Answer:
A. 5 seconds
Step-by-step explanation:
This quadratic (second degree polynomial) models parabolic motion. The vertex of the function is the projectile's max height. When the height of the object is 0 is when it hits the water. Set the function equal to 0 then and factor. I used the quadratic formula on my calculator, but if you need to, stick it into the quadratic formula and do it long hand. The values of x (which is actually time here) are -1 and 5. The two things in math that will never ever be negative are distance measurements and time, so we can disregard the -1 and say that it takes 5 seconds for the rocket to hit the water.
It would take 5 seconds for the rocket to hit the lake.
An equation is used to show the relationship between two or more variables and numbers.
Let g(x) represent the height of the rocket at time x seconds. Given that:
g(x)= -16x² + 64x + 80
The rocket touches the lake, when the height is 0. Hence:
0 = -16x² + 64x + 80
x = 5 seconds.
It would take 5 seconds for the rocket to hit the lake.
Find out more at: brainly.com/question/14114151
The sum of the probabilities of two complementary events is
Answer:
1
Step-by-step explanation:
"Complementary events" by definition have probabilities that total 1. An event is complementary to another if it occurs when the other one doesn't, and vice versa. That is, the outcome is always one or the other of the complementary outcomes--never both, never neither.
The sum of the probabilities of two complementary events is equal to 1.
Explanation:In probability theory, mutually exclusive events are events that cannot occur simultaneously. The sum of the probabilities of two complementary events is equal to 1. If events A and B are mutually exclusive, then the probability that at least one occurs (A or B) is equal to the sum of their individual probabilities (PA + PB).
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ6
Which shows the expressions rewritten with the least common denominator? 5x+3/3x and 7x/2x^2
Answer is B
Answer:
[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].
Step-by-step explanation:
The given expression is:
[tex]\frac{5x+3}{3x}[/tex] and [tex]\frac{7x}{3x^2}[/tex].
The least common denominator is: [tex]6x^2[/tex].
We collect LCM for the denominator to obtain;
[tex]\frac{2x(5x+3)}{6x^2}[/tex] and [tex]\frac{3(7x)}{6x^2}[/tex].
We multiply out the parenthesis to obtain;
[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].
Therefore the correct answer is B or the second option.
The graph shows the system of equations that can be used to solve x3+x2=x-1
Which statement describes the roots of this equation?
1 rational root and 2 complex roots
1 rational root and 2 irrational roots
3 irrational roots
3 rational roots
Answer:
A. 1 rational root and 2 complex roots
Step-by-step explanation:
The equation [tex]x^3+x^2=x-1[/tex] has the expression [tex]x^3+x^2[/tex] in the left side and the expression [tex]x-1[/tex] in the right side.
when ypu plot the graphs of the functions [tex]y=x^3+x^2[/tex] and [tex]y=x-1,[/tex] the number of intersection points shows the number of real solutions. These two graphs intersect only once, so the equation has one real solution. The third power equation should have three solutions, thus, two remaining solutions are complex.
Answer:
The answer is A
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Which equation matches the graph?
Answer: D) -2 |x| - 2
Step-by-step explanation:
A v-shaped graph is an absolute value graph.
The general form of an absolute value equation is: y = a |x - h| + k
where (h, k) represents the vertex and "a" represents the vertical stretch (aka slope).
The vertex of the given graph is (0, 2), however the graph is inverted (upside-down) which is a reflection across the x-axis. Therefore,
a = -2(h, k) = (0, -2) --> y = -2 |x| - 2Describe the set of numbers using interval notation.
x > 8 or x ≤ 2
A. [2, 8)
B. (–∞, 2] ∩ (8, ∞)
C.(–∞, 2] ∪ (8, ∞)
D. (–∞, 2) ∪ (8, ∞)
Answer:
Option C.(–∞, 2] ∪ (8, ∞)
Step-by-step explanation:
we know that
The solution of the inequality [tex]x > 8[/tex] Is the interval (8,∞)
The solution of the inequality [tex]x\leq 2[/tex] Is the interval (-∞,2]
therefore
The solution of [tex]x > 8[/tex] or [tex]x\leq 2[/tex] is equal to
(-∞,2] U (8,∞)
Final answer:
The correct interval notation for the inequality x > 8 or x ≤ 2 is (−∞, 2] ∪ (8, ∞), which represents all numbers less than or equal to 2 and all numbers greater than 8.
Explanation:
The question asks to describe the set of numbers using interval notation for the inequality x > 8 or x ≤ 2. Interval notation is a concise way of writing sets of numbers, using brackets to include endpoints and parentheses for exclusive limits. For an inequality like x > 8, we use the notation (8, ∞) to indicate all numbers greater than 8 but not including 8 itself. Likewise, for x ≤ 2, the interval notation is [−∞, 2] which includes all numbers less than or equal to 2. When we combine these with the union because of the 'or' condition, the correct interval notation is (−∞, 2] ∪ (8, ∞). Therefore, the correct answer is C. (8, ∞) indicates all the numbers larger than 8, and (−∞, 2] includes all the numbers up to and including 2.
Please help me out please
Answer:
262 m³
Step-by-step explanation:
The volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius of the base and h the height )
here diameter = 10 m, hence radius = 5 m
V = [tex]\frac{1}{3}[/tex]π × 5² × 10
= [tex]\frac{1}{3}[/tex] π × 250 = [tex]\frac{250\pi }{3}[/tex] ≈ 262 m³
Please please help me
Answer:
399.6 miles²
Step-by-step explanation:
The area (A) of the major sector is
A = area of circle × fraction of circle
= πr² × [tex]\frac{255}{360}[/tex]
= π × 13.4² × [tex]\frac{255}{360}[/tex]
= [tex]\frac{13.4^2(255)\pi }{360}[/tex] ≈ 399.6 miles²
Which correspondence is equivalent to Δ PQR↔ΔSTU?
A) Δ RQP ↔ ΔUTS?
B) Δ PRQ ↔ ΔTUS?
C) Δ RPQ ↔ ΔSUT?
D) Δ QRP ↔ ΔUST?
Answer:
A) Δ RQP ↔ ΔUTS
Step-by-step explanation:
Answer:
Option A) is correct
Step-by-step explanation:
Given : [tex]\Delta PQR \leftrightarrow \Delta STU[/tex]
We need to find which correspondence is equivalent to [tex]\Delta PQR \leftrightarrow \Delta STU[/tex] .
Solution :
One to one correspondence means measure of each side and each angle of one triangle is equal to the side and angle of the other triangle .
Here, we observe that option A) is equivalent to [tex]\Delta PQR \leftrightarrow \Delta STU[/tex] as explained below :
As per [tex]\Delta PQR \leftrightarrow \Delta STU[/tex] ,
[tex]PQ=ST\,,\,QR=TU\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]
Also, as per [tex]\Delta RQP \leftrightarrow \Delta UTS[/tex] , we have
[tex]PQ=ST\,,\,RQ=UT\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]
Therefore,
[tex]\Delta RQP \leftrightarrow \Delta UTS[/tex] is equivalent to [tex]\Delta PQR \leftrightarrow \Delta STU[/tex]
So, option A) is correct .
Marti has a jar of 161 coins consisting of pennies and nickels. The total value of the coins is $3.09. How many nickels does Marti have in the jar
Okay, so there are nickels and pennies in this jar.
So, let's call the number of pennies X
Since there are 161 coins altogether, the number of nickels is (161 - X)
So now we solve the equation:
.01X + .05(161 - X) = 3.09
.01X + 8.05 - .05X = 3. 09
4.96 = .04X
124 = X
So, there are 124 pennies
Therefore, there are 161 - 124 = 37 nickels
Let's check our answer:
124 x .01 + 37x .05 = 1.24 + 1.85 = 3.09
It works!
I think it is 18
nickels for $3.09
Kim has $1.65 in nickels, dimes and quarters. She has 10 coins all together and the number of quarters is equal to the number of nickels and dimes combined. Haw many of each coin does she have?
3 nickels, 2 dimes, 5 quarters
3 nickels, 2 dimes, 2 quarters
2 nickels, 3 dimes, 5 quarters
3 nickels, 5 dimes, 2 quarters
Answer:
2 nickels 3 dimes 5 quarters
Step-by-step explanation:
We know it cannot be the second option because there are only 7 coins and Kim has 10. It also cannot be the first option because the coins add up to $1.60, and Kim has $1.65. It could not be the last option either because the coins add up to $1.15, and Kim has $1.65.
Answer: Third option
Why? The third option has a total of $1.65, which is what Kim has. There are 10 coins all together, which is also what Kim has. And the number of nickels and dimes combined (5) is equal to the number of quarters (5).
Suppose you are a designer making the traffic sign below.
1. What is the sum of the interior angles of the equilateral triangle?
2. What is the measure of ∠N?
3. What is the measure of ∠M? Explain your reasoning.
4. What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X? Explain your reasoning.
Answer:
Part 1) The sum of the interior angles is equal to 180 degrees
Part 2) The measure of angle N is ∠N=60°
Part 3) The measure of angle M is ∠M=120°
Part 4) The sum of the the exterior angles is 360°
Step-by-step explanation:
Part 1) What is the sum of the interior angles of the equilateral triangle?
we know that
The sum of the interior angles of any triangle must be equal to 180 degrees
Part 2) What is the measure of ∠N?
we know that
An equilateral triangle has three equal sides and three equal internal angles ( each internal angle measure 60 degrees)
so
In this problem
∠N=60°
Part 3) What is the measure of ∠M? Explain your reasoning.
we know that
∠M+∠N=180° -----> by supplementary angles (linear pair)
we have
∠N=60°
substitute
∠M+60°=180°
∠M=180°-60°=120°
Part 4) What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X?
we know that
The sum of the the exterior angles of any polygon is equal to 360 degrees
In this problem
we have
∠M=∠R=∠X=120°
so
∠M+∠R+∠X=120°+120°+120°=360°
Answer:
Step-by-step explanation:
The sum of the interior angles is equal to 180 degrees. The measure of angle N is ∠N=60°. The measure of angle M is ∠M=120°. The sum of the the exterior angles is 360°
Find the solution(s) to 2x2 + 5x – 3 = 0.
Check all that apply.
A.x = – 1/2
x = 2
C.x = 1/2
x = 3
E.x = –3
Answer:
C and E
Step-by-step explanation:
Let's factor this the "old fashioned" way. The standard form of a quadratic is
[tex]y=ax^2+bx+c[/tex]
If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.
We need to find the product of our a and c. Our a = 2 and our c = -3. So that gives us a -6. Now we have to find the factors of 6 (the negative right now doesn't matter so much). The factors of 6 are 1, 6 and 2, 3. Both of those possibilities will work to give us a +5, which is the linear term. Puttng in the 2, 3 first:
[tex]0=2x^2+3x+2x-3[/tex]
Now group the terms together into groups of 2:
[tex]0=(2x^2+3x)+(2x-3)[/tex]
The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same. In the first term we can factor out a common x, and in the second term, the only thing common is a 1. So that looks like this:
[tex]x(2x+3)+1(2x-3)[/tex]
What's inside those parenthesis are not actually identical, so 2 and 3 won't work. Lets try 1 and 6. For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative. So let's try that:
[tex](2x^2+6x)+(-x-3)[/tex]
In the first term we can factor out the common 2x and in the second term we can factor out the common -1:
2x(x + 3) - 1(x + 3)
Now what's common is (x + 3), so we can factor THAT out and what is left over is 2x - 1:
(x + 3)(2x - 1) = 0
If x + 3 = 0, then x = -3
and if 2x - 1 = 0, then 2x = 1 and x = 1/2
I cleaned 6/9 of my room, and my friend cleaned 2/9 of my room. How much of my room do we still have to clean?
Answer:
1/9
Step-by-step explanation:
6/9+ 2/9= 8/9
then we subtract 8/9 from 1
1-8/9
then we have to convert 1 into a fraction
9/9-8/9
this leaves 1/9
Answer:
1/9
Step-by-step explanation:
We can make an equation that looks like this:
2/9+6/9+x/9=9/9
Let's cancel out the denominator:
2+6+x=9
Then combine like terms:
8+x=9
Then solve for x:
x=1
Then add in the denominator we canceled out:
x=1/9
Hope I helped, soz if I'm wrong!
~Potato.
Copyright Potato 2019.
P.S. Why would your friend clean your room lel :P
These are two angles that add up to 180° that share a common vertex. What do you call these angles?
Answer:
• linear angles
• supplementary angles (all linear angles are supplementary)
Step-by-step explanation:
If the angles share a side and are measured in opposite directions from that side, the non-common edges of these angles form a straight line, so these angles are sometimes called "linear" angles.
Since their sum is 180°, they are always "supplementary" angles. (Supplementary angles need not share a vertex or a side.)
A manufacturer finds that 10% of the flashlights in a sample are defective. Predict how many defective flashlights there will be in a shipment of 4,000 flashlights.
A.
4 flashlights
B.
40 flashlights *
C.
400 flashlights
please help quick
Answer:
400
Step-by-step explanation:
Just take 10% of 4,000 flashlights. 400 flashlights are likely to be defective.
A 15 ft ladder makes a 52° angle with the ground. How far will the top of the ladder be above the ground.
Answer:
11.820 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...
sin(52°) = height/(15 ft)
Multiplying by the denominator gives you ...
height = (15 ft)·sin(52°) ≈ 11.820 ft
___
You may need to round this number appropriately.
A number from 1 to 10 is chosen at random.
What is the probability of choosing a 4 or an odd number.
3/10
1/5
1/2
3/5
The answer is D 3/5
if you can pick 4 and odd it will be 1,3,4,5,7,9
that is 6 numbers, 3/5 5*2 is 10 so 3*2 is 6
3/5
What values for theta (0≤theta≤2π) cos theta- tan theta cos theta=0?
ANSWER
[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]
EXPLANATION
We want to solve the equation;
[tex] \cos( \theta) - \tan( \theta) \cos( \theta) = 0[/tex]
We factor to get:
[tex] \cos\theta(1 - \tan\theta) = 0[/tex]
Either
[tex]\cos\theta = 0[/tex]
Or
[tex]1 - \tan \theta = 0[/tex]
For
[tex]\cos\theta = 0[/tex]
We gave
[tex] \theta = \frac{\pi}{2} ,\frac{3\pi}{2}[/tex]
When
[tex]\tan \theta = 1[/tex]
Then,
[tex] \theta = \frac{\pi}{4} , \frac{5\pi}{4} [/tex]
Therefore the solution on the interval
[tex]0 \leqslant \theta \: \leqslant 2\pi[/tex]
is
[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]
Solve the equation for x. 4x + 7 = 31
4x + 7 = 31
-7 -7
4x = 24
/4 /4
x = 6 (Answer)
Prove.
4(6) + 7 = 31
24 + 7 = 31
31 = 31
True.
The solution to the given equation 4x + 7 = 31 is x = 6, which is determined by subtraction.
The equation is given as follows:
4x + 7 = 31
To solve the equation 4x + 7 = 31 for x, we want to isolate the variable x on one side of the equation.
First, we can begin by subtracting 7 from both sides of the equation:
4x + 7 - 7 = 31 - 7
Simplifying, we get:
4x = 24
Next, we want to isolate x, so we divide both sides of the equation by 4:
4x/4 = 24/4
This simplifies to:
x = 6
Therefore, the solution to the equation 4x + 7 = 31 is x = 6.
Learn more about the solution to the equation here:
brainly.com/question/15272274
#SPJ2
Jessica wants to take three books on vacation with her. She has five books to choose from. How many possible combinations of three books could she take on vacation?
It would have to be 3/5
Answer:
We use the combination formula:
combinations = n! / r! * (n-r)!
n = 5 and r =3
combinations = 5! / 3! * 2!
combinations = 5! / 12
combinations = 5 * 4 * 3 * 2 * 1 / 12
combinations = 5 * 2 = 10
Step-by-step explanation:
A diameter of a circle has end points P(-10,-2) And Q(4,6)
A. Find the center of the circle
B. Find the radius.if your answer is not an integer express it in a radical form.
C.write and equation for the circle
GIVING BRAINLIEST
Answer:
Step-by-step explanation:
A]
The center is the average values of the 2 endpoints (which is also the diameter).
x:(-10 + 4)/2 = -6/2 = -3
y:(-2 + 6)/2 = 4/2 = 2
Center(-3,2)
B]
The radius is the distance from the center to one of the end points.
r^2 = (-3 - 4)^2 + (2 - 6)^2
r^2 = (-7)^2 + (-4)^2
r^2 = 49 + 16
r^2 = 65
r = sqrt(65)
C]
(x + 3)^2 + (y - 2)^2 = 65
Graph
The graph has been included so that you can see that the center I have calculated is between (-10,-2) and (4,6)
Further, it shows the the circle goes the two end points of the diameter.
If m<a = 2 · m<b, m<c = 60°, and the right angles are labeled in the figure, which of the following produce an acute angle? Select all that apply.
A. m<c
B. m<a + m<c
C. m<b + m<d
D. m<a + m<d
E. m<c+ m<d
Answer: m<c, m<b + m<d
Step-by-step explanation: If you use the given information, you can find that
m<a = 60
m<b = 30
m<c = 60
m<d = 30
The angles that will produce an acute angle in the given diagram are; m<c, and m<b + m<d.
What is acute angle?Acute angles are angles that measure less than 90 degrees.
From the image we observe the following;
m<a = 60
m<b = 30
m<c = 60
m<d = 30
Thus, the angles that will produce an acute angle in the given diagram are; m<c, and m<b + m<d.
Learn more about acute angles here: https://brainly.com/question/6979153
Please help me out.........
Answer:
This is the answer : (answer given in the picture)
Answer:
vertex = (- 3, 24)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0, then
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = - x² - 6x + 15 ← is in standard form
with a = - 1, b = - 6, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-6}{-2}[/tex] = - 3
Substitute x = - 3 into the function for corresponding value of y
y = - (- 3)² - 6(- 3) + 15 = - 9 + 18 + 15 = 24
vertex = (- 3, 24)
What is the answer to life the universe, and ari waters his garden every 3 days and weeds it every Saturday. ari watered and weeded his garden this Saturday. how many days will it be until ari again waters both waters and weeds his garden on the same day?
Ari will water and weed his garden on the same day again in 21 days by finding the Least Common Multiple (LCM) of the watering and weeding cycles, which are 3 and 7 days respectively.
Explanation:The question asks us to find out how many days will pass until Ari once again waters and weeds his garden on the same day. This problem can be solved by finding the Least Common Multiple (LCM) of the watering and weeding cycles. Ari waters his garden every 3 days and weeds it every Saturday, which suggests a 7-day cycle for weeding.
To find the LCM of 3 and 7, we list the multiples of each number:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...
The smallest multiple they both share is 21. Therefore, Ari will water and weed his garden on the same day again in 21 days.
Learn more about Least Common Multiple here:https://brainly.com/question/30060162
#SPJ2
Solve the following equation for x.
225 = 27x -18
Answer:
Step by step explanation
the equation is 225=27x-18
the first step is to add the 18 to the other side to get
243=27x
now divide by 27 on both sides
243/27=27x/27
solve to get
9=x
HELP URGENT PLEASE
20 POINTS
A) How long does it take for it to rotate 225 degrees?
B) How long does it take to rotate 9π radians?
C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?
Answer:
A)
15 hours
B)
108 hours
C)
2074.29 miles
Step-by-step explanation:
Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.
A)
In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;
(24/360) = (x/225)
solving for x;
x = (24/360) * 225 = 15 hours
B)
In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;
(24/2π radians) = (x/9π radians)
Solving for x;
x = (24/2π radians)*9π radians = 108 hours
C)
If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;
circumference = 2*π*R = π*D
= 7920*3.142
= 24891.43 miles
Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;
(24891.43miles)/(24 hours) = 1037.14 miles/hr
The distance covered by the point in 2 hours will thus be;
1037.14 * 2 = 2074.29 miles
Let u = <7, -3>, v = <-9, 5>. Find 4u - 3v.
a. <55, -27>
b. <1, 3>
c. <16, 12>
d. <-8, -6>
Answer:
a.<55, -27>
Step-by-step explanation:
The given vectors are u = <7, -3>, v = <-9, 5>.
We want to find 4u - 3v.
We substitute the vectors and multiply by the scalars.
4u - 3v=4<7, -3>-3 <-9, 5>.
4u - 3v=<28, -12>- <-27, 15>.
4u - 3v=<28--27, -12-15>
4u - 3v=<55, -27>
Jamie evaluated this expression. step 1: step 2: step 3: 26 step 4: 64 Analyze the steps Jamie applied to evaluate the expression. Which rule of exponents was applied in each step? Step 1: Step 2: Step 3:
Answer:
step one: product of powers
step 2:power of powers
step 3: quotient of powers
Step-by-step explanation:
The rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.
What is the definition of arithmetic operation?Arithmetic is a branch of mathematics that studies numbers and the many operations that may be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.
The given expression is;
[tex]\frac{(2)^3(2)^4}{2^{10}}[/tex]
Step 1; Multiplication rule of exponents;
[tex]\frac{(2)^3(2)^4}{2^{10}} \\\\ \frac{2^{3+4}}{2^{10}} \\\\\frac{2^7}{2^{10}}[/tex]
Step 2;Division rule of exponents;
[tex]\frac{2^7}{2{10}} \\\\ (2)^{7-10}\\\\ (2)^{-3}[/tex]
Step 2;Inverse rule of exponents;
[tex](2)^{-3}\\\\ \frac{1}{2^3} \\\\\frac{1}{8}[/tex]
Hence, the rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.
To learn more about the arithmetic operations, refer:
brainly.com/question/20595275
#SPJ2
There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose paintings? A. 7920 B. 330 C.44 D. 121
Answer:
B. 330
Step-by-step explanation:
The question indicates the order doesn't matter, so it's a combination and not a permutation.
The combinations are calculated using this formula:
[tex]C(n,r) = \frac{n!}{r! (n-r)!}[/tex]
In this case we have a population of 11 (n = 11) and a selection of 4 (r=4), so...
[tex]C(11,4) = \frac{11!}{4! (11-4)!} = 330[/tex]
So, there are 330 different combinations that can be made of 4 paintings out of a selection of 11.
Answer:
The correct answer is option B. 330
Step-by-step explanation:
It is given that,There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window.
To find the possible ways
There are total 11 paintings.
We have to choose 4 of them
Possible number of ways = 11C₄
= (11 * 10 * 9 )/(1 * 2* 3 * 4)
= 330 ways
Therefore the correct answer is option B. 330
1. Solve |x| < 13
A) {-13, 13}
B) {x|-13 < x < 13}
C) {x|x < -13 or x > 13}
2. |x| > 4
A) {-4, 4}
B) {x|-4 < x < 4}
C) {x|x < -4 or x > 4}
Answer:
B) {x|-13 < x < 13}
C) {x|x < -4 or x > 4}
Step-by-step explanation:
Given in the question,
1.|x| < 13Remove the absolute value term.
If your absolute value is less than a number, then set up a three-part compound inequality that looks like this:
-(number on other side) < (quantity inside absolute value) < (number on other side)
-13 < x < 13
2.|x| > 4
If your absolute value is greater than a number, then set up an "or" compound inequality that looks like this:
(quantity inside absolute value) < -(number on other side)
OR
(quantity inside absolute value) > (number on other side)
x < - 4 or x > 4