bag contains one red pen, four black pens, and three blue pens. Two pens are randomly chosen from the bag and
are not replaced.
To the nearest hundredth, what is the probability that a black pen IS chosen first and then another black pen is
chosen?
ANSWER AT THE BOTTOM
Question:
There is a bag with 1 red pen, 4 black pens, and 3 blue pens. If 2 pens are chosen from the bag without replacement, what is the probability that you chose 2 black pens.
Explanation:
Right now there are a total of 8 pens. 4 of them are black. So, the probability of choosing a black pen right now is 4/8, or 1/2.
Lets assume we picked a pen and got black.
Now there are only 7 pens in the bag, and only 3 of them are black. The probability of choosing a black pen right now is 3/7.
So on the first draw, the probability is 1/2
And on the second draw, the probability is 3/7
To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.
For example, if we wanted to find the probability of rolling two 6's in a row on a dice, we would need to mutiply the individual probability together. The probability of rolling one 6 is 1/6, so the probability of rolling two 6's in a row is 1/6 MULTIPLIED BY 1/6, which is 1/36.
The probability of rolling two 6's in a row is 1/36.
Lets apply the same principle to our situation right now.
So on the first draw, the probability is 1/2
And on the second draw, the probability is 3/7
1/2 MULTIPLIED BY 3/7 = 3/14
3/14 in decimal form is 0.21
ANSWER:
0.21, OR 21%
Help needed
a hunid points :)
Answer:
the answer is C, 5a^6b
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
One leg of a right triangle is 2 inches and the hypotenuse is 6 inches.
Find the area of the triangle.
_[tex]\sqrt{x} \\[/tex]
We can see that the area of the triangle is: 5.65in².
What is a triangle?A triangle is actually known to be a shape that has three sides, three angles and three vertices. It's also known as a plane shape.
In order to find the area of the triangle, we will use Pythagorean Theorem: c² = a² + b².
Where c = hypotenuse = 6in.
b = 2in.
6² = a² + 2²
36 = a² + 4
a² = 36 - 4 = 32
a = √32
Area of the triangle = ½ × base × height.
Where base = √32
height = 2
Thus: A = ½ × √32 × 2
A = √32 = 5.65in².
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Situation:
A 45 gram sample of a substance that's
used to sterilize surgical instruments has
a k-value of 0.15.
N = Noe kt
No initial mass (at time t = 0)
N= mass at time t
k= a positive constant that depends on
the substance itself and on the units
used to measure time
t-time, in days
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Enter the correct answer.
DONE
+?
The substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We have an exponential function:
[tex]\rm N = N_oe^{-kt}[/tex]
Plug N = N⁰/2
[tex]\rm N_o/2 = N_oe^{-kt}[/tex]
[tex]\rm \dfrac{1}{2} = e^{-0.15t}[/tex]
Solving for t:
t = 4.62≈ 4.7 days
Thus, the substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15
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the bearing of two points x and y from z are 45° and 135° respectively . if |zx|=8cm and |zy|=6cm, find |xy|.
Answer:
[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].
Step-by-step explanation:
Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.
Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:
[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].
Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:
[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].
a-3/7 devided by 3-a/21
The answer is pretty simple but I put it in a picture below
The lengths represented by BE, EC, and CD on the diagram were determined to be 1800 feet, 200 feet, and 500 feet,
What is the length, in feet, across the lake?
Fill in the blank by entering only a number as your answer.
The length of lake is 4500 feet.
What is Triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.
Here, In ΔABE and ΔDCE
∠ABE = ∠DCE { each 90⁰ }
∠AEB = ∠CED { vertically opposite angle}
By AA similarity, we get
ΔABE ≈ ΔDCE
Now, AB/CD = BE/CE
AB/500 = 1800/200
AB/500 = 9
AB = 9 X 500
AB = 4500 feet.
Thus, the length of lake is 4500 feet.
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What is the sum? startfraction 2 over x squared endfraction startfraction 4 over x squared endfraction
Answer:
6/x²
Step-by-step explanation:
Rational expressions are added the same way numerical fractions are added. Their sum is the quotient of the sum of numerators, and the common denominator.
__
fraction sumThe given fractions already have the same denominator, so we simply add their numerators.
[tex]\dfrac{2}{x^2}+\dfrac{4}{x^2}=\dfrac{2+4}{x^2}=\boxed{\dfrac{6}{x^2}}[/tex]
Help please asap points an brainlist
Can someone help me please and thxxx
Answer:
C
Step-by-step explanation:
cos 30=12/x
[tex]x = 8 \sqrt{3} [/tex]
cos60=y/x
[tex]y =4 \sqrt{3} [/tex]
Answer:
x = [tex]8\sqrt{3}[/tex]
y = [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
• tan 60° = 12/ y [tan θ = opposite/ adjacent]
y = 12/ tan 60°
y = [tex]4\sqrt{3}[/tex]
• x² = y² + 12² [Pythagoras's theorem]
x² = ( [tex]4\sqrt{3}[/tex] )² + 144
x = [tex]\sqrt{(4\sqrt{3})^{2} \space\ + \space\ 144}[/tex]
x = [tex]8\sqrt{3}[/tex]
32 out of 40 kids said they prefer summer over winter. 25 out of 32 adults said they prefer summer. Did a larger percentage of kids or adults prefer summer.
Answer:
Larger percentage of kids
Step-by-step explanation:
Kids: 32/40 = 4/5
Adults: 25/32 = 5/8
4/5 > 5/8
1 − 2 + 3 −... + 99
Please solve!
Answer:
50
Step-by-step explanation:
So you can think of this by grouping it like this:
(1-2) + (3-4) + (5-6) + ... + (97-98) + 99
which is equal to: (-1) + (-1) + (-1)... + (-1) + 99
(each group is equal to -1, and 99 won't have a pair since it's the last one)
then, find how many groups of -1 there are:
the groups start at 1 and end at 98, but there are two in each group, so 98/2 = 49. this means there are 49 groups.
so now, you know that there are 49 -1s, so 49 * (-1) = -49.
finally, you can't forget the extra 99 that didn't have a pair, so -49 + 99 = 50.
If point d is placed on AC how will the measure of DAB relate to the measure of CAB
Angle DAB will be equal to angle CAB
What is trigonometry?
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
AC is a straight line and forms one of the sides of the triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.
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Justin and elena each launched a toy rocket into the air. the height of justin’s rocket is modeled by the equation h = –16t2 60t 2. elena launched his rocket from the same position, but with an initial velocity double that of justin’s. which equation best models the height of elena’s rocket? h(t) = at2 vt h0 h = –16t2 60t 4 h = –32t2 120t 4 h = –32t2 60t 2 h = –16t2 120t 2
HELP PLSSSSSS hdghgdhj
Answer:
A
Step-by-step explanation:
Use the Pythagorean Theorem: a^2 + b^2 = c^2
The cable will be the hypotenuse, so c = 11.3 m
One leg is the distance of the anchor, so a = 4.2 m
(4.2)^2 + b^2 = (11.3)^2
17.64 + b^2 = 127.69
Subtract 17.64 from both sides
b^2 = 110.05
Square root both sides
b = ~10.5 m
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?
There are 16 cups in a gallon.
Answer:
D
Hope this helps!
In a group of 20 pupils, 3 play the flute only.
6 play the piano only.
6 play both instruments.
A student is chosen at random.
What is the probability the student plays neither instrument?
Please answer in fractional form!!
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given information:
Total number of pupils = 203 pupils play the flute6 pupils play the piano only6 play both instrumentsWe can assume that 3 pupils play the flute only as we have also been told that 6 pupils play both instruments.
To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:
⇒ total number of pupils - pupils who play instruments
⇒ 20 - (3 + 6 + 6)
⇒ 20 - 15
⇒ 5
Therefore, 5 pupils do not play the piano and/or flute.
To calculate probability:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore:
[tex]\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}[/tex]
A sign on a roadway at the top of a mountain indicates that for the next 4 miles, the grade is 10.5°. Find the change in elevation over that distance for a car descending the mountain. Round to the nearest hundredth.
the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).
How to find the change in elevation?
To do this, we can think on the situation as a right triangle, where the hypotenuse is 4 miles, the angle that we look at measures 10.5°, and the change in elevation (let's call it x) will be the opposite cathetus to that angle.
Then we can use the relation:
Sin(a) = (opposite cathetus)/(hypotenuse)
Replacing what we know, we get:
sin(10.5°) = x/4mi
x = sin(10.5°)*4mi = 0.73mi
So the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).
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Probability and Two-Way Tables
Answer:
the answer are A and Y , B and X.
A and X are two independent events , Option A is the correct answer.
When is Probability ?Probability is the likelihood of an event to happen
A two way table is given
The two events will be independent when
If A is the first event and B is the second event , then
P(A) = P(A|B)
Here the P(A) = 30/100 = 0.3
P(B) = 20/100 = 0.2
P(A|X) = 15/50 = 0.3
P(A) = P(A|X)
Therefore A and X are two independent events , Option A is the correct answer.
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The question is the image below.
Answer:
Hence - 7 is the answer
Pls mark me brainliest plss
What is the polynomial function of lowest degree with lead coefficient 1 and roots i, –2, and 2?
Answer:
x^4 - 3x^2 - 4.
Step-by-step explanation:
Imaginary roots occur as conjugate pairs so a 4th roots is -i.
So in factor form we have:
f(x) = (x - 2)(x + 2)(x - i)x + i)
= (x^2 + 1)(x - 2)(x + 2)
= (x^2 + 1)(x^2 - 4)
= x^4 - 3x^2 - 4.
Answer:b.f(x) = x^4 – 3x^2 – 4
Step-by-step explanation:
Which of the following statements is false?
In quadrilateral PQRS, ∠P and ∠S are opposite angles.
If M is the midpoint in the figure, find MQ and PQ.
Answer:
pm = 4
M is the mid point of PQ which means that pm = mq
so MQ = 4
PQ = PM + MQ
= 4 + 4
= 8
(6 + 7) + 8 = 21
Choose an equivalent addition sentence that shows the associative property of addition.
Answer:
6 + (7 + 8) = 21
Step-by-step explanation:
the associative property of addition is: (a + b) + c = a + (b + c)
So the equivalent addition sentence would be:
(6 + 7) + 8 = 6 + (7 + 8) as they both equal 21
Unit 2 Show Your Work, BYU Geometry Part 1
The true statements about ∠MJK and ∠MJL are
The sum of the two angles is 180 degreesJK and JL are opposite raysJK and JL form a straight lineHow to determine the true statements?The statement is given as:
∠MJK and ∠MJL are a linear pair of angles and the angles are also supplementary
As a general rule, linear pair angles are adjacent angles that add up to 180 degrees. This means that:
They are supplementary anglesThey have a sum of 180 degreesThe angles may or may not be congruentThey have opposite rays i.e. straight lineThe above means that, the following options are true:
(e), (f) and (h)
Also, the converse of the statement is:
∠MJK and ∠MJL are supplementary angles and the angles are also linear pair of angles
This is false because not all supplementary angles are linear pair angles
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Given the following data points, calculate the curve of best fit. show all steps.
Based on the calculations, the equation for the curve of best fit is equal to y = -30.17x + 14.49.
How to calculate the curve of best fit?From the table of data points, we have the following:
∑x = 16∑y = 50.9∑xy = 24.6∑x² = 35Mathematically, the standard equation of a straight line is given by:
y = ax + b ....equation 1.
Thus, the equations that can be used to model the given data points are:
∑y = na + b∑x ....equation 2.
∑xy = a∑x + b∑x² ....equation 3.
Substituting the parameters into the equations, we have;
50.9 = 6a + 16b ....equation 4.
24.6 = 16a + 35b ....equation 5.
Solving eqn. 5 and 6 simultaneously, we have:
a = -30.17.b = 14.49.Substituting the value of a and b into eqn. 1, we have;
y = ax + b
y = -30.17x + 14.49.
Therefore, the equation for the curve of best fit is equal to y = -30.17x + 14.49.
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what is the length of the base? help me please thank u ;)
=============================================================
Explanation:
a = 26 and b = 26 are the congruent legs
angle C = 60 degrees is between sides 'a' and b
c = unknown base which is opposite angle C
We'll use the law of cosines to find this missing side.
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 26^2 + 26^2 - 2*26*26*cos(60)
c^2 = 676
c = sqrt(676)
c = 26
It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.
---------------
Here's another way to see why we have an equilateral triangle.
The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180
x+x+60 = 180
2x+60 = 180
2x = 180-60
2x = 120
x = 120/2
x = 60
Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.
If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.
[tex] \textsf{let each of those angles measure ' x ' } [/tex]
[tex]\qquad \tt \rightarrow \:x + x + 60 = 180[/tex]
[ sum of all interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \:2x + 60 = 180[/tex]
[tex]\qquad \tt \rightarrow \:2x = 180 - 60[/tex]
[tex]\qquad \tt \rightarrow \:2x = 120[/tex]
[tex]\qquad \tt \rightarrow \:x = \cfrac{120}{2} [/tex]
[tex]\qquad \tt \rightarrow \:x = 60 \degree[/tex]
Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.
henceforth, all its sides are equal to one another.
[tex]\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units[/tex]
NEED HELP TODAY PLEASE solve 4(2/5x+7)=−8−4/5x show your work
Answer:
x = -15
Step-by-step explanation:
Use the grouping method to factor x³ + x² + 3x+3.
A. (x²+1)(x+3)
B. x(x+3)(x + 1)
C. (x + 1)(x+3)
D. (x + 1)(x2+3)
Answer:
D. [tex](x + 1)(x^2 + 3)[/tex]
Step-by-step explanation:
Hello!
We can group the first two terms and the last two terms.
Factor by Grouping[tex]x^2 + x^2 + 3x + 3[/tex][tex]x^2(x + 1) + 3(x + 1)[/tex][tex](x^2 + 3)(x + 1)[/tex]Factoring by grouping is the process of breaking down larger polynomials to smaller ones to factor. We can then combine like factors.
In the second step, we can see that we can rewrite [tex]x^3 + x^2[/tex] as [tex]x^2(x + 1)[/tex], as both the two terms share a common factor of [tex]x^2[/tex]. We can pull out [tex]x^2[/tex] from that expression. Similarly, [tex]3x[/tex] and [tex]3[/tex] share a common factor of [tex]3[/tex], so we can pull that out.
please help guys how do i order fractions for least to greatest and greatest to least itll nean so much to me for my finals tmrw
Answer:
If the denominators are equal for all of the fractions, you can simply look at the numerator and order them. If the denominators aren't equal, you'll have to find the lcm (lowest common multiple), for example, if we have the fractions 3/6 and 1/4, we would find the lcm of 6 and 4, which is 12 and multiply the numerators accordingly. So the fractions would then become 6/12 and 3/12, this makes it easier for you to figure out their order from least to greatest.
Goodluck for your finals :)
