Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1=> 2b = b + 1
=> 2b - b = 1
=> b = 1
Since, YZ = 2b
=> YZ = 2 × 1
=> YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4 WZ = a + 2=> 3a - 4 = a + 2
=> 3a - a = 2 + 4
=> 2a = 6
=> a = 6/2
=> a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
=> 9 - 4
=> 5
XY = 5.
Therefore, Option D is the required answer.
10 POINTS FOR THE ANSWER
Explain in your own words using appropriate vocabulary on how you determine what side is opposite, adjacent and the hypotenuse.
It should be noted that the hypotenuse is the longest side in the triangle. The opposite is the side facing the angle and the adjacent is the last side.
How to illustrate the information?The hypotenuse is the longest side of a right triangle. An "opposite" side is one that is across from a given angle, while a "adjacent" side is one that is close to a given angle.
According on the angle requested, adjacent and opposing sides can differ. The side that is opposite to the requested angle is the opposite side, and the side that is immediately adjacent to the requested angle is the adjacent side.
In conclusion, the opposite is the side facing the angle and the adjacent is the last side.
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what are the correct steps in finding the linear equation of a line that passes threw the points (-1,7) and (2,4) using the point slope form method?
We have to find the equation of a line fo which we know two points, using the point-slope form.
The point-slope let us write the equation of the line knowing the value of the slope m and the coordinates of one point (x0,y0) of the line:
\(y-y_0=m(x-x_0)\)We use the two known points to calculate the slope m:
\(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-7}{2-(-1)}=\frac{-3}{3}=-1\)Using the point (-1,7), we can write the equation as:
\(\begin{gathered} m=-1 \\ (x_0,y_0)=(-1,7) \\ \\ y-7=-1\cdot(x-(-1)) \\ y-7=-(x+1) \\ y-7=-x-1 \\ y=-x-1+7 \\ y=-x+6 \end{gathered}\)Answer: From the options, the right ones are:
y-7=-1(x-(-1))
y-4=-1(x-2) --> this one would have been used if we picked the point (2,4) instead of (-1,7)
y=-x+6
find a 90onfidence interval for y when x = 69. (round your answers to one decimal place.)
the 90% confidence interval for y when x = 69 is (41.5, 52.3). This means that we are 90% confident that the true value of y is between 41.5 and 52.3 when x = 69.
To find the 90% confidence interval for y when x = 69, we need to use regression analysis. First, we need to fit a regression model to the data and obtain the regression equation. Once we have the regression equation, we can plug in the value of x = 69 and get the predicted value of y.
Assuming that we have already performed the regression analysis, let's say the regression equation is:
y = 4.5 + 0.6x
To find the predicted value of y when x = 69, we simply plug in x = 69 into the equation:
y = 4.5 + 0.6(69)
y = 46.9
So, the predicted value of y when x = 69 is 46.9.
To find the 90% confidence interval for this predicted value, we need to use the standard error of the estimate (SEE) and the t-distribution. The formula for the confidence interval is:
y ± t(0.05/2, n-2) x SEE
where y is the predicted value of y, t(0.05/2, n-2) is the critical value of the t-distribution for a 90% confidence level with n-2 degrees of freedom (n is the sample size), and SEE is the standard error of the estimate.
Let's say that the SEE is 3.2 (we obtain this value from the regression output) and the sample size is n = 50. Using a t-distribution table, we find that the critical value for t(0.05/2, 48) is 1.677.
Plugging in the values, we get:
46.9 ± 1.677 x 3.2
46.9 ± 5.4
(41.5, 52.3)
So, the 90% confidence interval for y when x = 69 is (41.5, 52.3). This means that we are 90% confident that the true value of y is between 41.5 and 52.3 when x = 69.
To provide a 90% confidence interval for y when x = 69, we need more information such as the regression equation, the standard error, and the critical value. Once you have this information, you can calculate the lower and upper bounds of the confidence interval. Please provide the necessary details, and I'll be happy to help you find the 90% confidence interval.
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a marble is selected from a bag containing eight marbles numbered to . the number on the marble selected will be recorded as the outcome. consider the following events. event : the marble selected has a number less than . event : the marble selected has an even number. give the outcomes for each of the following events. if there is more than one element in the set, separate them with commas.
Event A and B = 4
Event A or B = 2, 3, 4, 5, 6, 8
Complement of Event B = 1, 2, 7, 8
Event A: The marble selected has an even number.
The even numbers from 1 to 8 are 2, 4, 6, and 8. Therefore, the outcomes for Event A are: 2, 4, 6, 8.
Event B: The marble selected has a number from 3 to 6.
The numbers from 3 to 6 are 3, 4, 5, and 6. Therefore, the outcomes for Event B are: 3, 4, 5, 6.
Event A and B:
The outcomes that satisfy both Event A and Event B are the numbers that are both even and from 3 to 6. In this case, the only number that satisfies both conditions is 4.
Therefore, the outcome for Event A and B is: 4.
Event A or B:
The outcomes for Event A or Event B are the numbers that satisfy either Event A or Event B or both.
Combining the outcomes from Event A and Event B, we have: 2, 3, 4, 5, 6, 8.
Complement of Event B:
The complement of an event includes all the outcomes that are not part of the event.
In this case, the complement of Event B includes the numbers that are not from 3 to 6.
Therefore, the outcomes for the complement of Event B are: 1, 2, 7, 8.
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Complete question
A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on the marble selected will be recorded as the outcome.
Consider the following events.
Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
Event A and B =
Event A or B =
Complement of the event B=
True or False:With a sample size of 100 and a p of .5, the sampling distribution of the sample proportion will approximate a normal distribution.The formula for the test statistic for a one-sample significance test of a population proportion is p-PThe standard error of the sample proportion and the standard deviation of the sample proportion are usually the same.When doing significance tests for two proportions we can pool our estimates to compute the standard error because the null hypothesis assumes the two sample proportions are equal.One can never prove the truth of a statistical (null) hypothesis. One can only tend to discount it.A proportion is a special case of a mean when you have a dichotomous population.The margin of error describes a possible random sampling error that occurs within truly random samples.The margin of error is a calculation that describes the error introduced into a study when the sample isn't truly random.
True. With a sample size of 100 and a p of .5, the sampling distribution of the sample proportion will approximate a normal distribution.
This is because of the central limit theorem, which states that with a sufficiently large sample size, the sampling distribution of the sample proportion will approach a normal distribution regardless of the shape of the population distribution.
The central limit theorem is an important concept in statistics that allows us to make inferences about population parameters based on sample statistics. It states that with a large enough sample size, the sampling distribution of the sample mean or proportion will approximate a normal distribution, even if the underlying population distribution is not normal. In this case, with a sample size of 100 and a p of .5, we have a sufficiently large sample size to apply the central limit theorem and approximate a normal distribution. Conclusion: In conclusion, the statement that the sampling distribution of the sample proportion will approximate a normal distribution with a sample size of 100 and a p of .5 is true. The central limit theorem is a powerful tool that allows us to make inferences about population parameters with confidence, even if the underlying population distribution is not known.
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In XYZ, ZY = 78°. XY=9, and XZ= 12. To the nearest tenth, what is m
The measure of angle Z is 47.19°.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given a triangle XYZ.
m ∠Y = 78°, XY = 9, XZ = 12
We have to find the measure of angle Z.
Using the law of sines,
XZ / sin Y = XY / sin Z
12 / sin (78°) = 9 / sin Z
Cross multiplying,
12 × sin Z = 9 × sin (78°)
sin Z = (9 × sin (78°)) / 12
sin Z = 0.7336
Z = sin⁻¹ (0.7336)
Z = 0.8236 radians
= 47.19°
Hence the measure of Z is 47.19°.
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I need help with this question
work out the value of 2 ^ 4 - 3 ^ 2
Answer:
7
Step-by-step explanation:
4+9x6-4=22 where will we put brackets to be right ?
Answer:
I think we put the brackets here
4+(9×6)-4=22
Answer:
4+9 (6-4) = 22
Step-by-step explanation:
you subtract the numbers inside the brackets (6-4=2) and solve the problem.
4+9x2=22
4+18=22
i hope i helped you!
Write the equation of the line in standard form:
1/2y=-4/5x-2
The standard form of the equation is 8x+5y = -20.
What is standard form of the equation?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.
Here the given equation is
=> \(\frac{1}{2}y=\frac{-4}{5}x-2\)
=> \(\frac{1}{2}y=\frac{-4x-10}{5}\)
=> 5y = 2(-4x-10)
=> 5y = -8x-20
=> 8x+5y = -20.
Hence the standard form of the equation is 8x+5y = -20.
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Write an indirect proof of each statement.
a. If 7 x>56 , then x>8 .
To prove the statement "If 7x > 56, then x > 8" indirectly, we assume the opposite of the desired conclusion and show that it leads to a contradiction.
Assume that 7x > 56 but x ≤ 8. We will show that this assumption leads to a contradiction.
Since x ≤ 8, multiplying both sides of the inequality by 7 (which is a positive number) gives us:
7x ≤ 7 * 8
7x ≤ 56
However, this contradicts the initial assumption that 7x > 56. If 7x ≤ 56, then it cannot be simultaneously true that 7x > 56.
Since our assumption led to a contradiction, we conclude that the opposite of our assumption must be true. Therefore, if 7x > 56, then x > 8. This completes the indirect proof.
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Find the square of 7-2v10.
Answer:
89 - 28v10 = 0.456
Step-by-step explanation:
(7-2v10)² = 7² - 2*7*2v10 + (2v10)²
(7-2v10)² = 49 -28v10 + 40
(7-2v10)² = 89 - 28v10
can somebody help me plz
Answer:
126 people
Step-by-step explanation:
9/5 is the ratio tea/coffee
let x be the one who preferred coffee and x+36 preferred tea
9/5=x+36/x
9x=5x+5(36)
9x-5x=180
4x=180
x=180/4=45
x=45 coffee
x+36=45+36=81
45+81=126
check : 81/45= 9/5
for which sample sizes is the first quartile always equal to one of the values in the sample?
The first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.
This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is anThe first quartile is always equal to one of the valuesin the sample when the sample size is a multiple of 4. This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is an even number of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4. of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.
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Of the 645 students in the freshman class, 85 are left-handed. About what percentage of the students are left-handed? Round to the nearest tenth.
About % of the freshman class are left-handed.
Answer:
About 13% of the freshman class are left-handed
Step-by-step explanation:
To find the percentage of a whole you need to divide the part by the whole number (85/645 = 0.1316), then you round to the nearest tenth (0.13) and change it into a percentage by moving the decimal point 2 numbers to the right. (13%)
5 x f(1) + 5 x g(9)
Answer
5 x (f + 9g)
Step-by-step explanation:
I can add my step by step if u want
Answer:
-55
Step-by-step explanation:
got it right on edge
Given the following information, determine which lines are parallel and what justifies them being parallel.
Answers:
Blank 1 = p and r
Blank 2 = corresponding angles converse
==========================================================
Explanation:
Refer to the diagram below. I've marked lines p and r in red, and the angles 3 and 22 in blue. They are corresponding angles because they are both in the same southeast corner of their four-corner configuration.
If the corresponding angles are congruent, then the lines p and r are parallel by the aptly named corresponding angles converse
HELP PLEASE PLEASE PLEASE
Answer:
We'll need 2 points so we'll choose (-6, 0) and (0, -3).
Let's calculate the slope (or 'm') using
Slope or m = (Y2 -Y1) ÷ (X2 -X1)
Slope ('m') = (-3 -0) / (0, - -6) = -3 / 6 = -1/2
Then we calculate the equation using:
(y - y1) = m • (x -x1)
(y - 0) = -1/2 * (x - -6)
y = -1/2 x -3
Source: http://www.1728.org/distance.htm
Step-by-step explanation:
Answer:
x + 2y = - 6Step-by-step explanation:
X-intercept: (-6, 0)
Y-intercept: (0, -3) ⇒ b = -3
Slope: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)
\(m=\dfrac{0+3}{-6+0}=-\dfrac12\)
Slope-intercept form y = mx + b
\(y=-\frac12x-3\) {multiply both sides by 2}
2y = - x - 6 {add x to both sides}
x + 2y = - 6
Tommy has 5 more toy cars than Billy does. Tommy has 12 toy cars.
How many cars does Billy have?
Question 2 options:
A. 17 cars
B. 12 cars
C. 5 cars
D. 7 cars
Answer:
suppose X for billy and Y for tommy
now
X+5=12
or, X=12-5
or, X=7
hence answer is optionD
Answer:
D. 7 Cars
Step-by-step explanation:
If Tommy has 12 cars and it's 5 more than Billy
You do the inverse of addition which is Subtraction
12 - 5 = 7
In Detail:
a = Billy (Answer)
b = +5 (more or less / difference)
c = Tommy (12)
a + b = c
a + 5 = 12
Now you find out something that when you add 5 to it makes 12
You can do this by bringing the +5 to the 12 but you have to change it to a -5
So:
a + 5 = 12 turns to a = 12 -5
12 - 5 = a
7 = 12 - 5 or 12 - 5 = 7
The answer is 7
(sorry if I'm confusing)
To build a handicapped-access ramp, the building code
states that for every 1 inch of vertical rise in height, the
ramp must extend out 12 inches horizontally, as shown in
the diagram below.
*Show solving work on the sketch pad!*
(a) Set up your trig equation (before solving below):
(2 points)
hyp
1 opp
12
adj
Submit
(b) What is the angle of inclination, x, of this ramp, to the
nearest hundredth of a degree? (2 points)
85.22
4.76
85.24
4.78
Answer:4.76
Step-by-step explanation:
tan 0= opposite side/adjacent side
tan x = 1/12
x =tan-1 (1/12)
~~ 4.76 degrees
The angle of inclination x of this ramp is 4.76 degrees.
What is a right-angle triangle?'A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.'
According to the given problem,
Perpendicular = 1 inch
Base = 12 inches
Angle of inclination = x
We know,
tan (x) = \(\frac{Perpendicular}{Base}\)
⇒ tan(x) = \(\frac{1}{12}\)
⇒ x = \(tan^{-1} \frac{1}{12}\)
⇒ x = 4.76 degrees.
Hence, we can conclude, the angle of inclination is 4.76 degrees.
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Find all 3 solutions: 3 − 42 − 4 + 5 = 0
Answer:
Step-by-step explanation:
If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology
The roots are 14.09, 0.30 and -0.39 to nearest hundredth.
elie is now 4 times as old as her son. in 5 years time shes going to be 3 times as old as her son. how old is ellies son now?
Answer:
Her son is 10 years old.
Step-by-step explanation:
Let son be x
Ellie is 4x
In 5 years time: Her son = x + 5
Ellie = 4x + 5
Given that she will then be 3 times as old as her son: 4x + 5 = 3(x + 5)
Solve x: 4x + 5 = 3(x + 5) ,4x + 5 = 3x + 15
x = 10
suppose u is a uniform(0, 1) random variable. consider f-1(u), where f-1(.) is the inverse of the cdf of the random variable x. so, f-1(u) is a transformation of u. assume f-1(.) is strictly increasing. what is the distribution of f-1(u)?
The distribution of the given function is a uniform distribution.
A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).
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the measure of an angle in standard position is given. find two positive angles and two negative angles that are coterminal with the given angle.
To find coterminal angles, you have to either add or subtract 2π. In this case, you would use 8π/4 so there is a common denominator.
Positives:
-3π/4+8π/4 = 5π/4
5π/4+8π/4 = 13π/4
Negative:
-3π/4-8π/4 = -11π/4
-11π/4-8π/4 = -19π/4
What is the measure of an angle?In geometry, an angle measure is the length of the angle formed by two rays or arms intersecting at a common vertex.
Using a protractor, angles are measured in degrees (°). Joseph Huddart created the protractor in 1801. It was a more sophisticated protractor.
The angle created at the center of a circle is measured in radians, the unit of angular measurement. It is described as an angle that subtends from a circle's center and intercepts at an arc with a radius equal to the circle's radius. 57.3° is equal to one radian.
Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles.
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You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is $28.4 \mathrm{~N}$. You carefully add $1.25 \times 10^4 \mathrm{~J}$ of heat energy to the sample and find that its temperature rises $18.0 \mathrm{C}^{\circ}$. What is the sample's specific heat?
The specific heat of the given sample is approximately 239.6 J/(kg·°C). This value indicates the amount of heat energy required to raise the temperature of 1 kilogram of the sample by 1 degree Celsius.
To determine the specific heat of the given sample, we can use the formula Q = mcΔT, where Q is the heat energy added, m is the mass of the sample, c is the specific heat, and ΔT is the change in temperature. By rearranging the formula, we can solve for c.
In this case, we are given the heat energy Q = 1.25 × 10^4 J, the mass m = 28.4 N (weight in newtons), and the change in temperature ΔT = 18.0 °C. To calculate the specific heat c, we rearrange the formula Q = mcΔT and solve for c.
First, we convert the weight from newtons to kilograms by dividing it by the acceleration due to gravity (9.8 m/s^2). So, the mass of the sample in kilograms is 28.4 N / 9.8 m/s^2 = 2.90 kg.
Substituting the given values into the formula, we have 1.25 × 10^4 J = c × 2.90 kg × 18.0 °C. Now, we can solve for c by dividing both sides of the equation by (2.90 kg × 18.0 °C):
c = (1.25 × 10^4 J) / (2.90 kg × 18.0 °C) ≈ 239.6 J/(kg·°C).
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factorize= 21bq+14q-28qr
factorize= 4x-8(y-2z)
who ever gives correct answer with solution i will mark as brainliest.
gcf = 7
= 7q(3b + 2 - 4r)
2) 4x-8 ( y-2z )4x - 8y + 16z
gcf = 4
= 4(x - 2y + 4z)
1)
= 7q ( 3b+2-4r )
2)
= 4(x−2y+4z)
hope this helps
will give brainliest to quickest answer
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
Pls mark brainliest.
WILL GIVE BRAINLIEST + THANKS !
‘question’ 1 options: yes / no
‘question’ 2 options:
p= 5,184a
or
a = 5,184p
or
p= 0.0001929a
Yes, there is a relationship between the screen size and the number of pixels.
The equation representing the relationship will be a = 5,184p.
How to illustrate the information?It should be noted that the information is to simply know if there is a relationship between the screen size and the number of pixels.
The equation representing the relationship will be:
= Number of pixels / Screen size
= 31.104 / 6
= 5.184
Therefore, the equation representing the relationship will be a = 5,184p.
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Mr. Picasso would like to create a small rectangular vegetable garden adjacent to his house. He has 24 ft. of fencing to put around three sides of the garden. Explain why 24 – 2x is an appropriate expression for the length of the garden in feet given that the width of the garden is x ft.
The expression 24 - 2x is suitable for the length of the garden as it accounts for the width and represents the remaining length of fencing available for the garden.
To enclose a rectangular garden, three sides need to be fenced, while one side is already adjacent to Mr. Picasso's house. The remaining three sides will consist of two equal lengths for the width and one length for the length of the garden.
Since the total length of fencing available is 24 ft, the width requires two equal sides, each of length x ft, which amounts to 2x ft. Subtracting this width from the total length of fencing gives us 24 - 2x ft, which represents the remaining length available for the length of the garden.
Therefore, 24 - 2x is an appropriate expression for the length of the garden as it takes into account the already utilized length for the width and represents the remaining length available for the garden's length.
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The weight of corn chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 12.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 12-ounce bags contain more than the advertised 12 ounces of chips
The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.
The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips can be determined by finding the area under the normal distribution curve to the right of the mean.
To find this proportion, we can use the z-score formula:
z = (x - mean) / standard deviation
In this case, we want to find the proportion of bags that contain more than 12 ounces, so x = 12 ounces.
z = (12 - 12.5) / 0.2
z = -2.5 / 0.2
z = -12.5
Next, we need to find the cumulative probability associated with the z-score. We can use a standard normal distribution table or a calculator to find this probability.
Looking up the z-score of -12.5 in the table or using a calculator, we find that the cumulative probability is approximately 0.
Therefore, the proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.
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