Answer:
The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis
Step-by-step explanation:
* Lets explain how to solve the problem
- Any point will be equidistant from the x-axis and the y-axis must have
equal coordinates
- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis
because the distance from the x-axis to the point is 4 (y-coordinate)
and the distance from the y-axis and the point is 4 (x-coordinate)
- If (x , y) is the mid-point of a segment its endpoints are
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], then
[tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
* Lets solve the problem
∵ Point A has coordinates (p , q)
∵ Point B has coordinates (p + 2q , q + 2p)
- The mid-point of AB is (x , y)
∵ [tex]x=\frac{p+p+2q}{2}[/tex]
∴ [tex]x=\frac{2p+2q}{2}[/tex]
- Take 2 as a common factor from the terms of the numerator
∴ [tex]x=\frac{2(p+q)}{2}[/tex]
- Divide up and down by 2
∴ x = p + q
∵ [tex]y=\frac{q+q+2p}{2}[/tex]
∴ [tex]y=\frac{2q+2p}{2}[/tex]
- Take 2 as a common factor from the terms of the numerator
∴ [tex]y=\frac{2(q+p)}{2}[/tex]
- Divide up and down by 2
∴ y = q + p
∴ The mid point of AB is (p + q , q + p)
- p + q is the same with q + p
∵ The x-coordinate of the mid point of AB is p + q
∵ The y-coordinate of the mid point of AB is q + p
∵ p + q = q + p
∴ The coordinates of the mid-point of AB are equal
- According the explanation above
∴ The mid-point (p + q , q + p) of AB is the same distance from the
x-axis and the y-axis
Simplify by combining like
terms:
--6x - 12 + 8y + 16x
The answer is 10x+8y-12 if the problem was -6x - 12 + 8y + 16x because you added an extra negative at the start.
4. The annual salaries of employees in a large company are approximately
normally distributed with a mean of $50,000 and a standard deviation of
$20,000:1
a) What percent of people earn less than $40,000?
b) What percent of people earn between $45,000 and $65,000?
c) What percent of people earn more than $70.000
a. What percent of people earn less than $40000?
Solution: Let S be the random variable of a salary of employee (in $), S ~ N(50000,20000). Then the random
variable X =−50000
20000
~N(0,1).
( < 40000) = ( <
40000 − 50000
20000 ) = ( < −0.5) = (−0.5) = 0.3085375.
Here Φ(x) denotes the cumulative distribution function of a standard normal distribution.
Answer: 31%.
b. What percent of people earn between $45000 and $65000?
Solution:
(45000 < < 65000) = (
45000 − 50000
20000 < <
65000 − 50000
20000 ) = (−0.25 < < 0.75)
= (0.75) − (−0.25) = 0.7733726 − 0.4012937 = 0.3720789.
Answer: 37%.
c. What percent of people earn more than $70000?
Solution:
( > 70000) = ( >
70000 − 50000
20000 ) = ( > 1) = 0.8413447.
Answer: 84%.
By converting the salary amounts to Z-scores and checking a standard normal distribution table, the percentages of people earning less than $40,000, between $45,000 and $65,000, and more than $70,000 are approximately 30.85%, 37.21%, and 15.87%, respectively.
Explanation:In this question, we are dealing with what is known as a 'normal distribution' in statistics. The properties of a normal distribution allow us to calculate the percentages requested. First, we need to convert each salary to a 'Z-score'. A z-score will tell us how many standard deviations away from the mean the salary lies.
a) For $40,000, the Z-score will be (40000-50000)/20000, yielding -0.5. Looking up this Z-score in a standard normal distribution table, or using a calculator equipped with normal distribution functions, we find that roughly 30.85% of employees would earn less than $40,000.
b) For the range $45,000 to $65,000: the Z-scores will be -0.25 and 0.75 respectively. These correspond to about 40.13% and 77.34%. The percentage of people earning between these amounts would be 77.34% - 40.13% = 37.21%.
c) For over $70,000: the Z-score is 1.0 which corresponds to around 84.13%. Therefore, the percentage earning more than $70,000 is 100% - 84.13% = 15.87%
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Someone please help!!
Answer:
I believe the answer is D, 145 degrees
Step-by-step explanation:
180 - 35 = 145
Apologies if I am incorrect.
In which direction does the head of the molecules of the plasma membrane face?
O toward the head of another molecule
O toward the middle
O
away from water
O toward the outside
Answer:
toward the outside
Step-by-step explanation:
The plasma membrane is composed of the phospholipid bilayer and cholesterol.The phospholipids have a head and two tails.The head is water loving, hence it is termed as polar/hydrophilic.The tails are nonpolar/ water fearing/hydrophobic.Both inside and outside the cell, water is vital thus the phospholipid line up in two layers where the head points outwards and the tails hidden in the middle.
Answer:
to the middle
Step-by-step explanation:
6. What is 45% of 900?
Answer:
405
Step-by-step explanation:
45% of 900
=(45/100) . 900
=405
Can u guys answer these 3 questions for me w/ work shown and also label the ones u guys did so I won’t get them mixed up
8:
q/6 + p
12/6 + 10
2 + 10
12
10:
15 - m/p
15 - 3/10
14.7
12:
p - 2/qp
7 - 2/(4)(7)
7 - 2/28
7 - 1/14
6.928
a football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in the field position after the 3 plays
You would start out at in the middle of a number line (horizontal). After the first play, you would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position. You would do the same thing for the next two plays, moving 5 spots to the left each play and creating a new starting point each time. The total spots moved after the 3 plays is 15 spots to the left.
Suppose that y is inversely proportional to the square root of x. Find the constant of proportionality k if y=11 when x=7.
Answer: 11√7
Step-by-step explanation:
Inversely proportional means y√x=k, where k is the constant of proportionality
Find k, when x = 7 and y = 11 ----> 11√7 = k
Answer:
[tex]11\sqrt{7} = k[/tex]
Step-by-step explanation:
[tex]y\sqrt{x} = k \\ \\ therefore \\ \\ 11\sqrt{7} = k[/tex]
I am joyous to assist you anytime.
Suppose 4/5 of a different box of oranges weighs 8 pounds. How many pounds of oranges are in the full box?
Answer:
10
Step-by-step explanation:
x×4/5=8
x=8×5/4
x=10
Answer:
The correct answer is 10.
Step-by-step explanation:
One of the ways to find this answer is the following:
If 4/5 represent 8 pounds, it means that every fifth is two pounds.
If the total amount is five fifths, it is necessary to perform the following multiplication:
2 * 5 = 10, so it is the correct answer.
A 48ft wire is cut into 3 pieces. The 2nd is three times as long as the first piece. The third piece is 4 times as long as the second piece. How long is each piece?
Answer:
3,9,and 36
Step-by-step explanation:
small=x
median=3x
big=12x
x+3x+12x=48
16x=48
x=3
3=small
3*3=9 (median)
9*4=36(big)
3+9+36 = 48
The problem is solved by setting up and solving an equation where 'x' represents the length of the first piece. The three pieces of the wire measure 3ft, 9ft, and 36ft respectively.
Explanation:The question is about finding the length of each piece of a 48ft wire when it's divided into 3 pieces, with each piece having a specific relative length. Let's denote the length of the first piece as 'x'. According to the problem, the second piece is three times as long as the first one, so it's '3x', and the third is four times as long as the second, so it's '4*3x', which simplifies to '12x'.
Combining all these pieces, we get the total length of the wire: x + 3x + 12x = 48ft. This simplifies to 16x = 48ft. Finally, solving for 'x', we find that x = 48ft / 16 = 3ft. Therefore, the three pieces of the wire measure 3ft, 9ft, and 36ft respectively.
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Round 0.817 to the hundredth
Answer:
0.820
Step-by-step explanation:
7 is above five so round to the nearst tenth
If f(x) = 6x + 7, find the value of f (m).
Answer:
f(m) = 6m +7
Step-by-step explanation:
Given that,
f(x) = 6x + 7
∴f(m) = 6m +7
just put m instead of x .
which of these is not a possibe r-value?
a.1.75
b.-0.1
c.0.2
d.-0.5
Among the given options, "-0.1" is not a possible R-value. R-values represent the thermal resistance of a material, and they are always positive values.
What are R values used forR-values are used to measure the ability of a material to resist the flow of heat, and a higher R-value indicates better insulation. Therefore, values like 1.75, 0.2, and -0.5 could potentially be R-values, with 1.75 and 0.2 being good insulators and -0.5 indicating a poor insulator. However, a negative value like -0.1 does not make physical sense in the context of R-values.
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2. SALES TAX Olivia purchases a DVD movie priced
at $21.99. The sales tax is 6.5%. What is the total
price of the movie, including tax?
Answer:
$23.42
Step-by-step explanation:
To find the sales tax, you need to 6.5% of $21.99To do this you have to times need to turn 6.5% into a decimal, which is 0.065 (i moved decimal point 2 numbers to the left)then you do 0.065 × 21.99 which equals 1.42935now you have to add 21.99 with 1.42935 = 23.41935because of the context of the question, you need the answer needs to be rounded up to the nearest hundredth. making the answer $23.42 totalHelp answer if you know it 20 points
Answer:
1 4 x 25
2 25 x 4
Step-by-step explanation:
The function f(x) = StartRoot negative x EndRoot is represented by the graph. Which statement is correct?
The domain of the function is all real numbers greater than 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all values less than 0.
The range of the function is all real numbers greater than or equal to 0.
Answer:
D. The range of the function is all real numbers greater than or equal to 0.
Step-by-step explanation:
The graph of the function [tex]y=\sqrt{-x}[/tex] is shown in attached diagram.
1. The domain of the function is the set of all possible values for input (for x). Hence, the domain of this function is
[tex]x\in (-\infty,0][/tex]
2. The range of the function is the set of all possible values for output (for y), so the range of this function is
[tex]y\in [0,\infty)[/tex]
As you can see, only option D is true - The range of the function is all real numbers greater than or equal to 0.
Answer:
D on Edge 2021
Step-by-step explanation:
Use the Distributive Property to multiply 8 and 45 in your head.
What is the answer?
32 + 40 + 72
40 + 40 = 80
320 + 40 = 360
320 + 5 = 325
Answer:
320+40=360
Step-by-step explanation:
8(40+5)
320+40=360
Answer:
320+40=360
Step-by-step explanation:
First you split 45 to 40 and 5
45= 40+5
Next you multiply each piece of 45 by 8
(40x8)+ (5x8)
Simplify
320+40
Solve
320+40=360
45 = 5(3x – 6)
Help me
Answer is provided in the image attached.
The average distance from the sun to the planet mercury is about 58,000,000km the distance of a human hair is about 0.0025
What is the distance from the sun to mercury
Answer:
58,000,000 km
Step-by-step explanation:
the hair thing is just to throw you off
The average distance from the Sun to the planet Mercury is approximately 58 million kilometers, which also translates to 0.39 astronomical units (AU). Mercury's orbit varies from 46 million kilometers at its closest to 70 million kilometers at its farthest from the Sun due to its elliptical orbit.
Explanation:Distance from the Sun to Mercury
The average distance from the Sun to Mercury is about 58 million kilometers. This distance is known as the semimajor axis of Mercury's orbit. Since Mercury's orbit has a high eccentricity of 0.206, its actual distance from the Sun can vary significantly. The closest point, or perihelion, is about 46 million kilometers, and the farthest point, or aphelion, is about 70 million kilometers. The concept of astronomical unit (AU) is used as a standard measure within the solar system, defined as the average Earth-Sun distance, which is about 150 million kilometers or 1 AU. Consequently, Mercury's average distance from the Sun can also be expressed as 0.39 AU.
what is the point slope form of the line with slope -1/4 that passes through the point ( -2,9 )
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{9})~\hspace{10em} \stackrel{slope}{m}\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{1}{4}}[x-\stackrel{x_1}{(-2)}]\implies y-9=-\cfrac{1}{4}(x+2)[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each description with the correct inequality.
20 POINTS ANSWER ASAP
Which inequality has a solution set of {x ⎸x > 3 or x < –3}? Question 16 options: a) |2| < 6 b) |2| ≥ 6 c) |2| > 6 d) |2| ≤ 6
Answer:
Option C) |2x| > 6 is correct.
Step-by-step explanation:
Consider the provided solution set:
{x ⎸x > 3 or x < –3}
Now check which options are correct.
Option A) |2x| < 6
[tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]
[tex]-6<2x<6[/tex]
[tex]-3<x<3[/tex]
Thus, the option is incorrect.
Option B) |2x| ≥ 6
[tex]\mathrm{If}\:|u|\:\ge \:a,\:a\:>\:0\:\mathrm{then}\:u\:\le \:-a\:\quad \mathrm{or}\quad \:u\:\ge \:a[/tex]
[tex]2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6[/tex]
[tex]2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6[/tex]
Thus, the option is incorrect.
Option C) |2x| > 6
[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]
[tex]2x<-6\quad \mathrm{or}\quad \:2x>6[/tex]
[tex]x<-3\quad \mathrm{or}\quad \:x>3[/tex]
Thus, the option is correct.
Option C) |2x| ≤ 6
[tex]\mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a[/tex]
[tex]2x\ge \:-6\quad \mathrm{and}\quad \:2x\le \:6[/tex]
[tex]x\ge \:-3\quad \mathrm{and}\quad \:x\le \:3[/tex]
Thus, the option is incorrect.
Hence, Option C) |2x| > 6 is correct.
Enter an inequality that represents the description, and then solve.
Nine more than seven times a number (x) is at least thirty.
Inequality:
The solution to the inequality is
Answer:
7x + 9 ≥ 30
x ≥ 3
Step-by-step explanation:
7x + 9 ≥ 30
7x ≥ 21
x ≥ 3
Final answer:
The inequality 7x + 9 ≥ 30 represents the description given, and the solution is x ≥ 3, meaning any number greater than or equal to 3 satisfies the inequality.
Explanation:
The inequality that represents the description 'nine more than seven times a number (x) is at least thirty' is written as 7x + 9 ≥ 30.
To solve this inequality:
Subtract 9 from both sides of the inequality: 7x ≥ 21.Divide both sides by 7 to isolate x: x ≥ 3.Therefore, the solution to the inequality is that x must be a number greater than or equal to 3.
Richard Lens receives a 3.5% commission for selling cleaning supplies. What is his commission on sales of $122,591?
Answer:
$4,290.69
------------------------------------------------------------------------------------------------------
- To find the commission, just convert the percentage into a decimal (divide by 100) and multiply it by the sales.
3.5% = 0.035
122,591 x 0.035 = $4,290.69
Answer:
Richard Lens received a commission of $4,290.685 on a sale of $122,591.
Step-by-step explanation:
We are given the following information in the question:
Total sale made = $122,591
Commission received by Richard = 3.5%
Amount of commission relieved =
Formula:
[tex]\displaystyle\frac{\text{Percentage of Commission recived}}{100}\times \text{Total sales}[/tex]
= [tex]\displaystyle\frac{3.5}{100}\times 122591[/tex]
= $4290.685
Thus, Richard Lens received a commission of $4,290.685 on a sale of $122,591.
please answer this question
Hey!
------------------------------------------------
Solution:
In Picture!
------------------------------------------------
Answer:
[tex]\large\boxed{-\frac{9}{10} }[/tex]
------------------------------------------------
Hope This Helped! Good Luck!
Solve 12x + 6 ≥ 9x + 12. A. x ≥ 2 B. x ≥ 6 C. x ≤ 6 D. x ≤ 2
Answer:
A
Step-by-step explanation:
12x + 6 ≥ 9x + 12
12x-9x ≥ 12-6
3x ≥ 6
x ≥ 2
Answer:
A. x ≥ 2
Step-by-step explanation:
test approved
Do number one Show your work✨
3 in the power of ten word form
3 in the power of ten means "10^3."
[tex]10^3[/tex]
How to solve exponents is to multiply the number as many times as it's exponent. So in this case you will have to multiply ten, three times.
[tex]10\times10\times10=1000[/tex]
Which would mean that....
[tex]10^3=1000[/tex]
The answer is 10^3.
Hope this helps.
The Plumber charges $50 to come to her home an a additional $30.75 every hour he works on the job Sarah has $234 .50 in savings for the repairs what is the maximum amount of hours that the plumber worked on her faucet.
Answer:
6 hours
Step-by-step explanation:
234.50-50.00=184.50
184.50/30.75=6
6 hours
The local high school football team will be playing in the state championship. The coach has free tickets that he will be distributing to 52 football players for their friends and families. If he would like to give each player at least 3 tickets, what is the minimum total he must have?
Answer:
156
Step-by-step explanation:
52*3+156