Answer:
a. 4 possible outcomes.
b. Possible outcomes - the spinner will fall on a 17, 3, 11 or N.
c. {17, 3, 11, N}
d. P(z) = 1/4.
Step-by-step explanation:
The probability of a specific value on one spin P(z) = 1/4.
a) There are four possible outcomes in the experiment.
b) The possible outcomes are 17, 3, 11, and N.
c) The sample space for the experiment is {17, 2, 11, N}.
d) P(z) = 1/4.
What is sample space?It is the total number of possible outcomes from a given set.
We have,
The square spinner has the following sections.
17, 3, 11, N.
Now,
a)
The number of possible outcomes.
= 17, 3, 11, N
= 4
b)
The possible outcomes are:
= 17, 3, 11, and N
c)
The sample space.
= {17, 3, 11, N}
d)
The probability of getting one specific outcome.
P(z) = 1/4
Thus,
The answers for a), b), c), and d) are given above.
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Graham sold 6 magazines less than double what Adrianne sold, a. Which of the following expressions represents Graham's sales?
6a − 2
2(a − 6)
a^2 − 6
2a − 6
How many solution(s) are there
for this system?
6y=12x+36
15y=45x60
Final answer:
The given system of equations has one unique solution because the lines represented by the equations have different slopes, hence they intersect at exactly one point.
Explanation:
To answer how many solutions there are for the given system of equations:
6y=12x+36
15y=45x+60 (Assuming the '+60' was meant instead of '60', as '+60' makes it a linear equation)
We first simplify both equations to determine if they are identical, parallel, or intersecting.
For the first equation, we divide by 6:
y = 2x + 6
For the second equation, assuming a typo and it should be '+60', we divide by 15:
y = 3x + 4
Since the slopes (2 and 3) are different, the lines are not parallel and will intersect at exactly one point. Therefore, there is one unique solution to this system.
Simplify the expression 2(-9+9v)
Which graph represents the function y= 2/3x-2?
Answer:
third graph
Step-by-step explanation:
The cross section of a water bin is shaped like a trapezoid. The bases of the trapezoid are 28 feet and 6 feet long. It has an area of 34 square feet. What is the height of the cross section?
Answer:
The height of the cross section if 2 feet
Step-by-step explanation:
To solve this problem recall the formula for the area of a trapezoid of bases B (larger base) and b (smaller base) and height H:
[tex]Area = \frac{(B+b)\,H}{2}[/tex]
Therefore, for our case we have:
[tex]Area = \frac{(B+b)\,H}{2}\\34 \,ft^2 = \frac{(28\,ft+6\,ft)\,H}{2}\\34 \,ft^2 = \frac{(34 \,ft)\,H}{2}[/tex]
So, now we can solve for the height H:
[tex]34 \,ft^2 = \frac{(34 \,ft)\,H}{2}\\2\,*\,34 \,ft^2 =34\,ft\,* H\\H=\frac{2\,*\,34 \,ft^2}{34\,ft}\\ H=2\,ft[/tex]
Suppose you select a ball by first picking one of two boxes at random and then selecting a ball from this box. The first box contains two white balls and three blue balls and the second box contains four white balls and one blue ball. What is the probability that you picked a ball from the first box if you have drawn a blue ball
Answer:
Probability of selecting a ball from the first ball if it is a blue ball = = 0.75
Step-by-step explanation:
Number of blue balls in the first box = 3
Number of blue balls in the second box = 1
Total number of blue balls = 3 + 1
Total number of blue balls = 4
Probability = (Number of possible outcomes)/(Number of total outcomes)
Probability of selecting a ball from the first ball if it is a blue ball = 3/4
Probability of selecting a ball from the first ball if it is a blue ball = = 0.75
The video store is having a sale on movie videos. They normally sell for $24.99, but are on sale for $12.99. Mr. Berger purchased 3 videos on sale. How much did he save?
determine whether the vectors u and v are parallel, orthogonal, or neither. u=(9,0), v=(0,-9)
Answer:
orthogonal
Step-by-step explanation:
If the dot product of the two vectors is 0, then they must be orthogonal.
[tex]u*v=9(0)-9(0) = 0[/tex]
Answer: c
Step-by-step explanation: edge 2021
A high-speed bullet train accelerates and decelerates at the rate of 4 ft/s 2 . Its maximum cruising speed is 90 mi/h . (Round your answers to three decimal places.) (a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes
Answer:
22.9 miles
Step-by-step explanation:
We are given that
Acceleration=Deceleration=a=[tex]4ft/s^2[/tex]
Maximum cruising speed,v=[tex]90mi/h=90\times \frac{5280}{3600}=132ft/s[/tex]
1 hour=3600 s
1 mile=5280 feet
Time,t=15 minutes=[tex]15\times 60=900 s[/tex]
1 min=60 s
Initial speed,u=0
[tex]v=u+at[/tex]
Substitute the values
[tex]132=0+4t[/tex]
[tex]t=\frac{132}{4}=33 s[/tex]
[tex]s=u+\frac{1}{2}at^2=0+\frac{1}{2}(4)(33)^2=2178 ft[/tex]
Distance,d=[tex]speed\times time=vt=132\times 900=118800ft[/tex]
Total distance=s+d=2178+118800=120978ft
Total distance=[tex]\frac{120978}{5280}=22.9miles[/tex]
Hence, the maximum distance traveled by train =22.9 miles
4. 4csc^2x+3cscx-1=0
Answer: 8cxs^c= -3 csc (x) +1
Step-by-step explanation:
To solve for c you need to simplify both sides of the equation, then isolating the variable
Answer:
x = - π/2 or x = - π/2 + 2nπ n = integer
Step-by-step explanation:
4csc²x+3cscx-1=0
(csc x + 1) (4csc x - 1) = 0
csc x = - 1 or csc x = 1/4
1/ sin x = - 1 or 1 / sin x = 1/4
sin x = - 1 or sin x = 4 (x no solution when sin x = 4)
sin x = - 1
x = - π/2 or x = - π/2 + 2nπ n = integer
What is the least common denominator for:
3/x and 2/4xy
Answer:
the least common denominator is 4xy
I'll give points just please help(it's a little long sorry:( A student randomly selects some crayons from a large bag of crayons. He selects 10 brown
crayons, 5 blue crayons, 3 yellow crayons, 3 green crayons, 3 orange crayons, and 6 red
crayons. Answer the following questions based on this information. (You can write your
answer either as a fraction, decimal, or percent.) What is the estimate for the probability of selecting a blue crayon for the bag? What is the estimate for the probability of selecting a red crayon or a yellow crayon from the bag? Which color is most likely to be selected? If there are 300 crayons in the bag how many red crayons would you estimate to be in the bag?
Answer:
1/6 chance
Step-by-step explanation:
10+5+3+3+3+6=30 draws
out of 30 draws 5 blue
5/30 reduced is 1/6.
Sarah is fighting a sinus infection her doctor prescribed a nasal spray and I know a biotic to fight the infection the active ingredient in milligrams remaining in the bloodstream from the nasal spray in, tea, and the anabiotic a comity, our models in the functions below where tea is the time in hours and some medications were taken
Answer:
a) The antibiotic is made with a greater initial amount of active ingredient
b) The two medications will have the same amount of active ingredients in the blood stream at exactly 8 hours after first taking the medication.
Step-by-step explanation
Active ingredient of Nasal spray left in the bloodstream is modelled as
n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))
Active ingredient of Antibiotic left in the bloodstream is modelled as
a(t) = 9/(t+3)
with t in hours.
a) At the instance of usage, the active ingredient for both drugs are at their initial concentration as they appear in the drugs.
So, we find the amount of active ingredient for each drug in the bloodstream at t=0 and compare.
For nasal spray,
n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))
At t = 0
n(0) = (1/5) + (18/15) = 1.4
For antibiotics,
a(t) = 9/(t+3)
At t=0
a(0) = (9/3) = 3
3 > 1.4
Hence, the antibiotic is made with a greater initial amount of active ingredient.
b) when both medications will have the same amount of active ingredients in the bloodstream, n(t) = a(t)
n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))
a(t) = 9/(t+3)
Note that (t² + 8t + 15) = (t + 3)(t + 5)
When n(t) = a(t)
((t + 1)/(t + 5)) + (18/(t² + 8t + 15)) = 9/(t+3)
Multiplying through by (t² + 8t + 15) or more properly written as (t + 3)(t + 5)
(t+1)(t+3) + 18 = 9(t+5)
t² + 4t + 3 + 18 = 9t + 45
t² - 5t - 24 = 0
Solving the quadratic equation
t = 8 or t = -3
Time can't be negative, hence, t = 8 hours.
Hope this Helps!!!
Which expressions are equivalent to the one below click all that apply 21x/3x
After simplifying [tex]\(\frac{{21^x}}{{7^x}}\)[/tex], we find it equivalent to [tex]\(3^x\)[/tex], confirming options a, b, and f as correct.
To simplify the expression [tex]\(\frac{{21^x}}{{7^x}}\)[/tex], we can use the property of exponents which states that [tex]\(a^m/a^n = a^{m-n}\)[/tex]. Applying this property, we get:
[tex]\[\frac{{21^x}}{{7^x}} = \frac{{(7 \cdot 3)^x}}{{7^x}} = \frac{{7^x \cdot 3^x}}{{7^x}} = 3^x\][/tex]
So, the simplified expression is [tex]\(3^x\).[/tex]
Now, let's check each option:
a. [tex]\(\frac{{7^x \cdot 3^x}}{{7^x}} = 3^x\)[/tex]. This expression is equivalent to the simplified form.
b. [tex]\((\frac{{21}}{{7}})^x = 3^x\)[/tex]. This expression is equivalent to the simplified form.
c. [tex]\(3\)[/tex]. This expression is not equivalent to the simplified form.
d. [tex]\((21 - 7)^x = 14^x\)[/tex]. This expression is not equivalent to the simplified form.
e. [tex]\(3^{x-7}\)[/tex]. This expression is not equivalent to the simplified form.
f. [tex]\(3^x\)[/tex]. This expression is equivalent to the simplified form.
Therefore, the expressions equivalent to [tex]\(\frac{{21^x}}{{7^x}}\)[/tex] are options a, b, and f.
The question probable maybe:
Given in the attachment
A spinner has 8 congruent sides, 1,9,5,3,2,16,11, and 8 if it spun 120 times what it's a reasonable prediction for the number of times it will land on an even number?
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
120 x 3/8 = 360/8 = 45
The answer would be 45 times.
Find the length of the radius in a circle if the diameter is 10 feet
PLEASE HELP!!! AND EXPLAIN IF YOU CAN !!!
sin(-295°) = _____. sin 65° sin 295° sin 25° -sin 65°
Answer:
Step-by-step explanation:
sin(-295°)=-sin (295)=-sin (360-65)=-(-sin 65°)=sin (65°)
What is closest to the difference between the means of the two dot plots?
Answer: The answer is B. 1.0
Step-by-step explanation:
That’s the closest mean
Answer:
A is 15.27 and B is 12.05
Step-by-step explanation:
Fill in the numbers that go into the blank boxes. The numbers have to multiply to be the top number and add to be the bottom number.
Answer: 6 and 6
Step-by-step explanation:6x6=36
6+6=12
What is the solution to this system of equations?
x − 2y = 15
2x + 4y = -18
Answer:
The answer to your question is (3, -6)
Step-by-step explanation:
Data
x - 2y = 15 Equation l
2x + 4y = -18 Equation ll
Solve the system of equations by elimination
-Multiply equation l by 2
2x - 4y = 30
2x + 4y = -18
4x + 0 = 12
4x = 12
x = 12/4
x = 3
-Substitute x in equation l
3 - 2y = 15
-Solve for y
-2y = 15 - 3
- 2y = 12
y = 12/-2
y = -6
-Solution
(3, -6)
Answer:
C. x = 3, y = -6
Step-by-step explanation
Answer is correct from Plato
You randomly draw A marble from a bag, record it’s color, and then replace it. You draw a blue marble 11 out of 50 times. What is the experimental probability that the next marble will be blue?
Answer:
22/100 or 0.22 or 22%
Step-by-step explanation:
Out of the 50 times you drew a marble, you got 11 blue ones.
11/50
We can divide 11/50 and get 0.22, which is the same as 22/100 or 22%.
Hope this helps! ;-)
The required probability is,
[tex]P(B)=\frac{11}{50} [/tex]
The total number f marbles are 50
Now, the formula for finding the experimental probability is,
P(B)=Possible outcomes/ Number of outcomes
[tex]P(B)=\frac{11}{50} [/tex]
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!3 3/4 as an inproper fraction
Answer:
55/4
Step-by-step explanation:
13 3/4
(13×4 + 3)/4
55/4
Answer:
hope this helps!
If the length of AC equals 30, what is the length of the midsegment DE? A) 10 B) 15 C) 20 D) 25
Answer:15
Step-by-step explanation:
I’m on USA test prep
In a triangle, the midsegment is always half the length of the base. Given that the length of AC is 30, the midsegment DE will be half of this which is 15. Thus, the answer is B) 15.
Explanation:
In geometry, a midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle. For every triangle, the length of the midsegment is always half the length of the base of the triangle.
From your question, the length of AC (which is the base of the triangle) is 30. Therefore, the length of the midsegment DE would be half of 30, which is 15.
So the answer to your question is: B) 15.
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A right triangle whose hypotenuse is 3 centimeters long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the right cone that will have the greatest volume when constructed this way.
Answer:
The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.
The radius of the right circular cone when constructed this way is [tex]\sqrt6[/tex] cm.
The volume of the right circular cone when constructed this way is [tex]6\sqrt3 \pi[/tex] cm³.
Step-by-step explanation:
Given that,
A right triangle whose hypotenuse is 3 cm long is revolved .
Then other two legs of the triangle will be radius and height of the cone.
Assume the height and radius of the cone be h and r respectively.
From Pythagorean Theorem :
h²+r²=3²
⇒ r²= 9 - h²
Then the volume of the cone is
V= π r²h
⇒ V= π(9-h²)h [ ∵ r²= 9 - h²]
⇒V= π(9h - h³)
Differentiating with respect to h
V'=π(9 - 3h²)
Again differentiating with respect to h
V''= π(-6h)
⇒V''= (-6πh)
To maximum or minimum ,we set V'=0
π(9 - 3h²)=0
⇒3h²=9
⇒h²=3
[tex]\Rightarrow h=\sqrt3[/tex]
Now, [tex]V''|_{h=\sqrt3}=-6\pi (\sqrt3)<0[/tex].
Since at [tex]h=\sqrt3[/tex],V''<0.
The volume of cone is maximum at [tex]h=\sqrt3[/tex] cm when constructed this way.
The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.
The radius of the right circular cone when constructed this way [tex]r=\sqrt{9-(\sqrt3)^2[/tex]
= [tex]\sqrt{9-3}[/tex]
[tex]=\sqrt6[/tex] cm.
The volume of the right circular cone when constructed this way is
=π r²h
[tex]=\pi (\sqrt6)^2\sqrt3[/tex]
[tex]=6\sqrt3 \pi[/tex] cm³
How are the archetypes presented in these two passages
different?
The first passage shows Antigone as a warrior, and the
second passage shows Boadicea as a tragic heroine.
The first passage shows Antigone as a tragic heroine,
and the second passage shows Boadicea as a sage.
The first passage shows Antigone as a rebel, and the
second passage shows Boadicea as a warrior.
The first passage shows Antigone as a villain, and the
second passage shows Boadicea as a sage.
Answer: the third answer. Explanation below.
Step-by-step explanation:
The first passage shows Antigone as a rebel because she chooses to defy the State. The second passage shows Boadicea as a warrior because she "herself led the soldiers, encouraging them with her brave words."
Antigone and Boadicea are presented with different archetypal roles across the passages; Antigone as a warrior, tragic heroine, rebel, and villain; and Boadicea as a tragic heroine, sage, warrior, and sage again.
Explanation:The archetypes presented in these passages are different in the roles and characteristics assigned to Antigone and Boadicea. In the first set of passages, Antigone is depicted as a warrior, then as a tragic heroine, next as a rebel, and lastly as a villain. Conversely, Boadicea is presented as a tragic heroine, followed by a sage, then as a warrior, and finally as a sage once again. These variations represent unique depictions of these mythical figures, giving us different lenses to interpret their actions and significance within their respective narratives.
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Find the volume of the composite solid. Round your answer to the nearest tenth.
Answer: I think it's 50.2 but I might be wrong
The half-life of a radioactive element is 130 days, but your sample will not be useful to you after 80% of the radioactive nuclei originally present have disintegrated. About how many days can you use the sample? Round to the nearest day.
Answer:
We can use the sample about 42 days.
Step-by-step explanation:
Decay Equation:
[tex]\frac{dN}{dt}\propto -N[/tex]
[tex]\Rightarrow \frac{dN}{dt} =-\lambda N[/tex]
[tex]\Rightarrow \frac{dN}{N} =-\lambda dt[/tex]
Integrating both sides
[tex]\int \frac{dN}{N} =\int\lambda dt[/tex]
[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]
When t=0, N=[tex]N_0[/tex] = initial amount
[tex]\Rightarrow ln|N_0|=-\lambda .0+c[/tex]
[tex]\Rightarrow c= ln|N_0|[/tex]
[tex]\therefore ln|N|=-\lambda t+ln|N_0|[/tex]
[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex].......(1)
[tex]\frac{N}{N_0}=e^{-\lambda t}[/tex].........(2)
Logarithm:
[tex]ln|\frac mn|= ln|m|-ln|n|[/tex] [tex]ln|ab|=ln|a|+ln|b|[/tex][tex]ln|e^a|=a[/tex] [tex]ln|a|=b \Rightarrow a=e^b[/tex] [tex]ln|1|=0[/tex]130 days is the half-life of the given radioactive element.
For half life,
[tex]N=\frac12 N_0[/tex], [tex]t=t_\frac12=130[/tex] days.
we plug all values in equation (1)
[tex]ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130[/tex]
[tex]\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130[/tex]
[tex]\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130[/tex]
[tex]\rightarrow -ln|2|=-\lambda \times 130[/tex]
[tex]\rightarrow \lambda= \frac{-ln|2|}{-130}[/tex]
[tex]\rightarrow \lambda= \frac{ln|2|}{130}[/tex]
We need to find the time when the sample remains 80% of its original.
[tex]N=\frac{80}{100}N_0[/tex]
[tex]\therefore ln|{\frac{\frac {80}{100}N_0}{N_0}|=-\frac{ln2}{130}t[/tex]
[tex]\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t[/tex]
[tex]\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t[/tex]
[tex]\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}[/tex]
[tex]\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}[/tex]
[tex]\Rightarrow t\approx 42[/tex]
We can use the sample about 42 days.
Final answer:
The radioactive sample can be used for approximately 390 days.
Explanation:
The half-life of a radioactive element is the time it takes for half of the radioactive nuclei to decay. In this case, the half-life is 130 days. The sample is considered no longer useful when 80% of the nuclei have decayed. To determine how many days the sample can be used, we need to find the number of half-lives it takes for 80% of the nuclei to decay.
80% is the same as 0.8, which means 20% (or 0.2) of the nuclei remain. Each half-life reduces the amount of nuclei by half, so we can set up an equation:
0.2 = (1/2)^n
where n is the number of half-lives.
To solve for n, we can take the logarithm of both sides:
n = log_base(1/2)(0.2)
Using a calculator, we find n ≈ 2.737.
Since we can't have a fraction of a half-life, we round up to the nearest whole number, which gives us n = 3.
Now, we can find the number of days by multiplying the half-life by the number of half-lives:
Number of days = 130 days * 3 = 390 days.
Therefore, the sample can be used for approximately 390 days.
The fish population of a lake is decreasing each year. A study is conducted. But, unfortunately some data was lost. The researcher found in her notes that in year one the fish population was 18000 fish and in year three the fish population was 8000 fish. Assume a constant rate of decay. Find a formula F
Answer:
[tex]F(t) = 18000(0.6666)^{t}[/tex]
Step-by-step explanation:
The fish population after t years can be modeled by the following equation:
[tex]F(t) = F(0)(1-r)^{t}[/tex]
In which F(0) is the initial population and r is the constant rate of decay.
Year one the fish population was 18000
This means that [tex]F(0) = 18000[/tex]
In year three the fish population was 8000 fish.
Two years later, so [tex]F(2) = 8000[/tex]
[tex]F(t) = F(0)(1-r)^{t}[/tex]
[tex]8000 = 18000(1-r)^{2}[/tex]
[tex](1-r)^{2} = 0.4444[/tex]
[tex]\sqrt{(1-r)^{2}} = \sqrt{0.4444}[/tex]
[tex]1 - r = 0.6666[/tex]
[tex]r = 0.3334[/tex]
So
[tex]F(t) = 18000(0.6666)^{t}[/tex]
Please help!!!!!!!!!!!!!!!
Answer:
150
Step-by-step explanation:
1 box is 5 x 5 which=25 x 6 boxes=150
150 squared is your answer
Answer: 150
Step-by-step explanation:
The side of one cube is 5. 5 * 5 = 25 So 25 is the surface area of one cube side. A cube a 6 sides, and 25 * 6 = 150. Therefore, 150 is the surface area of the cube.
I need to k ow number four
Answer:
Step-by-step explanation: