Given:
Figure of similar triangles.
To find:
The value of x and the measure of NR.
Solution:
In triangle RST and RMN,
\(\angle SRT\cong \angle MRN\) (Vertically opposite angles)
\(\angle RST\cong \angle RMN\) (Alternate interior angles)
\(\Delta RST\sim \Delta RMN\) (By AA property of similarity)
We know that, corresponding sides of similar triangles are proportional.
\(\dfrac{RS}{RM}=\dfrac{RT}{RN}\)
\(\dfrac{40}{8}=\dfrac{60}{2x-2}\)
\(5=\dfrac{60}{2x-2}\)
\(2x-2=\dfrac{60}{5}\)
On further simplification, we get
\(2x=12+2\)
\(x=\dfrac{14}{2}\)
\(x=7\)
The value of x is 7.
Now,
\(NR=2x-2\)
\(NR=2(7)-2\)
\(NR=14-2\)
\(NR=12\)
Therefore, the value of x is 7 and the measure of NR is 12 units.
What percent of the youths surveyed prefer reading electronic books? Round your answer to the nearest tenth of a percent.
Total number of people surveyed that read print be 54.
What is meant by percent?A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified.
When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Total number of youths surveyed
= total number of those surveyed - total number of youths surveyed
= 119 - 64 = 55
Total number of youths that read electronic books 55 - 23 = 32
Total number of adults that read electronic books = 65 - 32 = 33
Total number of adults that read prints = 64 - 33 = 31
Total number of people surveyed that read print = 119 - 65 or 23 + 31 = 54
The complete question is:
A survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books.
23 youths said they preferred reading books printed on paper.
64 adults were surveyed.
65 total people said they preferred reading electronic books
119 total people were surveyed.
Fill in the missing values in the table below.
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For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)
Given,
The conditions
There are odd number of observationThe observation have been sorted from smallest to largest valuesWe know,
Median is the middle number of ordered data set.
Consider the number of observations as x
Then the median is located at \(\frac{x+1}{2}\)
Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)
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PLEASE HELP ME!!! Which of the following graphs represents a function?
I dont really know but I believe its D.
If Jada runs 5 laps around the track in 6 minutes how many minutes per lap is that
Answer:
1.2 minutes
Step-by-step explanation:
5 laps >> 360 ( 6×60)
1 lap >> x
cross multiplication
5x = 360
x = 360/5
x= 72 second
x = 72/60 = 1.2 minute
How to do [7^{6} * (2/7)^{5}] ÷ (2^{2}). FIRST TO ANSWER WILL BE MARKED AS BRAINLIEST/
Answer:
56
Step-by-step explanation:
7⁶ = ~117,649
(2/7)⁵ = ~0.0019
2² = 4
~117,649 x ~0.0019 = 224.
224 / 4 = 56
Which is an equation of a direct proportion?
A. =1/3−2
B. =3/
C. =−3+4
D. =−3
Answer:
D. y=-3x
Step-by-step explanation:
Direct Proportion
A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:
\(\displaystyle \frac{y}{x}=k\)
Where k is the constant of proportionality.
Solving for y:
y=kx
The only choice representing a direct proportion is:
D. y=-3x
Answer:
D
Step-by-step explanation:
Write the equation of the line in slope-intercept form (y=mx+b):
Answer: y = 3x + 0 OR y = 3x
Step-by-step explanation:
M = slope. rise/run. compare the points on the line by how much they rise and how much they run. In this case it is 3/1 (3). the B = the y-intercept. (the point where the line meets the y line, in this case the line meets at the origin which is 0.)
An accountant purchase of the T-bill with a face value of $6000 for 5945 Dollars if the term of the T-bill is 125 days What is the annual simple interest rate in percent earned by the client round to the nearest 10th of a percent use 360
Answer:
2.6%
Explanation:
We'll use the below formula to determine the interest rate;
\(Interest\text{ rate }=\frac{(face\text{ value - initial purchase prise)}}{\text{face value}}\cdot\frac{360}{days\text{ of maturity}}\)We're given the below parameters in the question;
*Initial purchase price = $5945
*Face value (future value) = $6000
*Days of maturity = 125
Let's now substitute the above values into our formula and solve for the Interest rate as seen below;
\(\begin{gathered} \text{Interest rate }=\frac{(6000-5945)}{6000}\cdot\frac{360}{125} \\ =\frac{55}{6000}\cdot\frac{360}{125} \\ =0.00916666667\cdot2.88 \\ =0.0264 \\ =2.6\text{\%} \end{gathered}\)I will give you brainliest if you help meeee
Answer:
5x+3°+62°=180° (adj angles on a str line)
5x+65°=180°
5x=180°-65°
=115°
x=115÷5
=23
the photo shows a woman watching a row of machines in a factory. a photo of a woman standing between two long rows of sewing machines in a factory. what advantages did machinery provide for factory owners?
A photo of a woman standing between two long rows of sewing machines in a factory. The factory owners relied on skilled workers to run the machines. Thus, option b is correct.
The manufacturing system's key advantages were lower costs for the business and increased worker productivity. The factory administration had direct control over the workers, allowing for regular monitoring of their output. Resources may be used more efficiently if they are shared across several employees.
First, equipment hastened the production of goods. This is because a machine might perform routine tasks skillfully and dependably. The ability of equipment to decrease the number of people required to complete a task is its second advantage. They were able to avoid paying employees by doing this, which allowed them to save money.
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The complete question is-
The photo shows a woman watching a row of machines in a factory. A photo of a woman standing between two long rows of sewing machines in a factory. what advantages did machinery provide for factory owners?
a. machines could do the work faster than skilled workers by hand.
b. factory owners relied on skilled workers to run the machines.
c. the machines produced a better product than skilled workers by hand.
d. factory owners needed more unskilled workers to run the machines.
I m struggle with this problem can someone help me
Check below, please
1) The way to tackle this problem, is by dividing those numerators by the denominators so we can get the decimal form of each fraction, and count the marks to plot them.
2) Let's divide them:
\(\begin{gathered} -\frac{5}{6}=-0.83 \\ \frac{17}{6}=2.83 \end{gathered}\)So now, we can plot them:
Thus, this the answer.
fiza is mixing antifreeze and water. she has 21 litres of a mixture of antifreeze and water in the ratio 5:2 .
A . how much water would she have to add to get1:1.
B . how much water would she have to add to get 1:2
9514 1404 393
Answer:
9 liters24 litersStep-by-step explanation:
The amount of water in the mix is 2/(5+2) = 2/7 of the volume of the mix. That amount is ...
(2/7)(21 liters) = 6 liters
Then the other 21-6 = 15 liters are antifreeze.
A) To make the mix 1 : 1, 15-6 = 9 liters of water need to be added.
__
B) To make the mix 1 : 2, The total amount of water needs to be brought to 30 liters. 15 more liters need to be added for a total of 24 added liters of water.
Answer:
Step-by-step explanation:
The family’s leaders have pulled off three of the great marketing triumphs of the modern era: The first is selling OxyContin; the second is promoting the Sackler name; and the third is ensuring that, as far as the public is aware, the first and the second have nothing to do with one another.
To the extent that the Sacklers have cultivated a reputation, it’s for being earnest healers, judicious stewards of scientific progress, and connoisseurs of old and beautiful things. Few are aware that during the crucial period of OxyContin’s development and promotion, Sackler family members actively led Purdue’s day-to-day affairs, filling the majority of its board slots and supplying top executives. By any assessment, the family’s leaders have pulled off three of the great marketing triumphs of the modern era: The first is selling OxyContin; the second is promoting the Sackler name; and the third is ensuring that, as far as the public is aware, the first and the second have nothing to do with one another.
If you head north on I-95 through Stamford, Connecticut, you will spot, on the left, a giant misshapen glass cube. Along the building’s top edge, white lettering spells out ONE STAMFORD FORUM. No markings visible from the highway indicate the presence of the building’s owner and chief occupant, Purdue Pharma.
Originally known as Purdue Frederick, the first iteration of the company was founded in 1892 on New York’s Lower East Side as a peddler of patent medicines. For decades, it sustained itself with sales of Gray’s Glycerine Tonic, a sherry-based liquid of “broad application” marketed as a remedy for everything from anemia to tuberculosis. The company was purchased in 1952 by Arthur Sackler, thirty-nine, and was run by his brothers, Mortimer, thirty- six, and Raymond, thirty-two. The Sackler brothers came from a family of Jewish immigrants in Flatbush, Brooklyn. Arthur was a headstrong and ambitious provider, setting the tone—and often choosing the path—for his younger brothers. After attending medical school on Arthur’s dime, Mortimer and Raymond followed him to jobs at the Creedmoor psychiatric hospital in Queens. There, they coauthored more than one hundred studies on the biochemical roots of mental illness. The brothers’ research was promising—they were among the first to identify a link between psychosis and the hormone cortisone—but their findings were mostly ignored by their professional peers, who, in keeping with the era, favored a Freudian model of mental illness.
Concurrent with his psychiatric work, Arthur Sackler made his name in pharmaceutical advertising, which at the time consisted al
If the equation 2x
2 – 8x – 42 = 0 is solved by factoring, what is its positive
solution set?
A. {-3} B. {5} C. {6} D. {7}
Answer:
B.{5}
Step-by-step explanation:
2-8x-42=0
(÷2), we get,
1-4x-21=0
-4x-20=0
-4x=20
x=20÷(-4)
x=(-5)
since the question asks for a positive set, the answer is [x=5]
The positive solution set is D. {7}.
What is a set ?A set is a well defined collection of objects written by commas and closed by second brackets.
According to the given question the equation 2x² - 8x - 42 = 0 have two factors and we have write the positive factor in form of a set.
2x² - 8x - 42 = 0
x² - 4x - 21 = 0
x² -7x + 3x - 21 = 0
x(x-7) + 3(x - 7) = 0
(X+3) = 0 OR (x-7) = 0
x = -3 OR x = 7.
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What is negative 8 times 9 times negative 5 minus negative 14
(-8 * 9 * -5 )- -14
360 - - 14 = 360 + 14 = 374
given list: ( 6, 13, 14, 30, 38, 50, 60, 72, 76, 87, 90, 92 ) ex: 42, 32, 12 which list elements will be compared to key 60 using binary search? enter elements in the order checked.
Using binary search to find the key 60 in the given list, the elements compared in order are: 38, 76, 60.
1. We start by comparing the key (60) to the middle element of the list, which is 38. Since 60 is greater than 38, we know that the key must be in the second half of the list.
2. Next, we compare the key to the middle element of the second half of the list, which is 76. Since 60 is less than 76, we know that the key must be in the first half of the second half of the list.
3. We then compare the key to the middle element of the first half of the second half of the list, which is 50. Since 60 is greater than 50, we know that the key must be in the second half of the first half of the second half of the list.
4. Next, we compare the key to the middle element of the second half of the first half of the second half of the list, which is 72. Since 60 is less than 72, we know that the key must be in the first half of the second half of the first half of the second half of the list.
5. Finally, we compare the key to the middle element of the first half of the second half of the first half of the second half of the list, which is 60. Since 60 is equal to 60, we have found the position of the key in the list.
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over a period of one year, two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart. what is this distance, in meters? (1 meter
As per the given points, the distance is 0.08 meter.
The term distance in math is known as the length of the line joining the two points.
Here we have given that over a period of one year and the two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart.
Here we have to calculate the distance between the two point in meter.
Let us consider that x be the distance between the two points.
As we know that in each side there is 4 centimeter distance.
Then the total distance between the two points,
=> 4 x 2 = 8 centimeter.
Then the meter equivalent is calculated as,
=> 8/100 = 0.08
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Find the zero of a function for n(x)= -6x+18, please show your work.
Answer:
3
Step-by-step explanation:
Find the value of x for which n(x) = 0.
-6x+18 = 0
6x = 18
x = 3
The graph of h(x) = (x - 3)2 is a translation of the
graph of f(x) ….. blank
by
…. Blank units.
Answer:
right by 3 I think
Step-by-step explanation:
Answer: Right by 3 Units
Step-by-step explanation:
Right on edge 2021
use the vectors in the figure below to graph the following vector
Given:
The given vector is w.
Required:
We need to draw 3w.
Explanation:
Use the Pythagorean theorem to find the magnitude AB.
Let the origin be (0,0).
Point A is (0,4) and point B is (3,0).
The magnitude of AB is (3-0,0-4)
\(w=(3,-4)\)Multiply the equation by 3 to find 3w.
\(3\cdot w=3\cdot(3,-4)\)\(3w=(3\cdot3,3\cdot(-4))\)\(3w=(9,-12)\)Consider any point on the graph and take it as the origin (0,0) and mark (9,-12) and joint them as follows.
Final answer:
If angle b is two more than three times angle c, angle b and c are complimentary what is the measure of each angle
Step-by-step explanation:
"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)
"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)
Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:
(3C + 2) + C = 90
4C + 2 = 90
4C = 88
C = 22
Plugging C = 22 back into either equation (1) or (2) gives us
B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)
Thus, ∠B = 68º; ∠C = 22º
Lainey bought a set of 20 markers for $6 sign
What is the cost of 1 marker?
Answer:
3 cents
Step-by-step explanation:
cost of 20 markers=$6
cost of 1 marker=?
Cost of 1 marker = 6/20 = 3/10 = 0.3
It costs 3 cents.
In a crowded arena, you notice that when others laugh, clap, or cheer on the speaker, you are more likely to follow along with their actions. This demonstrates the theory of __________. Group of answer choices
This behavior demonstrates the theory of social contagion, where individuals are influenced by the actions and emotions of others in a social setting.
The theory of social contagion suggests that individuals in a social setting can be influenced by the emotions, behaviors, and actions of those around them. When people laugh, clap, or cheer in a crowded arena, it creates a contagious atmosphere where the emotions and behaviors spread rapidly among the individuals present. This phenomenon can be attributed to various psychological mechanisms, such as conformity, social facilitation, and emotional contagion.
Conformity plays a role in this scenario, as individuals have a natural tendency to conform to the norms and expectations of the group. When others laugh, clap, or cheer, it signals social approval and acceptance of the speaker's performance. Consequently, individuals may feel inclined to join in, even if they do not genuinely find the speaker entertaining or compelling.
Social facilitation also contributes to this behavior. The presence of a large crowd can heighten arousal and increase individuals' performance on simple or well-practiced tasks. In this case, clapping, laughing, or cheering are relatively easy actions that require minimal cognitive effort, making it more likely for individuals to engage in these behaviors.
Emotional contagion is another factor at play. Humans are wired to empathize and connect with others emotionally. When people around us display positive emotions, such as laughter or excitement, we tend to "catch" those emotions and experience them ourselves. This emotional contagion further reinforces the tendency to follow along with the crowd's actions.
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Find a set of parametric equations for the line tangent to the space curve r(t)=(-2sint, 2 cost,4sin’t) at the point P(-13,1,3).
The set of parametric equations for the line is:
x = -13 - t
y = 1 - √(3)t
z = 3 + 2t
To find the set of parametric equations for the line tangent to the space curve r(t) = (-2 sin t, 2 cos t, 4 sin t) at the point P(-13, 1, 3), we need to find the derivative of r(t) and evaluate it at t = t₀, where t₀ is the value of t that corresponds to the point P.
The derivative of r(t) is:
r'(t) = (-2 cos t, -2 sin t, 4 cos t)
To find t₀, we need to solve the equation r(t₀) = P:
(-2 sin t₀, 2 cos t₀, 4 sin t₀) = (-13, 1, 3)
From the second component, we can see that cos t₀ = 1/2, which means t₀ = π/3 or t₀ = -π/3.
Substituting t₀ = π/3 into r'(t), we get:
r'(π/3) = (-2 cos(π/3), -2 sin(π/3), 4 cos(π/3)) = (-1, -sqrt(3), 2)
So the line tangent to the space curve at P has direction vector (-1, -√(3), 2), which means the set of parametric equations for the line is:
x = -13 - t
y = 1 - √(3)t
z = 3 + 2t
where t is a parameter that varies along the line.
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Suppose that yi (t) and y2 (t) are solutions to the following differential equation such that the Wronskian (yl. y2) (to=1) = 20. Find the Wronskian (y1, y2) (t) for any t. [Hint: see proof at top of page 143] dy(t) +e-3ty(t) = 0 dt d'y(t) (t + 4) dt2
Nissan Appliances bought three dozen camcorders at a total cost of $5,040. The markup on the camcorders is 30% of the selling
price. What was the original selling price of each camcorder?
Selling price- HELP DUE IN 10 MINUTES 25 POINTS
Answer:
(3*12) 36 Camcorders= $5040
1 Camcorder= $5040/36 = $140
Original= $140/1.03= $135.92
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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(5) Evaluate the limit: x³ + y² lim (x,y)-(0,0) x² + y²
To evaluate the limit of the function (x³ + y²)/(x² + y²) as (x, y) approaches (0, 0), we can use the Squeeze Theorem. By examining the function along different paths approaching the origin, we can determine that the limit is equal to 0.
Let's consider two paths: the x-axis (y = 0) and the y-axis (x = 0). Along the x-axis, the function simplifies to x³/x² = x. As x approaches 0, the function approaches 0. Along the y-axis, the function simplifies to y²/y² = 1. As y approaches 0, the function remains constant at 1.
Since the function is bounded between x and 1 along these two paths, and both x and 1 approach 0 as (x, y) approaches (0, 0), we can conclude that the limit of (x³ + y²)/(x² + y²) as (x, y) approaches (0, 0) is 0.
In conclusion, by considering the behavior of the function along different paths, we can determine that the limit of (x³ + y²)/(x² + y²) as (x, y) approaches (0, 0) is 0 using the Squeeze Theorem.
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is it possible to choose (2n 1)^2 points in the disc of radius n such that the distance between any two of them is greater than 1?
Answer: its (4f 5) ^3
Step-by-step explanation:
Select the correct choices that complete the sentence below.
The value of tan(-150) degrees is blank because -150 degrees is
in quadrant blank. The reference angle is blank and the exact value
of tan(
The reference angle is 30° and the exact value of tan is -√3/3.The correct options are:(i) -√3/3(ii) III(iii) 30°
The value of tan (-150) degrees is blank because -150 degrees is in quadrant blank. The reference angle is blank and the exact value of tan is ...It is to be noted that in trigonometry, all angles need to be expressed in the range of [0,360] or [0,2π] to apply the trigonometric functions. The negative angles need to be converted into positive angles. If we consider tan(-150), it would be the same as finding tan(150 + 360) or tan(150 + 2π).If we plot -150 degrees, it would be in the third quadrant as shown in the figure below:
Let us determine the reference angle of 150. To do so, we subtract 150 from 180° (one full rotation) as it lies in the third quadrant. We have:
Reference angle of 150 = 180° − 150°= 30°Hence, tan(-150°) is the same as tan(-180° + 30°), and we know that tan(-180° + θ) = tan(θ).tan(-150) degrees is equal to -√3/3 because it is in the third quadrant.
The reference angle is 30° and the exact value of tan is -√3/3.The correct options are:(i) -√3/3(ii) III(iii) 30°.
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this is what truthfully struggle with can someone explain how i do this please then imma try it on my own