Answer:
They earn $256 on the ninth day of school.
Step-by-step explanation:
A geometric sequence(in which each term is the previous term multiplied by the ratio) has the following format:
[tex]a_{n+1} = r \times a_{n}[/tex]
In which r is the common ratio.
We can also find the nth term as a function of the first term, by the following equation:
[tex]a_{n} = a_{1} \times r^{n}[/tex]
In which
[tex]r = \frac{a_{n+1}}{a_{n}}[/tex]
In this question:
On the first day, $0.50. So [tex]a_{1} = 0.5[/tex].
Day two $1.00, day three $2.00.
So
[tex]r = \frac{1}{0.5} = \frac{2}{1} = 2[/tex]
Then
[tex]a_{n} = 0.5 \times 2^{n}[/tex]
How much do students earn on the ninth day of school?
[tex]a_{9} = 0.5 \times 2^{9} = 256[/tex]
They earn $256 on the ninth day of school.
When you cough,the radius of your trachea (windpipe) decreases,affecting the speed S of the air in the trachea. If r0 is the normal radius of the trachea, the relationship between the speed S of the air and the radius r of the trachea during a cough is given by a function of the form
S(r) = (r0 - r) ar^2
where a is positive constant. Find the radius r for which the speed of the air is greatest.
Answer: 2r(0)/3.
Step-by-step explanation:
So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);
S(r) = (r0 - r) ar^2 -----------------------------(1).
We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:
dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).
dS/dr = 2ar(r0) - 2ar^2 - ar^2.
dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).
Note that dS/dr = 0.
Hence, - 3ar^2 + 2ar(r0) = 0.
Making ra the subject of the formula we have;
ra[ - 3r + 2r(0) ] = 0. -------------------------(4).
Hence, r = 0 and r = 2r(0) / 3.
If we take the second derivative of S(r) too, we will have;
d^2S/dr = -6ar + 2ar(0). -------------------(5).
+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.
Answer:
[tex]r =\frac{2r_{0}}{3}[/tex]
Step-by-step explanation:
We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.
Let's take the derivative:
[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]
[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]
Let's equal it to zero, to maximize S.
[tex]0=ar(2r_{0}-3r)[/tex]
We will have two solutions:
[tex]r = 0[/tex]
[tex]r =\frac{2r_{0}}{3}[/tex]
Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].
I hope it helps you!
1/5 of the shoes in a factory are green. If you pick a shoe, replace it, pick another shoe and replace it, and pick a third shoe, what is the probability that none of the shoes are green? The answer needs to be in fraction form.
Answer: I believe it’s 3/5
Step-by-step explanation:
Answer:
7/5
Step-by-step explanation:
just add gtwebtewgbrwgragtgwgtrwgtwebgrw
What is the circumference of the following circle?
9 cm
Answer:
9π or 28.27 cm
Step-by-step explanation:
The circumference formula is 2πr or dπ. The diameter is 9 cm so we multiply 9 with pi to get the answer.
The value of the circumference of the given circle is 9π cm OR 28.278 cm
Calculating circumference of a circleFrom the question, we are to determine the circumference of the circle.
The circumference of a circle can be calculated by using the formula,
C = πd
Where C is the circumference of the circle
and d is the diameter
From the diagram,
d = 9 cm
Therefore,
Circumference of the circle = π × 9
Take π = 3.142
Then,
Circumference of the circle = 28.278 cm
Hence, the value of the circumference of the given circle is 9π cm OR 28.278 cm
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Given f(x) = -4x + 7 and g(x) = x, choose
the expression for (fºg)(x).
Answer:
-4x^2+7x
Step-by-step explanation:
Multiply -4x+7 and x.
You get -4x^2+7x.
Factor.
Z^2- 3z – 18
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
z^2-6z + 3z -18
z(z-6)+3(z-6)
(z+3)(z-6)
what is (4 to the square root of 81)5?
Answer:
1310720
Step-by-step explanation:
Find out the frist part "4 to the square root of 81" 262144
then times it by 5
to get 1310720
Given the equation StartFraction 2 x + 2 Over y EndFraction = 4 w + 2 what is the value of x?
Question:
Given the equation (2x + 2)/y = 4w + 2.
What is the value of x?
Answer:
x = 2wy + y - 1
Step-by-step explanation:
Given
(2x + 2)/y = 4w + 2
Required
Find x
To find the value of x; the following steps will be used.
First, Multiply both sides by y
y * (2x + 2)/y = (4w + 2) * y
2x + 2 = 4wy + 2y
Subtract 2 from both sides
2x + 2 - 2 = 4wy + 2y - 2
2x = 4wy + 2y - 2
Multiply both sides by ½
½ * 2x = ½(4wy + 2y - 2)
x = ½(4wy + 2y - 2)
Open bracket
x = ½ * 4wy + ½ * 2y - ½ * 2
x = 2wy + y - 1
Hence, the value of x is 2wy + y - 1
Answer:
B
Step-by-step explanation:
I took the test
Find the volume of a block of woods
Answer:volume=125 cm^3
Surface area=150 cm^2
Step-by-step explanation:
Part A:
volume=length x width x height
volume=5 x 5 x 5
Volume=125 cm^3
Part B:
Surface area=6x5x5
Surface area=150 cm^2
Need help. not in college
1. To measure the resting heart rate of an animal biologist use the function h(m) = 530m-C), where h
is resting heart rate in beats per minute, given the mass m in pounds.
Part A: What is a feasible domain for the function him?
Answer:
Step-by-step explanation:
In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y. Since a function is defined on its entire domain, its domain coincides with its domain of definition, the subset of the domain for which the function associates an image. However this coincidence is no longer true for a partial function since the domain of definition of a partial function can be a proper subset of the domain.
You score a 65% on your AP Statistics Exam and a 78% on your Economics Exam. The AP Statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. The Economics scores were also normally distributed with an average of 75% and standard deviation of 2.5%. In which class did you perform better relative to the class average? Be sure to justify your answer.
Answer:
His economics grade had a higher z-score, so you performed better relative to the class average in economics.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.
In which class did you perform better relative to the class average?
In whichever class you had the higher z-score.
Statistics:
Scored 65, mean 60, standard deviation 6. So [tex]X = 65, \mu = 60, \sigma = 6[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 60}{6}[/tex]
[tex]Z = 0.83[/tex]
Economics:
Scored 78, Mean 75, Standard deviation 2.5. So [tex]X = 78, \mu = 75, \sigma = 2.5[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{78 - 75}{2.5}[/tex]
[tex]Z = 1.2[/tex]
His economics grade had a higher z-score, so you performed better relative to the class average in economics.
This area model shows 50 X 38 Which number is missing from the model
Answer:
69
Step-by-step explanation:
Which number line represents the solution set for the inequality 2x24?
+
-10
-8
-6
4
- 2
0
2
4
6
8
10
+
+
+
+
+
-4
-10
-8
-6
-2
0
+
6
+
10
2
4
8
+
+
-10
-8
--6
-4
O
-2
2
4
6
8
10
-10
-8
--6
-4
-2
0
2
4
6
8
10
Answer:
the answer is what I think 46
The solution of the inequality - 1/2x ≥ 4 is shown in Option 2.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
Inequality is,
⇒ - 1/2x ≥ 4
Now, We can simplify as;
⇒ - 1/2x ≥ 4
⇒ 1/2x ≤ - 4
⇒ x ≤ - 8
When we plot this inequality on a number line,
An arrow starting with a solid point from x = -8 and arrow directing towards negative numbers will represent the given inequality.
Hence, Option (2) will be the answer.
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Please Help me
A restaurant has a build your own personal pizza on their express lunch menu. A customer can only choose one item from each category. The table below shows the different choices. How many different ways can a person order a lunch pizza?
A. 3
B. 9
C. 18
D. 27
Which goes with which
Find the sum of the geometric series 1−0.99+0.99^2−0.99 ^3 +...−0.99
Answer:
0.28
Step-by-step explanation:
The sum of the geometric value progression is S = 0.28
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the sequence be A = { 1 - 0.99 + 0.99² - 0.99³... - 0.99⁷⁹ }
So , A = 1 - { 0.99 - 0.99² + 0.99³... + 0.99⁷⁹ }
Let the first term of the GP be a₁ = 0.99
Now , the common ratio of GP , r = 0.99
And , the number of terms in GP = 80
And , Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
On simplifying , we get
S₈₀ = 0.99 ( 1 - 0.99⁸⁰ ) ( 1 - 0.99 )
On further simplification , we get
S₈₀ = 0.7224
So , the sum of the GP is S = 1 - S₈₀ = 0.28
Hence , the sum of GP is 0.28
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B(4,8) and C(8,0) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.
Answer:
(6,4)
Step-by-step explanation:
I just did quick math in my head.
x^2 = 8x - 15
.......................
Answer: x= 5
Step-by-step explanation: Lets solve by completing the square.
You first need to get -15 by itself.
x^2-8x=15 Now you need to complete the square my finding a perfect constant that will go with x^2-8x, then add it to the other side containing -15 to balance the equation out.
-8x/2= -4^2=16 This will be the perfect square.
x^2-8x+16 = -15 + 16
(x-4)^2 = 1 factor into a binomial, then use the square root on both sides.
√ x-4 ^ 2 = √ 1
x-4 = 1
x=5
Question 11 of 15
Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45
millimeters. How much water can Micah fill in his cup?
Answer:
36.644 mL . . . . depending on your value of π (see below)
Step-by-step explanation:
The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...
45² = 36² +h²
h = √(45² -36²) = 27 . . . . . mm
The volume is given by the formula ...
V = (1/3)πr²h
V = (1/3)π(36 mm)²(27 mm) = 11664π mm³
For π = 3.14
11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL
For π = 3.14159265
11665π mm³ = 36,644 mm³ = 36.644 mL
_____
Comment on units
A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.
Answer:
The answer is 11664pimm^3
Step-by-step explanation:
Complete A and B for 5-8 points.
Answer:
a) 4 hours
b) 11 am
Step-by-step explanation:
So say the number of hours is x
a) 72 + 6x = 96
6x = 24
x = 4
b) 7am + 4 hours = 11am
Find the radius of Circle M, if the area of a sector is 36.07 cm^2 and the central angle of that sector is 58º. Round your answers to the hundredths place if necessary
Answer:
r = 5.97 cm
Step-by-step explanation:
The area of the sector is given by the following equation:
[tex]A = r*S = 2\pi*r^{2}*\frac{58}{360}[/tex]
Where:
r: is the radius
A: is the area
The radius is:
[tex]r = \sqrt{\frac{A}{2*\pi*58/360}} = \sqrt{\frac{36.07 cm^{2}}{2*\pi*58/360}} = 5.97 cm[/tex]
Therefore, the radius of Circle M is 5.97 cm.
I hope it helps you!
Calcula el 23 % de 175
Answer:40.25
Step-by-step explanation:
23% of 175
23/100 x 175
(23 x 175)/100
4025/100=40.25
15. When coffee is packed by machine into 16-ounce cans, the amount can vary. The mean weight is 16.1 ounces and the standard deviation is 0.04 ounce. The weight of the coffee approximates a normal distribution. a. What percent of the cans of coffee can be expected to contain less than 16 ounces of coffee
TBH i found it online because im not that smart but the answer is
.6 %
and if the online question is correct there is another question connected to the question you asked, which the answer is 98.8%
can u pls gimme brainly?
faz um bom tempo que não faço expressões numéricas,vcs podem me ajudar!
Answer:
English Plz
Step-by-step explanation:
On the first day of school, each student is given $0.50 to attend. On day two, each student earns $1.00. on day 3, $2.00, etc. How much do students earn on the 9th day
Answer:
255.50
Step-by-step explanation:
If each day the number is doubled, then all you must do is keep on doubling to the ninth day and then add it all together
How many unique ways are there to arrange the letters in the word PRIOR?
Answer:
60
Step-by-step explanation:
Answer:
it is 60
Step-by-step explanation:
What is the volume of a sphere with a diameter of 6 m, rounded to the nearest tenth of a cubic meter?
Answer:113 cubic meter
Step-by-step explanation:
Diameter=6
Radius=r=6/2
Radius=r=3
π=3.14
Volume of sphere=4/3 x π x r x r x r
Volume of sphere=4/3 x 3.14 x 3 x 3 x 3
Volume of sphere=(4x3.14x3x3x3) ➗ 3
Volume of sphere=339.12 ➗ 3
Volume of sphere=113.04
Volume of sphere =113 cubic meter
What are prime number
A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.
In other words, prime numbers are the numbers
divisible by 1 and the number itself.
For example, let us take 2.
2 has only two factors and those are 1 and 2 so it's prime.
Similarly, 7 is also a prime number because it has only two factors
and these are 1 and the number itself which is 7.
Answer:
A number that is only divisible by itself and 1
Step-by-step explanation:
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
Suppose it takes about 0.5 seconds to hear the echo. How far away is the canyon wall, in feet?
feet
Now let's generalize that result. Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n?
Answer:
The sound takes time to go to a point and reflect back to your position.
It means the sound went twice a distance.
=> Suppose it takes about 0.5 seconds to hear the echo, the canyon wall would be [750 x (0.5/3600)]/2 = 0.052 miles
=> Suppose it takes about n seconds to hear the echo, the canyon wall would be [750 x (n/3600)]/2 miles
Hope this helps!
:)
The distance the canyon wall is away is 33000 feet.
The distance the canyon is away in terms of n is 66000n feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Speed = 750 miles per hour
Time = 0.5 seconds
Distance = Speed x Time
Now,
1 mile = 5280 feet
750 miles = 3960000 feet
1 hour = 60 seconds
So,
Speed = (3960000/60) feet per second
Distance = 66000 x 0.5 feet = 33000 feet
This means,
The canyon wall is 33000 feet away.
Now,
For n seconds,
The canyon wall is 66000n feet away.
Thus,
The canyon wall is 33000 feet away.
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Five subtracted from the product of 8 and x is greater than or equal to 51.
