Lines or points, are said to be coplanar when they line in the same plane.
Given the figure below:
Points A, B, C are coplanar points because they lie in one plane(plane x).
While noncoplanar points or lines do not lie in the same plane.
Given the figure below:
The points, A, B, C are noncoplanar because they do not lie in the same plane.
Two buckets, each with a different volume of water, start leaking water at the same time, but at different rates. Assume the volumes are changing linearly.
Bucket volume (mL)
Times: min Bucket A. Bucket B.
1 min 2,900 2,725
10 min 2,000 2,050
What was the difference, in milliliters, of their starting volumes? Do not include units in your answer.
The difference in starting Volume is 175 and after 8 minutes both buckets have same volume.
What is Rate of Change?The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time.
Given:
The leakage rate of A
= (2000- 2900)/ (1- 10)
= -900/ (9)
= -100 ml/min
The leakage rate of B
= (2050- 2725)/ (1- 10)
= -675/ (9)
= -75 ml/min
Now, 2900- 100t = 2725 - 75t
25t = 175
t= 7
So, when t= 1 min and after 7 min both buckets have the same volume of water.
So, t= 1+ 7 = 8 mins
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Twelve people ordered calculators. The least expensive was $5.95 and the most expensive was $12.95. Half ordered a $9.95 calculator. Select the best estimate of the amount spent on calculators.(1 point)
$125
$90
$160
$140
Answer:
Round up all costs
Least expensive: $6
Most expensive: $13
Half (half of 12 people is 6) ordered $10 calculators so 6x10=$60
Other half
(6+13)/2= $9.5 round up to $10 so 6x10=$60
$60 + 60=$120 best estimate $125
Step-by-step explanation:
The required, best estimate of the amount spent on calculators is $125. Option A is correct.
What is rounding of values?The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Since half of the twelve people ordered a calculator costing $9.95, there are 6 such people. Let the remaining 6 people have ordered the cheapest calculator, which costs $5.95. Then the total amount spent on calculators is:
6 x $5.95 + 6 x $9.95 = $35.70 + $59.70 = $95.40
However, we also need to take into account the possibility that some people may have ordered more expensive calculators. We know that the most expensive calculator costs $12.95, so let's assume that all 12 people ordered this calculator. Then the total amount spent on calculators would be:
12 x $12.95 = $155.40
Since the actual amount spent is somewhere between $95.40 and $155.40, the best estimate of the amount spent on calculators is around the midpoint of these values:
($95.40 + $155.40) / 2 = $125.40
Therefore, the best estimate of the amount spent on calculators is $125.
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34) A dice is rolled and a coin is tossed. What is the probability that the dice shows an even number and the coin shows tails?
===================================================
Work Shown:
A = probability of even number = 3/6 = 1/2
B = probability of tails = 1/2
C = probability events A and B happen simultaneously
C = A*B
C = (1/2)*(1/2)
C = 1/4
This is equivalent to 0.25 and 25%
0.5% of what number is 5?
Let us call the unknown number "unknown number". Then we know that 0.5% of the number is 5, in other words
\(\frac{0.5}{100}\times unknown\text{ number = 5}\)multiplying both sides by 100 gives
\(100\times\frac{0.5}{100}\times unknown\text{ number = 5}\times100\)\(0.5\times unknown\text{ number = }500\)and then dividing both sides by 0.5 gives
\(\frac{1}{0.5}\times0.5\times unknown\text{ number = }\frac{500}{0.5}\)\(unknown\text{ number = }\frac{500}{0.5}\)\(unknown\text{ number = }1000.\)Hence, 0.5% of 1000 is 5.
The activity fee for an arts camp is $250. If the activity fee increases by 20%, what will be the new activity
fee?
050
If activity fee for an arts camp is $250. If the activity fee increases by 20% then $300 will be the new activity fee.
What is Percentage?Percentage is a relative value indicating hundredth parts of any quantity.
Given activity fee for an arts camp is $250.
The activity fee increases by 20%.
We need to convert percent to decimal.
20%=20/100=0.2
We need to find what is 20% of $250.
So 0.2*250=50
So 50 is 20% of 250.
As activity fee increases by 20% the new fee will be
$250+$50=$300.
Therefore $300 will be the new activity fee.
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Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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The ratio using a colon is
82 and 23. Plzz. Help
Find the midpoint of the line segment connecting the two points (5,-3) (-4,7)
Answer:
The answer is
\(( \frac{1}{2} \: , \: 2)\)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\)where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(5,-3) and (-4,7)
The midpoint is
\(M = ( \frac{5 - 4}{2} , \: \frac{ - 3 + 7}{2} ) \\ = ( \frac{1}{2} \: , \: \frac{4}{2} )\)We have the final answer as
\(( \frac{1}{2} \: , \: 2)\)Hope this helps you
What is the answer?? 3(b-5)<-2b
Answer:
b < 3
Step-by-step explanation:
3 ( b - 5 ) < - 2b
3 ( b ) - 3 ( 5 ) < - 2b
3b - 15 < - 2b
3b + 2b < 15
5b < 15
b < 15/5
b < 3
Hello! Need some help on parts A and B, the rubric and question is attached. Thank you!
Part A.
We need to find cos 240º using the cosine sum identify.
This identity is given by the formula:
\(\cos(a+b)=\cos a\cos b-\sin a\sin b\)Now, we can write:
\(\cos240\degree=\cos(180\degree+60\degree)\)Then, we obtain:
\(\begin{gathered} \cos240\degree=\cos(180\degree+60\degree) \\ \\ \cos240\degree=\cos180\degree\cos60\degree-\sin180\degree\sin60\degree \\ \\ \cos240\degree=-1\cdot\frac{1}{2}-0\cdot\frac{\sqrt{3}}{2} \\ \\ \cos240\degree=-\frac{1}{2} \\ \\ \cos240\degree=-0.5 \end{gathered}\)Part B.
We need to find sin 240º using the sine difference identity.
This identity is given by:
\(\sin(a-b)=\sin a\cos b-\sin b\cos a\)We can write:
\(\sin240\degree=\sin(270\degree-30\degree)\)Then, we obtain:
\(\begin{gathered} \sin240\degree=\sin270\degree\cos30\degree-\sin30\degree\cos270\degree \\ \\ \sin240\degree=-1\cdot\frac{\sqrt{3}}{2}-\frac{1}{2}\cdot0 \\ \\ \sin240\degree=-\frac{\sqrt{3}}{2} \end{gathered}\)Answers
\(\begin{gathered} \text{ Part A. }\cos240\degree=-\frac{1}{2} \\ \\ \text{ Part B. }\sin240\degree=-\frac{\sqrt{3}}{2} \end{gathered}\)See attached for the problem
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
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HELPPP LAST ATTEMPT!!
help i’m so confused on what’s the difference in rays and lines
Rays: BD, AC, CA, AB. Lines: AC
How to differentiate between a ray and a line?A line is a straight path of points that has no beginning or end
A ray is a portion of a line which has one endpoint and extends forever in one direction
Let's put the definitions:
Note: the arrow is an indication no endpoint
So we have ray BD (it starts from the dot at B and the arrow shows it extends forever in the direction of D)
We have ray AC (it starts from the dot at A and the arrow shows it extends forever in the direction of C)
We also have ray CA (it starts from the dot at C and the arrow shows it extends forever in the direction of A)
Then ray AB (it starts from the dot at A and the arrow shows it extends forever in the direction of B)
Then line AC (it's bounded by 2 arrows, so it has no endpoint)
Therefore, the rays are BD, AC, CA and AB, and the line is AC. So the 1st option is the answer
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The double number line shows that the distance from the start of a hiking trail to a cave
entrance is 700 m.
Answer:
100, 25, 50
Step-by-step explanation:
\(700: \frac{700}{700} \times 100=100 \\ \\ 175: \frac{175}{700} \times 100=25 \\ \\ 350: \frac{350}{700} \times 100=50\)
procedures that help organize or describe data collected from a sample or a population are called . group of answer choices a. inferential statistics b. analytical variables c. dependent variables d. descriptive statistics
Procedures that help organize or describe data collected from a sample or a population are called Descriptive statistics.
Hence, option D is correct answer.
Descriptive statistics and examples: what are they?Data can be meaningfully and effectively described or summarised using descriptive statistics. For instance, knowing that everyone in our scenario wore blue shoes wouldn't be helpful. It would be helpful to know how evenly distributed their anxiety scores were. Measures of central tendency and measurements of variability make up descriptive statistics (spread).
The mean, median, and mode are measurements of central tendency, while the standard deviation, variance, minimum and maximum variables, kurtosis, and skewness are measures of variability.
Why do we utilise descriptive statistics?
In order to emphasise potential correlations between variables and to give basic information about the variables in a dataset, descriptive statistics can be helpful for both of these aims. The three most used descriptive statistics, which represent the following three variables: graphical/illustrative techniques.
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tell me the answer to pls 40 divided by m
The expression of the statement 40 divided by m is 40/m
How to determine the expressionFrom the question, we have the following parameters that can be used in our computation:
40 divided by m
The above statement is a mathematical statement
The mathematical statement can be expressed as an expression
Recall that, we have
40 divided by m
The term "divided by" means a quotient expression
To divide is represented as / i.e. quotient
So, the expression that represents 40 divided by m is 40/m
Hence, the complete expression is 40/m
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A poll found that 5% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 11 teenagers sleeping in each tent. Assume that these 11 teenagers are independent of each other. (Round your answers to four decimal places.)
a) Calculate the probability that at least one of them suffers from arachnophobia. - 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
c) Calculate the probability that at most 1 of them suffers from arachnophobia? What is C?
Answer:
a) Calculate the probability that at least one of them suffers from arachnophobia.
x = number of students suffering from arachnophobia
= P(x ≥ 1)
= 1 - P(x = 0)
= 1 - [0.05⁰ x (1 - 0.05)¹¹⁻⁰ ]
= 1 - (0.95)¹¹
= 0.4311999 = 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
= P(x = 2)
= (¹¹₂) x (0.05)² x (0.95)⁹
where ¹¹₂ = 11! / (2!9!) = (11 x 10) / (2 x 1) = 55
= 55 x 0.0025 x 0.630249409 = 0.086659293 = 0.0867
c) Calculate the probability that at most 1 of them suffers from arachnophobia?
P(x ≤ 1)
= P(x = 0) + P(x = 1)
= [(¹¹₀) x 0.05⁰ x 0.95¹¹] + [(¹¹₁) x 0.05¹ x 0.95¹⁰]
= (1 x 1 x 0.5688) + (11 x 0.05 x 0.598736939) = 0.5688 + 0.3293 = 0.8981
The radius of a circle is 8 cm. Find the circumference of the circle. Use 3.14
for Pi.
Answer:
50.24 cm
Step-by-step explanation:
For the easier computation of a circle's circumference, pi's value is taken to be 3.14 (π = 3.14). Let's see a few examples below to polish the concept of the circumference. Find the circumference of the circle with a radius of 8 cm. = 50.24 cm.
Answer:
Hello! answer: 50.24
Step-by-step explanation:
To find circumference you just have to do diameter × pi Since we arent given the diameter we have to figure it out BUT REMEMEBER diameter is just twice the radius so 8 × 2 = 16 so 16 is our diameter! Now we just multiply that by pi so 16 × 3.14 = 50.24 So 50.24 is the circumference! Hope this helps!
4) Amy traveled to the recycling plan
back. It took one hour less time to get
there than it did to get back. The average
speed on the trip there was 50 km/h. The
average speed on the way back was 40
km/h. How many hours did the trip there
take?
The time taken by Amy to travel to the place was t = 4 hours.
What is average speed?A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.
In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.
Let the time taken to get back = t + 1.
Now, it took one hour less time to get there thus time = t.
Now, average speed is given as:
average speed = total distance / total time
Substituting the values:
50 km/h = d / t
d = 50t .........(1)
40 km/h = d / (t + 1)
d = 40(t + 1)......(2)
Setting the value of d as equal we have:
50t = 40(t + 1)
50t = 40t + 40
10t = 40
t = 4
Hence, the time taken by Amy to travel to the place was t = 4 hours.
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Create polynomial functions using the given information:
A degree 9 polynomial with at max 5 positive zeros and at max 3 negative zeros
It's pretty much simple. Since we can factor a polynomial by its zeros, lets write one of degree nine :
X(X-1)(X-2)(X-3)(X-4)(X-5)(X+1)(X+2)(X+3)= X^9-9X^8+6X^7+126X^6-231X^5-441X^4+944X^3+324X^2-720X
This polynomial is of degree 9 and has exactly 5 strictly positive zeros : 1, 2, 3, 4, 5
And it has 3 negative zeros : - 1, -1, - 3
And it has 0 as a zero too.
There is also this one :
(X-1)(X-2)(X-3)(X-4)(X²+1)(X+1)(X+2)(X+3) = X^9-4X^8-13X^7+52X^6+35X^5-140X^4+13X^3-52X^2-36X+144
It has 4 positive zeros : 1, 2, 3, 4.
It has complex zeros : i and - i
3 negative zeros : - 1, - 2 , - 3
Good Luck
HELP ME ILL GIVE YOU BRAINLY IF U GET IT RIGHT AND EXPLAIN HOW PLEASE
Answer:
59
Step-by-step explanation:
A is a 90 degree angle, we can see the other side is 31
so we subtract 90-31=59
An angle measures 43.4° less than the measure of its complementary angle. What is the measure of each angle? please answer
The complementary angles are: 66.7° and 23.3°.
What are Complementary Angles?Two angles are said to be complementary if they both have a sum of 90 degrees when added.
Thus, we have the following:
One of the angles is represented as x.
Second angle = x - 43.4
Therefore:
x + x - 43.4 = 90
2x - 43.4 = 90
2x = 90 + 43.4
2x = 133.4
2x/2 = 133.4/2
x = 66.7°
First angle = x = 66.7°
Second angle = 66.7 - 43.4 = 23.3°
Therefore, the complementary angles are: 66.7° and 23.3°.
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Error Analysis:
Describe and correct the error made in the reasoning:
If a/5 = b/3, then 5/a = b/3 * x
The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.
To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:
a/5 = b/3
5/a = 3/b (multiplying both sides by 5/a)
5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)
5/a = 1
Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".
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2 planes leave the airport at the same time. their speeds are 140 mph and 170 mph and the angle between their courses is 25 degrees. how far apart are they after 2.5 hours
Answer:
183.27miles
Step-by-step explanation:
Note that we are considering two planes.
Plane 1
Speed = 140 mph
Time = 2.5 hours
Distance = ?
Speed = distance/time
140 mph = distance/2.5hrs
Distance = 140×2.5
= 350miles
Plane 2
Speed = 170 mph
Time = 2.5 hours
Distance = ?
Speed = distance/time
170 mph = distance/2.5hrs
Distance = 170×2.5
= 425miles
The angle between side is 25 degree
From cosine rule
c^2 = a^2 + b^2 − 2abcos(tetha)
Where a = 350
b = 425miles
c^2 = 350^2+425^2-2(350×425)(cos25)
c^2 = 122500+180625-297500(0.906)
c^2 = 303125-269535
c^2 = 33590
C = √33590
C = 183.27miles
The distance they flew apart after 2.5hrs is 183.27miles
The regression analysis below rotates the value of new car sales (In millions of dollars) and the independent variables "compensation" (in billions of dollars) and "employment level In the non-agricultural sector" (In thousands) for 44 consecutive quarters. Compare this multiple regression to the simple regressions with compensation and employment level of the respective Independent variables. Which of the following Is the likely culprit of the dramatic Increase In the p-value for employment level in the multiple regression?
1. Nonlinearity.
2. Heteroskedasticity.
3. Multicollinearity
4. None of the above.
Answer:
The answer is option (3) Multicollinearity
Kindly find an attached copy of a diagram to the given question
Step-by-step explanation:
Solution
The method that would be responsible for causing the p-value to increase or go higher is Multicollinearity.
Multicollinearity: Refers to a method where variables that are independent in a regression model are associated.
This correlation or association of variables tends to be a problem, because variables that are independent should remain independent.
a store is having a sale on trail mix and jelly beans. for 3 pounds of trail mix and 5 pounds of jelly beans the total cost is $21. for 6 pounds of trail mix and 2 pounds of jelly beans. the total cost $24 find the cost for each pound of trail mix and each pound of jelly beans
What would need to be used to show the triangles are congruent by AAS?
A: Nothing as the triangles can not be proved congruent by AAS.
B: Angles are congruent by vertical
angles.
C: Sides are congruent by the
reflexive property.
D: Angles are congruent by the
reflexive property.
Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given two triangles, Where the base of these triangles are same
And also given that the two angles are the same.
Since,
Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).
Thus, the third angle is also equal
From AAS:
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,
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can u pls and this question
Answer:
option a: -120
Step-by-step explanation:
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)
Step-by-step explanation:
We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:
\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)
Hi I am in need of help I am just trying to help my grandson but this math is so new I just don't understand it.
Thank you
Desperate grandma
Answer:
That image ma small
Step-by-step explanation:
Answer:
thank you for helping your grandson, you seem so nice. the photo's too tiny for me to see so is there another way you could crop it maybe
Step-by-step explanation: