Answer:
c. quadrilateral
Step-by-step explanation:
All of the sides are different lengths, so the quadrilateral cannot be a parallelogram, rhombus, or square.
Its best descriptor is parallelogram.
_____
A parallelogram has opposite sides parallel and congruent. A rhombus also has adjacent sides congruent. A square is a special case of rhombus in which the corner angles are right angles.
Question 8 The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by = (1.61 x 10'i +3.00 x 10°j)m and 7 = +(150î - 21ị) m The plane is most likely just touching down. in level flight in the air. taking off. ascending descending < Previous
The plane is most likely taking off.The two vectors provided, position and velocity, indicate that the plane is moving eastward with a velocity of 150 m/s and is ascending with a vertical velocity of 21m/s.
This indicates that the plane is taking off, and not just touching down, ascending, or in level flight.
The position and velocity vectors of the plane indicate that the plane is moving in an eastward direction with a velocity of 150 m/s, and is also ascending with a vertical velocity of 21 m/s. This indicates that the plane is taking off, and not just touching down, ascending, or in level flight. This means that the plane is most likely taking off from the origin and is in the process of gaining altitude.
the complete question is :
( figure attached below )
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2. Jamal makes $11.50 an hour and works 37.5 hours a week. Jamal's friend, Trenten,
makes $13.45 an hour and works 32 hours a week. Jamal thinks he should quit his job
and get a job with Trenten.
Does Jamal make more money than Trenten in a week?
O
O
CLEAR ALL
Yes
No
rechna notices her car driving at 40km/hr and knows that at that speed she will reach home in 2 hours if she wants to reach her home only in an half hour by what percentage does she need to increase her speed choose the correct answer 50%,100%,200%,400%
To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.
What is speed?Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.
To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.
If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.
By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.
Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.
The time taken to reach her destination while travelling at her initial speed is 2 hours.
To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.
Therefore, the percentage increase in speed
= (30/120) x 100
= 25%.
Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.
To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.
Therefore, the correct answer is 200%.
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Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answer:
3
Step-by-step explanation:
By going up 3 and right 1 you get 3/1, aka 3
The line of the equation is y=3x+2
A baker is making cakes for a big party. She uses 1/4 cup of oil for each cake. How many cakes can she make if she has a bottle of oil that has 6 cups in it? PRITTY PLEASE HELP!!! NOW (ASAP)
Answer:
24 Cups
Step-by-step explanation:
you just need to divide 6 by 1/4, whihc equals 24/1
PLEASE! help me I don't understand
The trapezoid ABCD have the measure of angles m∠A and m∠B equal to 79° and 66° respectively.
How to evaluate for the angle of the trapezoid.The sum of the interior angles of a quadrilateral is equal to 360°, so the sum of angles, m∠A, m∠B, m∠C, and m∠D is equal to 360°.
2x - 19 + x + 17 + 3x + 7 + 2x - 37 = 360°
8x - 32 = 360°
8x = 360° + 32°
8x = 392
x = 392/8 {divide through by 8}
x = 49
m∠A = 2(49) - 19 = 79°
m∠A = 49 + 17 = 66°
Therefore, the trapezoid ABCD have the measure of angles m∠A and m∠B equal to 79° and 66° respectively.
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Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time. When circuit switching is used, how many users can be supported? For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting. Suppose there are 120 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution.) Find the probability that there are 21 or more users transmitting simultaneously.
Answer:
The probability that a given user is transmitting is 0.1 = 10%.
The probability that at any given time, exactly n users are transmitting simultaneously is \(P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}\).
0.0048 = 0.48% probability that there are 21 or more users transmitting simultaneously.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
\(E(X) = np\)
The standard deviation of the binomial distribution is:
\(\sqrt{V(X)} = \sqrt{np(1-p)}\)
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).
Each user transmits only 10 percent of the time.
This means that \(p = 0.1\)
Find the probability that a given user is transmitting.
The probability that a given user is transmitting is 0.1 = 10%.
Suppose there are 120 users.
This means that \(n = 120\)
Find the probability that at any given time, exactly n users are transmitting simultaneously.
This is \(P(X = n)\).
This n is different from the n of total number of users(120 in this case) from the standard binomial formula. This is the number of successes, which is the equivalent of x. So
\(P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}\)
The probability that at any given time, exactly n users are transmitting simultaneously is \(P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}\)
Find the probability that there are 21 or more users transmitting simultaneously.
Now we use the binomial approximation to the normal. We have that:
\(\mu = E(X) = np = 120*0.1 = 12\)
\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.1*0.9} = 3.2863\)
Using continuity correction, this probability is \(P(X \geq 21 - 0.5) = P(X \geq 20.5)\), which is 1 subtracted by the pvalue of Z when X = 20.5. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{20.5 - 12}{3.2863}\)
\(Z = 2.59\)
\(Z = 2.59\) has a pvalue of 0.9952
1 - 0.9952 = 0.0048
0.0048 = 0.48% probability that there are 21 or more users transmitting simultaneously.
A scooter travels 30 feet in 2 seconds what is the spend of the scooter in feet per second
Answer:
15 feet per second
Step-by-step explanation:
30÷2=15
Answer:
15 feet per second.
Step-by-step explanation:
30 feet in 2 seconds.
30 = 2x
Divide both sides by 2 so u can leave the x alone, and it gives you 15 = x.
which sides form a right triangle
Answer:
c
Do i get brainliest lol
Last year, Josh biked b miles. This year, he biked 430 miles. Using b, write an expression for the total number of miles he biked.
Answer:430 + b
Step-by-step explanation:Last year he biked b miles. This year he biked 430 miles. Add the two to get your answer. Hope this helps!
Answer: b+430= total number of miles biked
Step-by-step explanation:
What other combinations of sides and angles do you think we can use to conclude that the triangles are congruent?
Ansi need this too
Step-by-step explanation:
3
2
1
-1
-2
-3
Determine the period.
2
4
6
8
10 12 14
The calculated period of the function is 12
How to determine the period of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
By definition, the period of the function is calculated as
Period = Difference between cycles or the length of one complete cycle
Using the above as a guide, we have the following:
Period = 13 - 1
Evaluate
Period = 12
Hence, the period of the function is 12
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A bag contains 8 red marbles, 4 white marbles, and 5 blue marbles. You draw one marble at random. Find Pared and blue) (1 point) 40 o 17 00 o SIAMO 0
Answer:
5/(8+4+5) = 5/17
Step-by-step explanation:
total has (8 red +4 white+5 blue)= 17
we looking for blue , so is 5.
5/17
Find the mean of 35,42,41,32,30
Answer:
The mean is 36
Step-by-step explanation:
The mean of these numbers is 36.
This just isn’t making any sense to me please help before 11pm
8 AB has endpoints A(-5, 0) and B(4, 3). CD has endpoints C(-3, 9) and
D(1, -3). The equations of the lines containing AB and CD are x - 3y = -5
and 3x + y = 0, respectively.
a. How could you quickly check that these equations are correct?
b. Verify that the lines are perpendicular.
c. Find the point of intersection of AB and CD by solving the system
of equations.
d. Find the midpoints of AB and CD. Compare your results with Part c.
e. What kind of quadrilateral is ACBD? Explain your reasoning.
Part (a)
To verify a point is on the line, we plug the coordinates into that equation. If we get a true result at the end, then we've confirmed the point is on that line.
For point A(-5,0) we have x = -5 and y = 0 pair up together. Let's plug these coordinates into x - 3y = -5 to get the following steps shown below.
x - 3y = -5
-5 - 3(0) = -5
-5 - 0 = -5
-5 = -5
We get a true statement at the end, which confirms x-3y = -5 is true when x = -5 and y = 0. Therefore, point A is definitely on the line x - 3y = -5
Repeat similar steps for B(4,3) to show that this point is also on x - 3y = -5
x - 3y = -5
4 - 3(3) = -5
4 - 9 = -5
-5 = -5
This confirms point B is also on this line.
We have confirmed line AB is x-3y = -5
I'll let you check to see if C(-3,9) and D(1,-3) are on the line 3x+y = 0. The steps will follow the same outline as shown above.
=========================================================
Part (b)
The standard form equation Ax+By = C has the slope m = -A/B, where B cannot be zero.
The equation x-3y = -5 has A = 1 and B = -3 to give us a slope of m = A/B = -1/(-3) = 1/3
Meanwhile the equation 3x+y = 0 gives the slope of A/B = -3/1 = -3
Notice that slopes 1/3 and -3 multiply to -1. This is one useful property of perpendicular lines. Their slopes always multiply to -1; this is assuming neither line is vertical, nor horizontal.
Put another way, the slopes are negative reciprocals of one another. We flip the fraction and flip the sign to go from 1/3 to -3, or vice versa.
I recommend using GeoGebra to plot out the points mentioned, and forming the lines AB and CD. This helps give a quick visual confirmation the lines are perpendicular.
----------
To summarize: We found the slopes of line AB and CD to be 1/3 and -3 respectively. The slopes multiply to -1 which is sufficient to conclude the lines are perpendicular.
=========================================================
Part (c)
We have this system of equations
x - 3y = -5
3x + y = 0
To represent lines AB and CD respectively.
Let's triple everything in line CD to go from 3x+y = 0 to 9x+3y = 0
Therefore, an equivalent system is this
x - 3y = -5
9x + 3y = 0
The first equation hasn't changed. After this point, we can see the y terms add to 0 since -3y+3y = 0y = 0. Therefore, the y terms cancel which lets us solve for x.
10x = -5
x = -5/10
x = -0.5
Then we use this to find y
x-3y = -5
-0.5-3y = -5
-3y = -5+0.5
-3y = -4.5
y = -4.5/(-3)
y = 1.5
The point of intersection is (-0.5, 1.5)
Notes:
-0.5 = -1/2
1.5 = 3/2
=========================================================
Part (d)
The x coordinates of points A and B are -5 and 4 in that order.
Add them up: -5+4 = -1
Divide the result in half: -1/2 = -0.5
This is the x coordinate of the midpoint of segment AB.
Repeat for the y coordinates
Add: 0+3 = 3
Divide in half: 3/2 = 1.5
The midpoint of segment AB is (-0.5, 1.5) which is exactly the result of part (c).
You should find that the midpoint of segment CD is also (-0.5, 1.5)
I'll let you do those steps.
=========================================================
Part (e)
Quadrilateral ACBD is a kite because of the perpendicular diagonals. This was confirmed in part (b).
The sides aren't all the same length (which you can confirm with the distance formula), which means we don't have a rhombus.
Answer:
a) See below.
b) See below.
\(\textsf{c)} \quad \left(-\dfrac{1}{2},\dfrac{3}{2}\right)\)
\(\begin{aligned}\textsf{d)} \quad \textsf{Midpoint of $\overline{AB}$}&=\left(-\dfrac{1}{2},\dfrac{3}{2}\right)\\ \textsf{Midpoint of $\overline{CD}$}&=(-1,3)\end{aligned}\)
e) Kite
Step-by-step explanation:
Given endpoints:
A = (-5, 0)B = (4, 3)C = (-3, 9)D = (1, -3)Given equations of the lines:
AB: x - 3y = -5CD: 3x + y = 0Part aTo quickly check that the given equations are correct, input the x-value of a point on the line into the given equation of the line containing that point. If the y-value corresponds with the y-value of the point, the equation is correct.
Using point A to check equation AB:
\(\begin{aligned}x=-5 \implies -5-3y&=-5\\-3y&=0\\y&=0\end{aligned}\)
As point A is (-5, 0), the equation is correct.
Using point C to check equation CD:
\(\begin{aligned}x=-3 \implies 3(-3)+y&=0\\-9+y&=0\\y&=9\end{aligned}\)
As point C is (-3, 9), the equation is correct.
Part bIf two lines are perpendicular, their slopes are negative reciprocals.
The negative reciprocal of a number is -1 divided by the number.
Rearrange each equation to slope-intercept form, then compare slopes.
\(\begin{aligned}\textsf{Line}\;AB: \quad x-3y&=-5\\-3y&=-x-5\\3y&=x+5\\y&=\dfrac{1}{3}x+\dfrac{5}{3}\end{aligned}\)
Therefore, the slope of line AB is ¹/₃.
\(\begin{aligned}\textsf{Line}\;CD: \quad 3x + y &= 0\\y&=-3x\end{aligned}\)
Therefore, the slope of line CD is -3.
\(\textsf{As} \;\dfrac{-1}{-3}=\dfrac{1}{3}, \textsf{ the slopes are negative reciprocals}.\)
Hence, the lines are perpendicular.
Part cTo find the point of intersection of AB and CD, solve the system of equations.
\(\begin{cases}x - 3y = -5\\3x + y = 0\end{cases}\)
Rearrange the second equation to isolate y:
\(\implies y=-3x\)
Substitute the found expression for y into the first equation and solve for x:
\(\implies x-3(-3x)=-5\)
\(\implies x+9x=-5\)
\(\implies 10x=-5\)
\(\implies x=-\dfrac{5}{10}\)
\(\implies x=-\dfrac{1}{2}\)
Substitute the found value of x into the expression for y and solve for y:
\(\implies y=-3\left(-\dfrac{1}{2}\right)\)
\(\implies y=\dfrac{3}{2}\)
Therefore, the solution to the system of equations is:
\(\left(-\dfrac{1}{2},\dfrac{3}{2}\right)\)
Part d\(\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}\)
\(\begin{aligned}\textsf{Midpoint of $\overline{AB}$}&=\left(\dfrac{x_B+x_A}{2},\dfrac{y_B+y_A}{2}\right)\\&=\left(\dfrac{4+(-5)}{2},\dfrac{3+0}{2}\right)\\&=\left(-\dfrac{1}{2},\dfrac{3}{2}\right)\end{aligned}\)
\(\begin{aligned}\textsf{Midpoint of $\overline{CD}$}&=\left(\dfrac{x_D+x_C}{2},\dfrac{y_D+y_C}{2}\right)\\&=\left(\dfrac{1+(-3)}{2},\dfrac{-3+9}{2}\right)\\&=\left(-1,3\right)\end{aligned}\)
The midpoint of line segment AB is the solution to the system of equations.
Part eQuadrilateral ABCD is a kite:
The diagonals of a kite are perpendicular to each other, as proven in part b.The longer diagonal of a kite bisects the shorter diagonal. As the midpoint of line segment AB is the same as the solution to the system of equations, this proves that the longer diagonal (CD) bisects the shorter diagonal (AB).The two diagonals of a kite are not of the same length. As the longer diagonal bisects the shorter diagonal, and the midpoints of line segments AB and CD are not the same, this proves that the diagonals are not the same length.Luca had a large container of yogurt with 1 and StartFraction 5 Over 8 EndFraction pounds of yogurt left in it. If a serving of yogurt is StartFraction 3 Over 8 EndFraction of a pound, to the nearest whole serving, how many servings of yogurt are in the container?
Answer:There are 4 serving in the container.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Took Edge 2020 Fraction Multiplication and Division Test
~~~~~~~~~~~`````````````````
Answer:
Step-by-step explanation:
(-3/4)x + 9 = (-1/2)x + 8
9 - 8 = (-1/2)x + (3/4)x
1 = (1/4)x
x = 4
y = (-3/4)4 + 9
y = -3 + 9
y = 6
Simplify 3(8x+2y)
A. 30x+y
B. 24x+2y
C. 24x+6y
D. 30xy
Answer:
The choose C. 24x+6y
Step-by-step explanation:
\(3(8x + 2y) = 24x + 6y\)
I hope I helped you^_^
Someone please help! No link answer please :(
Answer:
55 degrees (a)
Step-by-step explanation:
complementary means they equal 90 degrees
so 90-35= 55 degrees
a family rents a cottage for $79.95 a day for 7 days. about how much does the family pay for the cottage?
Answer:
$560
Step-by-step explanation:
Since the family rents a cottage for 7 days, 79.95 dollars each day, we multiply 79.95 by 7 and get 559.65. Since the question asks about how much does the family pay, we round 559.65 to get $560.
Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,-3). Find the coordinates ofvertex M.The coordinates are MOD.
Given data:
The coordinate of first vertex is J(1, 4).
The coordinate of second vertex is K(5, 3).
The coordinate of third vertex is L(6,-3).
Assume the coordinate of M is (x, y).
The diagonal of the parallelogram intersect at the mid point, the mid point of the diagonal JL is,
\(\begin{gathered} a=\frac{1+6}{2} \\ =\frac{7}{2} \\ b=\frac{4-3}{2} \\ =\frac{1}{2} \end{gathered}\)This is also the mid point of KM diagonal.
\(\begin{gathered} \frac{7}{2}=\frac{x+5}{2} \\ x=2 \\ \frac{1}{2}=\frac{y+3}{2} \\ y=-2 \end{gathered}\)Thus, the coordinate of M is (2, -2).
find the perimeter of OQR
The perimeter of the triangle OQR is 68 cm
How to determine the perimeter of the triangle OQRFrom the question, we have the following parameters that can be used in our computation:
Circles with the centers O, Q and R
When these centers are connected, the connection forms a triangle
The triangle OQR
Also from the question, we have the following values of radii
Radii = 8 cm, 11 cm and 15 cm
The perimeter of the triangle OQR is calculated as
Perimeter = Twice the sum of the radii
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 *(8 + 11 + 15)
Evaluate the sum
Perimeter = 2 * 34
Evaluate the products
Perimeter = 68
Hence, the perimeter is 68 cm
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On its own, 5 � � 5ab5, a, b is the product of
The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form
The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.
The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.
The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.
Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.
Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.
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The volume of a square pyramid with a height of 30 feet is 360 cubic feet. What are the side lengths of the base?
Justify your answer.
Answer:
对不起兄弟我不知道Duìbùqǐ xiōngdì wǒ bù zhīdàocyclone are also known as twisters,
helppppppppp plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
B
Step-by-step explanation:
simplify the following
(4x + 3) (5x + 2)
Answer:
20x^2+23x+6
Step-by-step explanation:
(4x+3)(5x+2)
(4x)(5x)+2(4x)+(5x)3+3(2)
20x^2+8x+15x+6
20x^2+23x+6
Hope that helps :)
Answer:
20x^2 + 23x + 6
Step-by-step explanation:
4x (5x + 2) + 3(5x + 2)
20x^2 + 8x + 15x + 6
20x^2 + 23x + 6
When an automobile travels uphill or downhill on a highway, it experiences a force due to gravity. This force in pounds is called grade resistance and is modeled by the equation below, where theta is the grade and W is the weight of the automobile.
F = Wsin theta
A 2710-lb car traveling uphill has a grade resistance of 160 lb. What is the angle of the grade?
theta =__.
(Type your answer in degrees. Round to the nearest hundredth as needed.)
Based on the calculations, the angle (θ) of the grade to the nearest hundredth is equal to 3.38 degrees.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In Science, grade resistance simply refers to force in pounds and can be modeled by the following equation:
F = Wsinθ
Where:
F represents the grade resistance or force in pounds.θ represents the grade W represents the weight of a physical object.Making theta (θ) the subject of formula, we have:
θ = sin⁻¹(F/W)
Substituting the given parameters into the formula, we have;
θ = sin⁻¹(160/2710)
θ = sin⁻¹(0.0590)
Theta, θ = 3.38 degrees.
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pliz solve this question
Answer:
i) (-3,0)ii) (0,5)Step-by-step explanation:
Coordinates of points
i) lies on x- axis with abscissa - 3
If it lies on x- axis, it has zero y-coordinateIt is (-3, 0)ii) lies on y-axis with ordinate 5
It lies on y-axis, it has zero x-coordinateIt is (0, 5)Suppose 1 in 5 (1/5) JWU students own their own car. If four students are randomly selected, what is the probability that all four own their car?
Answer:
1/625 = 0.0016
Step-by-step explanation:
update, oh sorry, this is about 4 picks and not 5.
so, it is 1/5⁴ = 1/625 = 0.0016
1 in 5 own their own car.
that is 20% or a chance of 1/5 = 0.2 of picking a student owning a car.
let's assume that the total number of students is large enough that each pick does not change the individual probabilities.
each event (picking a student and checking the ownership of a car) is independent and non-overlapping.
so, the probability that all 5 own a car is the chance of picking the 5th student owning a car AND all 4 previous student picks owning a car.
the probability that all 4 previous picks own a car is the chance of picking the fourth student owning a car AND all 3 previous student picks owning a car.
the probability that all 3 previous picks own a car is the chance of picking the third student owning a car AND all 2 previous student picks owning a car.
the probability that all 2 previous picks own a car is the chance of picking the second student owning a car AND the previous student pick owning a car.
the probability that the first student pick owns a car is 1/5 or 0.2
so, we have a clean
1/5×1/5×1/5×1/5×1/5 = 1/5⁵ probability = 1/3125 = 0.00032
The endpoints of diameter in a circle form an angle with point C. What is the measure of angle BCD?
Answer:
90 degrees
Explanation:
Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;
\(\therefore\angle BCD=90^{\circ}\)