Answer:
x = - 5
Step-by-step explanation:
[tex]Let \ (x _ 1 , y _ 1 ) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ points. \\\\The \ distance \ between \ the \ points \ be ,\ d = \sqrt{(x_2 - x_1)^2 + ( y _ 2 - y_1)^2}[/tex]
Given : d = 10 units
And the points are ( x , - 4) and ( 3 , 2 ).
Find x
[tex]d = \sqrt{( 3 - x)^2 + ( -4 - 2)^2} \\\\10 = \sqrt{( 3 - x)^2 + ( -6)^2} \\\\10^2 = [ \ \sqrt{( 3 - x)^2 + 36} \ ]^2 \ \ \ \ \ \ \ \ \ [ \ squaring \ both \ sides \ ] \\\\100 = ( 3 - x )^2 + 36\\\\100 - 36 = ( 3 - x )^ 2\\\\( 3 - x ) = \sqrt{64}\\\\3 - x = \pm 8\\\\3 - x = 8 \ and \ 3 - x = - 8\\\\-x = 8 - 3 \ and \ -x = - 8 - 3\\\\-x = 5 \ and \ -x = - 11\\\\x = - 5 \ and \ x = 11\\\\[/tex]
Check which value of x satisfies the distance between the points.
x = 11
[tex]d = \sqrt{(3-11)^2 + (-2--4)^2} = \sqrt{(-8)^2 + (-2+4)^2}= \sqrt{64+4} = \sqrt {68} \ units[/tex]
does not satisfy.
x = - 5:
[tex]d = \sqrt{ (3 -- 5)^2 + ( - 4 - 2)^2} = \sqrt{8^2 + 6^2} = \sqrt{100} =10 \ units[/tex]
Therefore , x = - 5
A few people gather together to play a game in which one needs to roll 3 six-sided dice. One person notices that the sum of the number of spots on three dice comes up as 11 (the event E1) more often than it does 12 (the event E2) even though it looks like it should be even. This person argues as follows: E1 occurs in just six ways:
{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}, and E2 occurs also in just six ways: {(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}.
Therefore E1 and E2 have the same probability P(E1) = P(E2). Why isn’t it?
Answer:
Yes, P(E1)=P(E2)
Step-by-step explanation:
We are given that
Number of dice=3
Total outcomes of 1 die=6
Therefore,
Total number of outcomes =[tex]6^3=216[/tex]
E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}
E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}
We have to show that E1 and E2 have the same probability P(E1) = P(E2).
Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]
Using the formula
[tex]P(E_1)=\frac{6}{216}[/tex]
[tex]P(E_1)=0.0278[/tex]
[tex]P(E_2)=\frac{6}{216}[/tex]
[tex]P(E_2)=0.0278[/tex]
Hence, P(E1)=P(E2)
List all the elements of the following set. Use set notation and the listing method to describe the set. The set of all counting numbers less than or equal to 2. Express the set using set notation and the listing method. (Use a comma to separate answers as needed. Use ascending order.)
Answer:
different question
Step-by-step explanation:
question is wrong
In which month was the peak, the largest deposit, made?
A histogram titled Savings Account Deposits has Months on the x-axis and amount deposited on the y-axis. January is 50 dollars; February is 80 dollars; March is 110 dollars; April is 100 dollars: May is 95 dollars; June is 250 dollars; July is 320 dollars; August is 300 dollars; September is 80 dollars.
January
June
July
August
Your answer is July.
From least to greastest:
January: $50
February: $80
September: $80
May: $95
April: $100
March: $110
June: $250
August: $300
July: $320
I hope this helps!
The month that had the largest deposit is the month of; July
How do you Interpret a Histogram?
From the given histogram with savings account on the x-axis and amount deposited on the y-axis, we can see the following amounts deposited for each month as follows;
January = $50February = $80March = $110April = $100May = $95June: $250July: $320August: $300September: $80The month with the largest deposit is clearly July
Read more about Histograms at; https://brainly.com/question/25983327
A recent national study about the effectiveness of Echinacea in cold treatments for adults was performed by a medical school in Kansas City. The results stated that 22.5% of the randomly chosen 250 adult subjects in the placebo group in the study noted that their treatment appeared to shorten the length of their colds. In an attempt to determine the average high school GPA of all students enrolled at a Regents University in Kansas, a researcher first randomly selects one of the six Regents Universities, then selects a random sample of 50 students from that University from which to gather data. The descriptive statistic of interest in this study is
Answer:
The average high school GPA of all students enrolled at a Regents University in Kansas
Step-by-step explanation:
Descriptive statistics refers to aspect of statistics which is employed when summarizing data. Descriptive statistics often use measure of center such as, mean, median and mode to give consider summary of both sample and population data. Measures of spread such as standard deviation and variance and so on also form part of descriptive statistics used for data summarization.
In the scenario described above, the descriptive statistic which the study intends to infer is the average or mean high school GPA of all students enrolled at a Regents University in Kansas. This mean value will be a single value which describes the GPA of all high school students.
Simplify by expressing fractional exponents instead of radicals.
Simplify the given expression into the form a+bi, where a and b are rational numbers.
2(-36 - 3i) +(5 +2i)(12 - 2i)
Answer:
[tex]2(-36 - 3i) +(5 +2i)(12 - 2i) \\ \implies - 72 - 6i + 60 - 10i + 24i + 4\\ \implies \: - 8 + 8i[/tex]
hlo all here is your question in this question the chooses are below
Answer:
1. centimeter
2. kilogram
3. gram
4. milligram
5. centimeter
6. meter
7. kilometer
8. liter
9. kiloliter
10. millimeter
Step-by-step explanation:
you really cannot answer that yourself ?
you don't understand yet the difference between length or distance, area, volume, weight, ... ?
I how this helps then
1. is length, and it is rather short. so, we use a rather small unit to express it.
2. is weight. and a big one. so, we use a bigger unit.
3. is weight. but a small one.
4. is weight. and a really tiny one.
5. is length. similar dimension of size as the finger.
6. is length. and a bigger one.
7. is length. and a truly big one.
8. is volume. liquid volume at that. but rather small.
9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...
10. is length. and a very tiny one.
A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample of 18 trees from this forest. The researcher found that the average height was 4.8 meters with a standard deviation of 0.55 meters. Assume that the distribution of the heights of these trees is normal. For this sample what is the margin of error for her 99% confidence interval
Answer:
The margin of error for her confdence interval is of 0.3757.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Standard deviation of 0.55 meters.
This means that [tex]s = 0.55[/tex]
What is the margin of error for her 99% confidence interval?
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]
[tex]M = 0.3757[/tex]
The margin of error for her confdence interval is of 0.3757.
Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.
What is the margin of error for small samples?Suppose that we have:
Sample size n < 30
Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Degree of freedom = n-1Then the margin of error(MOE) is obtained as
Case 1: Population standard deviation is knownMargin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]
where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance
For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.
Then, by the given data, we get:
[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18
The degree of freedom is n-1 = 17
Level of significance = 100% - 99% = 1% = 0.01
The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)
Thus, margin of error for 99% confidence interval for considered case is:
[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]
Thus, the margin of error for the given condition is 3.28 approximately.
Learn more about margin of error here:
https://brainly.com/question/13220147
Iceberg lettuce is grown and shipped to stores for about 40 cents a head, and consumers purchase it for about 92 cents a head. Find the percent increase.
Answer: 130%
Step-by-step explanation:
percent increase = x[tex]40 + 40(x) = 9240\\40(1 + x) = 92\\1+x=\frac{92}{40} \\x=\frac{92}{40} -1=2.3-1=1.3[/tex]
x = 1.3 = 130%
How many students rank themselves as introverts? Demonstrate your work!!
Answer:
36 (maybe...)
Step-by-step explanation:
Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts. But if we a supposed to assume that all adults are students:
The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.
In other words for every 10 people (total introvert+extrovert) there are 3 introverts.
So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3
The answer would be 36
Solve using suitable arrangement and properties.
a) 417×1002
b) 4×573×25
c) 8312+284+788+716
d) 125×44+56×125
Answer:
Step-by-step explanation:
A- 417 × 1002
= 417 × (1000+2)
= 417× 1000+ 417×2
= 417000+ 834
= 417834
B- 4× 573×25
= 4× 25+ 573
= 100+ 573
= 57300
C- 8312+284+788+716
= (8312+284) + (788+716)
= 8596+ 1504
= 10,100
D- 125×44+56×125
= 125× (44+56)
= 125× 100
= 12500
Please mark me as brainlist
It took me alot of time to type sorry for that...
Find the volume of the solid lying between two planes perpendicular to the x-axis at x = −1 and x = 1. The cross sections perpendicular to the x-axis are squares whose diagonals run from y = x 2 to y = 2 − x 2
I've attached a sketch of one such cross section (light blue) of the solid (shown at x = 0). The planes x = ±1 are shown in gray, and the two parabolas are respectively represented by the blue and orange curves in the (x, y)-plane.
For every x in the interval [-1, 1], the corresponding cross section has a diagonal of length (2 - x ²) - x ² = 2 (1 - x ²). The diagonal of any square occurs in a ratio to its side length of √2 : 1, so the cross section has a side length of 2/√2 (1 - x ²) = √2 (1 - x ²), and hence an area of (√2 (1 - x ²))² = 2 (1 - x ²)².
The total volume of the solid is then given by the integral,
[tex]\displaystyle\int_{-1}^1 2(1-x^2)^2\,\mathrm dx = \int_{-1}^1 (2-4x^2+4x^4)\,\mathrm dx = \boxed{\frac{32}{15}}[/tex]
find the slope of the line passing through the points (6,-7) and (3,-3) .
Answer:
y2-y1 / x2-x1
-4/3
Step-by-step explanation:
Answer:
-4/3
Step-by-step explanation:
When given two points, the slope is found by
m = (y2-y1)/(x2-x1)
= (-3- -7)/(3 -6)
= (-3+7)/(3-6)
= 4/-3
= -4/3
PLEASE HELP! ILL MARK !!
Answer:
c) tan
Step-by-step explanation:
tan = Opposite side / close side
When close side = v and Opposite side = 2,8m
A gym at a school is being painted. The four walls and the ceiling are to be painted (but not the floor). The gym measures 100 ft x 65 ft x 25 ft. A 5 gallon can of paint costs $151.99 and covers 1750 ft. How many cans should be purchased? What will it cost to paint two coats for this gym (include HST)?
9514 1404 393
Answer:
17 cans$2,971.40Step-by-step explanation:
We assume ...
the 25' dimension is the wall heightthe HST rate is 15% (the paint is not purchased in Ontario)only full cans of paint can be purchasedThe wall area is the wall height times the perimeter of the room.
wall area = (25')(2(100' +65')) = 8250 ft²
The ceiling area is the product of length and width.
ceiling area = (100')(65') = 6500 ft²
Then the area to be painted with each coat is ...
painted area = wall area + ceiling area = (8250 +6500) ft² = 14750 ft²
Then two coats of paint will require sufficient paint to cover ...
(2 coats)×(14750 ft²/coat) = 29,500 ft²
__
If each can of paint covers 1750 ft², the number of cans required is ...
(29,500 ft²)/(1750 ft²/can) = 16.86 cans
17 cans must be purchased
__
The cost of 17 cans of paint with sales tax will be ...
(17 cans)($151.99/can)(1 +15%) = $2971.40
The triangles are similar by:
the ASA similarity theorem.
the SSS similarity theorem.
the AAS similarity theorem.
the AA similarity postulate.
the SAS similarity theorem.
Answer:
E. by the SAS similarity theorem.
Step-by-step explanation:
Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)
DC/BC = 240/150 = 1.6
EC/AC = 320/200 = 1.6
This implies that the ratio of two corresponding sides of both triangles are the same.
Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.
Use the given information to answer the questions and interpret key features. Use any method of graphing or solving. Round to one decimal place, if necessary.
The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x) -.25x^2 + 3.42, where x is the number of feet away from the golf club (along the ground) the ball is.
The ball starts ____ feet above the ground.
The ball reaches a maximum height of _____ feet at a horizontal distance of ____ feet away from the golf club 19 it was hit with
The ball returns to the ground at about ____ feet away.
HELP PLEASE! I tried everything from multiplying, dividing, adding, and subtracting but still no correct answer. Can someone please help me out here?
=============================================================
Explanation:
There are a few ways to do this.
One method involves drawing a horizontal line to form three rectangles as show below. Note the labels A,B,C.
Rectangle A in the upper left corner has area of base*height = 6*7 = 42 square miles. I'll let A = 42 since we'll use it later.Rectangle B is 20 miles across horizontally (base) and 2 miles tall vertically (height). The 2 miles is from 9-7 = 2. The area of rectangle B is 20*2 = 40 square miles. Let B = 40.Then finally, C = 28 because rectangle C is 4 miles across and 7 miles tall, so 4*7 = 28.Add up those three sub areas found: A+B+C = 42+40+28 = 110 square miles
----------------
There are other methods you could do. A second method is to draw two vertical lines to form 3 other rectangles, then add up the sub areas to get 110.
A third method is to draw a horizontal line across the top to form one large rectangle (20 mi by 9 mi) and subtract off the area of the 7 mi by 10 mi inner rectangle (the empty space), so you'd say 20*9 - 7*10 = 180-70 = 110
Is 237405 divisible by 11
Hello!
237405 | 11 ?
237405 : 11 = 21582,(27)
Answer: false
Good luck! :)
Hello,
Is 237405 divisible by 11?
a=sum of digits in rank odd : 5+4+3 = 12
b=sum of digits in rank even: 0+7+2=9
Calculate the difference: d=a-b=12-9 =3
d is not a multiple of 11 so, then number 237405 is not divisible by 11.
Pls help! Answer the question
===============================================================
Explanation:
The given stem and leaf plot leads to this data set
68,68,69,69
71,72,77,77,78,78
80,81
I broke it up to have each tens digit get its own row. That way it's bit more readable.
Unfortunately, the term "average" in math is very vague. It could mean one of the following
meanmedianmodeTo get the mean (specifically the arithmetic mean), we will add up the values and then divide by n = 12 because there are 12 values in the list above. Adding said values gets us
68+68+69+69+71+72+77+77+78+78+80+81 = 888
Dividing that over 12 then leads to 888/12 = 74
The arithmetic mean is 74.
-------------
To get the median, we would first sort the data set. Though that is already done for us. From here, we locate the middle-most item.
Since there are n = 12 items here, the middle item is between slot n/2 = 12/2 = 6 and slot 7
The values in slots 6 and 7 are 72 and 77 respectively. The midpoint of those values is (72+77)/2 = 149/2 = 74.5
The median is 74.5
-------------
The mode is possibly the quickest measure of center or average we can compute. We simply look at the value that shows up the most. In this case, the following values show up twice (which is the most frequent of all the values)
68697778They are all tied for the title of "mode". It's possible to have more than one mode, so we say the mode is the set {68,69,77,78}.
Due to the nature of multiple modes, the mode is often not a good measure of center (but it's still a possibility; especially for categorical data).
In this case, I think the mean or median is a better measure of center.
Since there aren't any outliers, the mean is the best measure of center in this case. Luckily, the mean and median (74 and 74.5 respectively) are fairly close to one another.
-------------
To summarize everything, the term "average" is too vague and it could refer to the mean, median or mode. In this problem, the mean is possibly the best measure of center since there aren't any outliers and the mode isn't one single value.
We found the following:
mean = 74median = 74.5mode = {68,69,77,78}It's very likely your teacher is wanting the mean.
98 POINTS!!!
Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Consider the graph of f(x) = 5x + 1. Explain how to find the average rate of change between x = 0 and x = 4. What is the average rate of change?
Answer:
The average rate of change is 5.
Step-by-step explanation:
First plug in the x values.
y=5x+1
=(0)5+1
=1
y=5x+1
=(4)5+1
=21
Average rate of change = the change in the output divided by the change in the input.
Output change: 21-1=20
Input change: 4-0=4
20/4=5
Find three consecutive odd integers whose sum is -213.
Answer:
-73, -71, -69
Step-by-step explanation:
Suppose the middle of the 3 integers is x.
(x-2)+(x)+(x+2)=-213
x-2+x+x+2=-213
3x=-213
x=-71
The integers are -69, -71, and -73
Answer:
-73,-71,-69
Step-by-step explanation:
Let x represent an odd interger
Odd intergers are serpated by the value of 2 so let the three consective intergers be represented by
[tex](x )+ (x + 2) +( x + 4)[/tex]
Set that equation equal to 213.
[tex]x + x + 2 + x + 4 = - 213[/tex]
[tex]3x + 6 = - 213[/tex]
[tex]3x = - 219[/tex]
[tex]x = - 73[/tex]
Plug -73 in the consective intergers expression.
[tex] - 73 + ( - 73 + 2) + ( - 73 + 4)[/tex]
So our three intergers are
[tex] - 73[/tex]
[tex] - 71[/tex]
[tex] - 69[/tex]
HELP PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
12
Step-by-step explanation:
10 - 1/2 x = 12-4/3x
60 - 3x = 72-2x
-12 = - x
What is the product of 2x(5+3)-4^2
Answer:
2×8-4^2
=16-16
=0
0 is the porduct
The mathematical expressions of the thermal conditions at the boundaries are called the _____ conditions.
Answer:
Heat flux boundary condition.
Step-by-step explanation:
Heat flux is boundary condition in positive x-direction. The specified temperature is constant and steady heat conduction. Temperature of exposed surface can be measured directly with the thermal condition expression.
please i need help with this rn
Hi there!
[tex]\large\boxed{f(9) = 12}[/tex]
Evaluating f(x) at x = 9 means we must use the piecewise function where x = 9 is included.
f(x) = 12 includes 9 because a "≤" is inclusive of the interval. Thus:
f(9) = 12
ANSWER ASAPPPP I WILL GIVE BRAINLIEST AND DROP POINTS AFTER
The function f(t) = t2 + 4t − 14 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for f(t). (2 points)
(10 points)
Answer:
A: f(t) = t2(4t) - 14
B: It is a maximum because it continues redistributing forever.
C: Assuming you plotted this on a 0/0 grid, your axis of symetry would be at 18/28
Hope this helps, please mark brainliest
Step-by-step explanation:
A: it is simple really, your just redistributing each T to itself, which is what makes a square / vertex.
Which rectangle has an area of 18 square units? On a coordinate plane, a rectangle is 2 units high and 7 units wide. On a coordinate plane, a rectangle is 2 units high and 6 units wide. On a coordinate plane, a rectangle is 3 units high and 5 units wide. On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
option "B"
You Welcome
Step-by-step explanation:
Suppose X has a normal distribution with mean 10.0 and standard deviation 5.0 what is the P(2.0
Answer:
what r u answers picks
Step-by-step explanation:
cant answer with out of t
Solve the two step equations
1. -3x - 4 = 23
2. x/2 - 12 = -4
3. 6a + ( -1) = 10
4. - ( x + 2 ) = 12
5. 7a + 12 = 10
6. -4 ( a + 2 ) = 12
Hello!
1) -3x - 4 = 23
-3x = 23 + 4
-3x = 27
x = 27 : (-3)
x = -9
2) x/2 - 12 = -4
x - 24 = -8
x = -8 + 24
x = 16
3) 6a + (-1) = 10
6a - 1 = 10
6a = 10 + 1
6a = 11
a = 11 : 6
a = 11/6
4) -(x + 2) = 12
x + 2 = -12
x = -12 - 2
x = -14
5) 7a + 12 = 10
7a = 10 - 12
7a = -2
a = -2 : 7
a = -2/7
6) -4(a + 2) = 12
a + 2 = -3
a = -3 - 2
a = -5
Good luck! :)
