔ \(\frac{15}{30}\) hours
In the same way, 24 episodes watching time calculated as:
24 episodes watching time ⇔ 24( \(\frac{15}{30}\) ) hours = 12 hours
Hence for 24 episodes of Captain's Cove, Lily will spend 12 hours to watching this season.
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write and solve a real world problem in which you find the commission
A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?
($27,990)*(0.03) = $839.70
The Jones family will pay their insurance broker a commission of $1,750.00.
Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.
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A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
(x + 5)x = 104
x2 + 5x – 104 = 0
Determine the solutions of the equation. What solution makes sense for the situation?
x =
What are the dimensions of the rectangle?
width =
inches
length =inches
The breadth is 8 inches, the height is 13 inches, and the supplied statement indicates that x = 8.
What is the rectangle's response?If the circumference and one of the sides of the rectangle are known, the area may be computed. The missing side may be located using the perimeter, and or the area of a triangle can then be calculated using the same formula: Area of triangle = Length * Width.
They inform us that the rectangle in this instance, which has a surface area of 104 square inches, has a length that is 5 inches longer than its breadth. Also, we get the equation (x+5)x = 104, where "x" stands for the thickness of the rectangular.
The area of a rectangle is determined by the following formula:
A = l*x
Where:
l: It's the lenght
x: It is the width
A = 104 square inches
We factor the equations to discover the answers for the width. To do this, we seek for two integers that, when multiplied, yield the result -104 and, when added together, yield the result +5. Hence, these are really +13 & -8.
13 * (-8) = -104
13 - 8 = +5
So, we have:
(x+13) (x-8) = 0
The roots are:
x₁ = -13
x₂ = 8
The answer that provides context for the rectangle's width is: x_ 2 = 8.
Hence, the rectangle's width of x = 8 inches.
If the breadth is 5 inches wider than with the thickness, then
l = 5+8
l = 13 inches
Verifying the area, we have:
A = 13*8 = 104 square units
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What is the meaning of ^
Answer:
Symbol. ^ or (English symbol name wedge) (mathematics, logic) The conjunction operator, forming a Boolean-valued function, typically with two arguments, returning true only if all of its arguments are true. (mathematics) wedge product
Answer;
It is the symbol used in computer language to denote the square or cube or other power of any number . for example; 2^2, it means the square of 2.
What is the equation, in slope-intercept form, of a line that passes through the points (-2, 4) and (3, -1)?
Answer:
Step-by-step explanation: The equation of the line passing through the points (2, –1) and (5, –10) is y = -3x + 5 .Jun 9, 2017
pls help me solve this question
Answer:
1 . x 3 + 3 x 2 y + 3 x y 2 + y 3
2. x 3 - 3 x 2 y + 3 x y 2 - y 3
3. a + b
4 . a - b
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
Which of the following describes a situation in which it is safe to employ t-procedures
(a) n1=10, n2=40; both samples are moderately skewed.
(b) n1=10, n2=8; sample 1 is approximately normal, while sample 2 is skewed right.
(c) n1=6, n2=6; both samples are approximately normal.
(d) n1=35, n2=40; both samples are approximately normal, sample 2 has two outliers.
(e) It is safe to use t-procedures in more than one of the situations above.
The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.
option (c) is identified as the situation where it is safe to use t-procedures.
t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.
Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.
Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.
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Juan alquiló un auto por un día. La tarifa mínima es $490.00, con un cargo adicional de $9.70 por cada kilómetro que maneje. Juan pagó $2847.10 cuando entregó el auto. ¿Qué cantidad de kilómetros manejó? kilómetros Х $ ?
Answer:
243 km
precio de los kilómetros: $2357.10
Step-by-step explanation:
precio total = tarifa mínima + precio de los kilómetros
Para x kilómetros,
P = 490 + 9.7x
P = 2847.1
490 + 9.7x = 2847.1
9.7x = 2357.1
x = 243
precio de los kilómetros: 243 × $9.70/km = $2357.10
Respuesta: 243 km
precio de los kilómetros: $2357.10
is 1:5 and 6:30 porportion
Answer: no
Step-by-step explanation: if not the same
PLEASE HELP WILL GIVE BRAINLIEST
What is the domain of H? a -3
b The x -values —3.0, and 4
c -7
d The x-values –7, -4, 0, 4, and 7
Answer:C
Step-by-step explanation:
Domain is the range of x so it would be -7 to 7 so It would be C
Which ordered pair shows an equivalent ratio of hours to miles?
Answer:
(90 , 9)
(70 , 7)
Step-by-step explanation:
I'm not too sure of the answer, thanks
The table for the quadratic functions f(x) and g(x) are given.
x f(x) g(x)
−6 36 4
−3 9 1
0 0 0
3 9 1
6 36 4
Determine the type of transformation and the value of k.
1. g(x) = 3f(x)
2. g(x) = f(3x)
3. g of x equals one third times f of x
4. g of x equals f of one third times x
The value of k is 1, which is the value of g(x) (and f(x)) when x = -3 or x = 3.
We can determine the type of transformation and the value of k for each of the aforementioned functions using the tables provided for f(x) and g(x).
g(x) = 3f(x) (x)
Here, there occurs a vertical stretch/compression transformation. The function g(x) is a three-fold vertical expansion or contraction of f(x). G(x) has a value of 4, which is identical to the value of k, whether x = -6 or = 6.
g(x) = f(3x) (3x)
Here, there occurs a horizontal stretch/compression transformation. A horizontal stretch or compression of f(x) by a factor of 1/3 results in the function g(x). When x = -3 or x = 3, the value of k is 1, which is also the value of g(x) and f(x).
g(x) = (1/3)f(x) (x)
Here, there occurs a vertical stretch/compression transformation. A vertical stretch or compression of f(x) by a factor of 1/3 results in the function g(x). G(x) has a value of 4, which is identical to the value of k, whether x = -6 or = 6.
g(x) = f(x/3)
Here, there occurs a horizontal stretch/compression transformation. The function g(x) is a three-fold horizontal stretching or compression of f(x). When x = -3 or x = 3, the value of k is 1, which is also the value of g(x) and f(x).
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Solve and graph the following inequality:
x + (-15) > 12
Answer:
x>27
Step-by-step explanation:
x−15>12
Step 1: Add 15 to both sides.
x−15+15>12+15
x>27
hope it help
cylinder a has a radius of 10 inches and a height of 5 inches. cylinder b has a volume of 750π. what is the percentage change in volume from cylinder a to cylinder b?
There is 50% increase in the change in the volume of cylinder A to A
The formula for the volume of the cylinder is given as
V = Πr^2h (1)
Where, r = radius of the cylinder
h = height of the cylinder
We have been given the radius and height of cylinder A which are,
r = 10 inches
h = 5 inches
Now putting the required values in equation (1) we get
V = Π(10)^2(5) cubic inches
V = Π*100*5 cubic inches
V = 500Π cubic inches
We have also been given the volume of cylinder B = 750Π
Thus percentage change in volume of cylinder = (750Π - 500Π)/500Π * 100
= 50%
Hence there is 50% increase in the change of the volume from cylinder A to B
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Question 1: Are the following two monomials multiplied correctly?
Yes or no
Chase has 40 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 168 square meters. List each set of possible dimensions (length and width) of the field.
They have a perimeter of 40 meters, and an area of 168 square meters. Therefore, either set of dimensions would work for Chase's fence.
Let's assume the rectangular plot of land has length L and width W. We can use the given information to set up the following system of equations:
2L + W = 40 (since there are three sides and the total length of fencing is 40 m)
LW = 168 (since the area of the land is 168 square meters)
Solving the first equation for W, we get:
W = 40 - 2L
we get:
L(40 - 2L) = 168
we get a quadratic equation:
\(2L^2\) - 20L + 84 = 0
Using the quadratic formula, we can solve for L:
L = (20 ± sqrt(\(20^2\) - 4(2)(84))) / (2(2))
L = (20 ± 4sqrt(11)) / 4
L = 5 ± sqrt(11)
Therefore, we have:
L = 5 + sqrt(11) or L = 5 - sqrt(11)
W = 30 - 2sqrt(11) or W = 30 + 2sqrt(11)
(5 + sqrt(11)) m by (30 - 2sqrt(11)) m
and
(5 - sqrt(11)) m by (30 + 2sqrt(11)) m
Note that both sets of dimensions satisfy the given conditions: they have a perimeter of 40 m (2L + W = 40) and an area of 168 square meters (LW = 168).
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Distribute: -1/2(10b + 18)
please i need this before 8:00pm
Answer:
-5b - 9
Step-by-step explanation:
-1/2 (10b) = -5b
-1/2 (18) = -9
A point is reflected across the x-axis. The new point is located at (4.75, -2.25) Where was the original point located.
Answer:
(4.75, 2.25)
Step-by-step explanation:
Given the coordinate (x,y). If this coordinate is reflected over the x axis, the resulting coordinate will be (x, -y)
Note that the y coordinate was negated.
Let the original point needed be (x, y)
If the new point is located at (4.75, -2.25)
Since the y coordinate was negated, then;
-y = -2.25
y = 2.25
x = 4,75 (x coordinate remains the same)
Hence the original point is (4.75, 2.25)
Which phrase represents this expression? 6×(5+2)
A. The total of 5 and 2 is multiplied by 6
B. The product of 6 and the sum of 5 and 2
C. 6 multiplied by the product of 5 and 2
D. 2 more than the product of 6 and 5
please help me if u know <3333
The correct phrase represents the expression 6×(5+2) is B. The product of 6 and the sum of 5 and 2.
Basic Concepts of Mathematical ModelingThe following are some of the benefits obtained when using a mathematical model, namely:
Adds speed, clarity, and power of ideas in a relatively short period of time. The problem description takes center stage. Get an understanding or clarity of the mechanism in the problem. Can be used to predict events that will arise from a phenomenon or its expansion. As a basis for planning and control in policy making, and others.In the given expression, 6×(5+2), the first step is to add 5 and 2, which gives a sum of 7.
Then, the sum of 5 and 2 is multiplied by 6, giving a product of 42.
This is represented by the phrase "The product of 6 and the sum of 5 and 2."
Therefore, the correct answer is B. The product of 6 and the sum of 5 and 2.
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Evaluate the expression for s = 2.
9s- 2(s+ 1)2 =
Answer:
s=\(\frac{40}{21}\)
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
My teacher isn't helping me
If I'm not mistaken, the form for slope intercept form is y=mx+b, so look for y/slope then x/intercept
find the unit rate pls
Answer:
1.875 or 1.9 mi/h
Step-by-step explanation:
2.50 miles in 45 minutes
2.50-25%=1.875
5) Alex's house (point F) lies on the same street as her school (point H). Alex's bus stop (point G) lies between her
house and her school. Given FG equals (2x) meters, GH = 1,000 meters, and FH equals 1.200 meters, what is z?
Answer:
Answer:
100 meters
Step-by-step explanation:
Given the following :
Alex house = F
Alex school = H
Alex bus stop = G
FG = 2x meters
GH = 1000meters
FH = 1200 meters
Hence,
FH = FG + GH
1200 = (2x + 1000) meters
1200 = 2x + 1000
1200 - 1000 = 2x
200 = 2x
x = 100meters
Hence, x = 100 meters
Each grape at the supermarket weighs 5 grams. If Eric buys a bag of grapes that weighs 50 grams, how many grapes did he buy?
Answer:
10 grapes
Step-by-step explanation:
50 divided by 5 is 10
5) A warehouse outside of a factory currently has an inventory of 1245 boxes. After an 8-
hour work day, the warehouse has 2000 boxes. Assume the warehouse was being filled at a
constant (linear) rate.
a) How many boxes per hour is the factory able to provide to the warehouse?
b) What would be the inventory at the end of a 40-hour work week?
c) How long will it take to fill the warehouse to its 50,000 box capacity?
6) In the year 2007, a FOREVER stamp cost cost $0.41. In 2023, the cost of a FOREVER
stamp was $0.63. Assume that the cost of stamps increased at a constant (linear) rate.
a) If price increases continue at the current rate, how much will a FOREVER stamp
cost in 2035?
b) In what year would you expect a FOREVER stamp to cost one dollar?
7) In January of 2021, there were 980,000 games available on the Apple App Store. By July
of 2021, there were 984,200 games available. If we assume that the number of available
games is steadily increasing at a constant (linear) rate,
a) How many games does this pattern predict will be available in January 2022?
b) At this rate, when will there be 1,000,000 games available for purchase in the Apple
App Store?
Thee factory is able to provide 94.38 boxes per hour to the warehouse.
How to calculate the valueRate = (2000 - 1245) / 8 = 94.38 boxes per hour
Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.
Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2
Therefore, the inventory at the end of a 40-hour work week would be:
1245 + 3775.2 = 5020.2 boxes
rate = (50000 - 1245) / time
Simplifying this equation, we get:
time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).
Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,
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pl help me to do it
Answer:
Step-by-step explanation:
Assuming you want to find the value of n.
\(\sqrt{\frac{p}{q} } =(\frac{q}{p}) ^{1-2n} \\\)
Remember when bases are same exponents can be made equal
Here the bases are different
because notice on one side there is p/q and on the other q/p
what can we do to make them same?
You can invert the any side you want either make leftside as q/p or make right one as p/q
I will make left side as q/p
All you do is flip the denominator and numerator to do so. But that can only be done if you put a (-1) in the exponent
so underroot p/q means (p/q)^1/2 when i make it q/p
a negative one needs to be put in the exponent. That -1 when multiplied by 1/2 makes it -1/2
Now the bases are same such like.
\((\frac{q}{p} )^{-1/2} = (\frac{q}{p}) ^{1-2n}\)
See now the bases are same, the powers can be made equal
so
-1/2=1-2n
here n is the variable we need to find
rearrange the equation
n=3/4
A random sample of n = 25 observations is taken from a N(µ, σ ) population. A 95% confidence interval for µ was calculated to be (42.16, 57.84). The researcher feels that this interval is too wide. You want to reduce the interval to a width at most 12 units.
a) For a confidence level of 95%, calculate the smallest sample size needed.
b) For a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.
Answer:
Step-by-step explanation:
a) The sample mean is computed as the mid point of the given confidence interval. It is computed as:
\(\bar X=\frac{42.16+57.84}{2} \\\\=50\)
From standard normal tables, we have:
P( -1.96 < Z < 1.96 ) = 0.95
Therefore the margin of error here is computed as:
\(MOE=z*\frac{\sigma}{\sqrt{n} }\)
\(1.96*\frac{\sigma}{\sqrt{n} } =57.84-50\\\\1.96*\frac{\sigma}{\sqrt{25} } =57.84-50\\\\ \sigma=\frac{7.84 \times 5}{1.96} \\\\=20\)
Now for confidence interval width as 12, and above standard deviation the minimum sample size is computed as:
\(1.96 \times \frac{20}{\sqrt{n} } =\frac{12}{2} \\\\1.96 \times \frac{20}{\sqrt{n} }=6\\\\n=(1.96*\frac{20}{6} )^2\\\\=42.7\)
≅ 43
Therefore 43 is the minimum sample size required here.
b) Here for n = 25, we need to find the critical z value first. It is computed as
\(z*\frac{20}{\sqrt{25} } =6\\\\z=\frac{6 \times 5}{20} \\\\=1.5\)
We now have to find the probability now:
P( -1.5 < Z < 1.5)
= 2*P(0 < Z < 1.5)
From standard normal tables, we have:
P(Z < 1.5) = 0.9332
Therefore P( 0 < Z < 1.5) = 0.9332 - 0.5 = 0.4332
Therefore the required probability here is:
= 2*P(0 < Z < 1.5) = 2*0.4332 = 0.8664
Therefore the largest confidence interval here is given as 86.64%
What is an equation of the line that passes through the point (−1,6) and is parallel to the line 2x+y=92x+y=9?
A linear equation is the equation of a line.The equation which is passing through the point (-1,6) and parallel to the line -2x+y=9 is -2x + y = 8.
What is a linear equation?A straight line on the coordinate plane is represented by a linear function.
A linear function is a function that varies linearly with respect to the changing variable.
A linear equation in slope y-intercept form is written as,
y = mx + c where m is the slope while c is the y-intercept.
Given equation is -2x+y=9
y = 2x + 9 so slope m is 2.
Since parallel lines have the same slope so equation will be,
y = 2x + c
Substitute,(-1,6)
6 = 2(-1) + c → c = 8
So,
y = 2x + 8 → -2x + y = 8.
Hence "A linear equation is the equation of a line. The equation which is passing through the point (-1,6) and parallels to the line -2x+y=9 is -2x + y = 8".
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The given question is incorrect correct question follows ;
Find the equation of the line passing through the point (-1,6) and parallel to the line -2x+y=9
Consider the time series xt = Bit + B2 + Wt where B1 and B2 are known constants and wt is a white noise process with variance oz. a. Find the mean function for yt = xt - Xt-1 b. Find the autocovarianc
The mean function for yt, which is defined as the difference between xt and Xt-1, can be calculated as E(yt) = B1 + B2.
a. To find the mean function for yt, we take the expectation of yt:
E(yt) = E(xt - Xt-1)
= E(B1 + B2 + Wt - Xt-1)
= B1 + B2 - E(Xt-1) (since E(Wt) = 0)
= B1 + B2
b. The autocovariance function for yt depends on the time lag, denoted by h. If h is 0, the autocovariance is the variance of yt, which is given as o^2 since Wt is a white noise process with variance o^2. If h is not 0, the autocovariance is 0 because the white noise process is uncorrelated at different time points. Therefore, the autocovariance function for yt is given by:
Cov(yt, yt+h) = o^2 for h = 0
Cov(yt, yt+h) = 0 for h ≠ 0
In this case, the autocovariance is constant at o^2 for a lag of 0 and 0 for any other non-zero lag, indicating that there is no correlation between consecutive observations of yt except at a lag of 0.
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