[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=14137 \end{cases}\implies 14137=\cfrac{4\pi r^3}{3}\implies 42411=4\pi r^3 \\\\\\ \cfrac{42411}{4\pi }=r^3\implies \sqrt[3]{\cfrac{42411}{4\pi }}=r\implies 14.99994\approx r\implies \stackrel{\textit{rounded up}}{15=r}[/tex]
Please help...........
Answer:
x=18
Step-by-step explanation:
The two triangles are similar. The ratio of the sides are the same.
20/20=40/(40+x)
Cross multiply and solve. Hint: the easiest way to solve is to simplify, then solve.
Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.
Answer:
(1 , 1)
Step-by-step explanation:
Given in the question two equations
Equation 1
y = x² – x + 1
Equation 2
y = x
Equate both equations
x² – x + 1 = x
0 = x² – x + 1 - x
x² – 2x + 1 = 0
x² - x - x + 1 = 0
x(x - 1) -1(x - 1) = 0
(x - 1)(x - 1) = 0
(x-1)² = 0
x - 1 = 0
x = 1
Plug x = 1 in first equation
y = 1² – 1 + 1
y = 1
Answer:
The answer is option A, or (1,1)
Step-by-step explanation:
I just took the test
A total of 150 students have taken an Algebra 2 final exam. The scores are normally distributed with a mean of 71% and standard deviation of 6%. How many students would you expect have scored between 65% and 77%?
Answer:
102 students
Step-by-step explanation:
Note that 65% and 71% are both 1 standard deviation from the mean (71%). According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.
68% of 150 students would be 0.68(150 students) = 102 students
68% of 150 students would be 0.68 (150 students) is, 102 students.
What it means to be normally distributed?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.What does it mean if your data is not normally distributed?Collected data might not be normally distributed if it represents simply a subset of the total output a process produced. This can happen if data is collected and analyzed after sorting.What are the 4 characteristics of a normal distribution?Here, we see the four characteristics of a normal distribution. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal. A normal distribution is perfectly symmetrical around its center.According to the question:
65% and 71% are both 1 standard deviation from the mean (71%).
According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.
68% of 150 students would be 0.68(150 students) = 102 students.
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Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=12⋅P(x)?
Answer:
The picture where the red image is the skinniest
Step-by-step explanation:
The graph P(x) is the parent graph for all absolute functions. It has a vertex of (0,0) and has the following points:
x f(x)
-2 2
-1 1
0 0
1 1
2 2
The image of l(x) = 12P(x) changes the points of the function to
x f(x)
-2 24
-1 12
0 0
1 12
2 24
This makes the graph much skinnier. The graph with the skinniest red graph is the graph.
Answer:
The second graph is the right answer.Step-by-step explanation:
The parent function is
[tex]P(x)=|x|[/tex]
(Remember, a parent function refers to the simplest function of its type)
The image function is
[tex]I(x)=12P(x)[/tex]
Which is [tex]I(x)=12|x|[/tex].
Observe in the image attached, the image function is vertically stretched by a factor of 12.
Therefore, the right answer is the second graph.
HELP PLEASE!!! I WILL FIVE STAR!!
Answer:
Step-by-step explanation:
You can't answer c. There is not enough information. Other than there are 14 boys that went, you know nothing about how many went.
Girls going = (3/5) * 20 = 12
Girls not going = 20 - 12 = 8
A theater can hold 160 giants or 240 elves. If 109 giants are inside how many elves can also be admitted.
Answer:
it depends
Step-by-step explanation:
If the tradeoff between giants and elves is linear, then about 76 elves can be admitted. If it is non-linear, we need more information about the tradeoff.
For example, elves may fit in the spaces between giants in such a way that they take up proportionately less room. Or, elves may repel giants in such a way that they take up proportionately more room.
See the attached graph for some possibilities.
_____
The linear equation can be written as ...
g/160 + e/240 = 1
Then for g=109, we can solve for "e" as ...
109/160 + e/240 = 1
240(1 -109/160) = e = (3/2)(51) = 76.5
If the tradeoff is linear, 76 elves can be admitted.
Use the drop-down menus to identify the key values of the box plot. The median is . The minimum is . The maximum is . The lower quartile (Q1) is . The upper quartile (Q3) is .
ANSWERS:
C
A
E
B
D
Answer: The lower quartile is Q1) is your minimum & your maximum is quartile Q3) bc is the larger one
Step-by-step explanation:
c
a
e
b
d
is none of your answer.
Answer:
person above is correct
Step-by-step explanation:
show them some love
Which of the following ordered pairs represents an output of 5 and an input of -8?
(-8,-8)
(-8,5)
(5, 5)
(5, -8)
Answer:
(-8,5)
Step-by-step explanation:
The output corresponds to the y-value of an ordered pair while the input corresponds to the x-value of an order pair.
An ordered pair is written like this (x,y)
How do I algebraically solve this? (solve for x)
Check the picture below.
Determine the area of a sector with a central angle of 90° and a radius of 10 meters.
A. 25 meters2
B. 90π meters2
C. 100π meters2
D. 25π meters2
Area of circle
= 90/360 x π x (10)^2
= 1/4 π x 100
= 25 π meter^2
Final answer:
The area of a sector with a central angle of 90° and a radius of 10 meters is calculated using the formula A = θ/360 × πr². Substituting the given values, the area is found to be 25π m². The correct answer is D. 25π meters².
Explanation:
Finding the Area of a Sector
To find the area of a sector with a central angle of 90° in a circle with a radius of 10 meters, we use the formula for the area of a sector, which is A = θ/360 × πr², where θ is the central angle in degrees, π is the mathematical constant approximately equal to 3.14159, and r is the radius. Since the central angle θ is 90°, and the radius r is 10 meters, we have:
A = 90°/360° × π × (10 m)²
= 0.25 × π × 100 m²
= 25π m².
Therefore, the correct answer is D. 25π meters².
Need help
Choices
4
3
2
1
Answer:
1
Step-by-step explanation:
The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.
Answer:
1
Step-by-step explanation:
It took Otis 6 hours to travel to the Grand Canyon. Along the way he took 18 minutes to get gasoline and 53 minutes to eat. How much time did Otis spend driving? With work
The answer is 4 hours and 49 minutes HERE IS MY WORK
4 hours and 49 minutes
Prove or disprove the identity. if you find the identity is true, state the first line of the proof. if you find the identity is false, write the correct equation by replacing the right side. sec2 x(1 – sin2 x) = csc2 x cos x
Answer:
False
Step-by-step explanation:
Using the trigonometric identities
• sin²x + cos²x = 1
• secx = [tex]\frac{1}{cosx}[/tex]
Consider the left side
sec²x(1 - sin²x)
= [tex]\frac{1}{cos^2x}[/tex] × cos²x = 1
The correct identity is
sec²x(1 - sin²x) = 1
Please help me out please
Answer:
h = 10.92 m.
Step-by-step explanation:
The small triangle on the left is similar to the whole triangle, so:
12/20 = h/18.2
h = 12*18.2 / 20
h = 10.92 m.
Solve: 110°20'
PLS TRY to translate degrees and minutes to degrees! BRAINLIEST for 1st answer :)
Answer:
110 1/3 or 100.33 degrees (to the nearest hundredth).
Step-by-step explanation:
There are 60 ' (minutes) in a degree.
So 20' = 20/60 = 1/3 of a degree.
Answer:
110 1/3°
Step-by-step explanation:
Recall that 1° = 60'. Then 20' is 1/3 of 1°, or (1/3)°.
Then 110° 20' = 110° + (1/3)° = 110 1/3°.
Please help with #5 only
Answer:
1680Step-by-step explanation:
[tex]\sum\limits_{n=1}^{42}2n-3\\\\a_n=2n-3\\\\a_{n+1}=2(n+1)-3=2n+2-3=2n-1\\\\a_{n+1}-a_n=(2n-1)-(2n-3)=2n-1-2n+3=2=constant\\\\\text{Therefore it's an arithmetic sequence with first term}\\\\a_1=2(1)-3=2-3=-1\\\\\text{and common difference}\\\\d=2[/tex]
[tex]\text{The formula of a sum of terms of an aithmetic sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{Substitute:}\\\\n=42,\ a_1=-1,\ d=2:\\\\S_{42}=\dfrac{2(-1)+(42-1)(2)}{2}\cdot42=[-2+(41)(2)](21)=(-2+82)(21)\\\\=(80)(21)=1680[/tex]
What is the maximum number of turns in the graph of this function?
[tex]f(x) = x^4-x^3+3x+1[/tex]
Answer:
The maximum number of turns is 3
Step-by-step explanation:
The given function is
[tex]f(x)=x^4-x^3+3x+1[/tex]
The degree of this polynomial is 4.
If the degree of a given polynomial is n, then the polynomial has at least n-1 turns.
Therefore the number of turns of this 4th degree polynomial is at least 3.
Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
A:Point B is the result of a 180° rotation.
B:Point A and B have the same x-coordinate.
C:Point B is the result of a 90° counterclockwise rotation.
D:Point A and point B are the same distance from the origin.
Answer:
D:Point A and point B are the same distance from the origin.
Step-by-step explanation:
hope this helps :)
Answer:
D
Step-by-step explanation:
Hit the THANKS button pls >.<
V
V
V
The center is a(?,?)
The radius is _____ units.
Answer:
The center is at [tex](2,4)[/tex]
3 units
Step-by-step explanation:
You can observe in the graph a circle.
The x-coordinate and the y-coordinate of the center of the circle shown in the figure are:
[tex]x=2[/tex] and [tex]y=4[/tex]
Therefore, the point of the center of the circle is:
[tex](2,4)[/tex]
You can observe that the diameter goes from -1 to 5, then the diameter is:
[tex]diameter=1units+5units\\\\diameter=6units[/tex]
The radius is half the diameter. Therefore, you can say that the radius of this circle is:
[tex]radius=\frac{diameter}{2}\\\\radius=\frac{6units}{2}\\\\radius=3units[/tex]
ANSWER
The center is (2,4)
The radius is 2√2 units
EXPLANATION
Each of the ticks is 1 unit
Counting two ticks from the origin to the right and 4 units up will land us at the center of the circle.
Hence the center is (2,4)
The circle passes through (0,2).
The radius is
[tex]r = \sqrt{ {(2 - 0)}^{2} + {(4 - 2)}^{2} } [/tex]
[tex]r = \sqrt{8} = 2 \sqrt{2} [/tex]
Decide which trigonometric ratio to use. Solve for x in the triangle below. Round your answer to the hundredths place.
Options
4.59
0.07
6.55
5.60
Answer: 4.59
sin(35)=x/8
8*sin(35)=x
x=4.59
The value of x in the given triangle round to the nearest hundredths is:
4.59
Step-by-step explanation:From the given triangle we observe that the side x is the opposite side corresponding to angle 35°.
i.e. we will use sine trignometric ratio in the triangle to get the value of x.
We know that:
[tex]\sin 35=\dfrac{x}{8}ddd[/tex]
Since the sine of an angle is the ratio of opposite side to the hypotenuse of the right angled triangle.
i.e.
[tex]x=8\times \sin 35\\\\i.e.\\\\x=8\times 0.5736\\\\i.e.\\\\x=4.588[/tex]
which is approximately equal to 4.59 units.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule?
Enter your answer, as a decimal, in the box.
Answer:
0.22
Step-by-step explanation:
The point estimate is the average of the upper and lower bounds of the interval.
The logistic equation below can be used to model population growth. In the equation, P is population, t is time, and e = 2.72.
Given this information, which is a correct description of the logistic function?
A. a constant function divided by a polynomial function
B. a constant function divided by an exponential function
C. a constant function divided by the sum of a constant function and a polynomial function
D. a constant function divided by the sum of a constant function and an exponential function
Answer:
D. a constant function divided by the sum of a constant function and an exponential function
Step-by-step explanation:
It's all about the meaning of the math symbols used to create the function. The exponential function is called that because the variable (t) is in the exponent of the expression.
The "numerator" is the part of the expression above the "divided by" line. The "denominator" is the part below that line. When describing a fraction like this, we say, "<the numerator> divided by <the denominator>."
The numerator is a number with no math symbols or variables: it is a constant. The same is true of the left term of the denominator.
The plus sign between the denominator terms indicate these terms are added together. The result of that addition is called a "sum." The terms either side of the plus symbol are those that the symbol is indicating the sum of.
So, we can describe the expression as ...
a constant function divided by the sum of a constant function and an exponential function
The logistic equation is a model of population growth, correctly described as a constant function divided by the sum of a constant function and an exponential function. This matches option D from the choices provided.
Explanation:The logistic equation is a model of population growth where the growth rate decreases as the population approaches its carrying capacity. The equation structure is generally given as a constant function divided by the sum of a constant function and an exponential function. Thus, the correct description from the options provided would be D. A constant function divided by the sum of a constant function and an exponential function.
As an example, the basic form of a logistic function is P(t) = c / (1 + ae-bt). Here c is the constant function representing the maximum achievable population and ae-bt is an exponential function that models the population growth over time 't'.
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A Ferris wheel has a radius of 35 m. Its center is 36 m above the ground. It rotates once every 60 s. Suppose you get on the bottom at t = 0 .
Write an equation that expresses your height as a function of elapsed time.
h = 36 cos 2π (t - 30) / 60 + 35
h = 60 cos 2π (t - 35) / 36 +60
h = 35 cos π (t - 30) / 60 + 36
h = 35 cos 2π (t - 30) / 60 +36
The equation expressing the height as a function of elapsed time for the provided Ferris wheel scenario is: h = 35 cos 2π (t - 30) / 60 + 36. This assumes the highest point is reached halfway through the rotation and uses a cosine function to map the cycle.
Explanation:The subject of this question is mathematics, specifically it's about trigonometric functions and their applications to real world scenarios. The question is seeking for an equation that can express the height of a point on a Ferris wheel as a function of elapsed time.
Here's the solution: The highest height will be the radius of the Ferris wheel (35m) plus the height of the wheel's center above the ground (36m), which is a total of 71m. This height will be reached halfway through the rotation period of the wheel (30s). So, as the function of time, height can be represented by a cosine function shifted to the right by 30s with a period of 60s. Therefore, the equation to represent this scenario correctly is:
h = 35 cos 2π (t - 30) / 60 + 36
In this equation, 'h' stands for height, 't' represents time, 'cos' is the cosine function, 'π' is pi, and '35', '60', '30', and '36' are specific constants representing the radius of the Ferris wheel, the period of rotation, the time shift, and the wheel's center height respectively.
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Identify the volume of the composite figure rounded to the nearest tenth. HELP PLEASE ASAP!!
Answer:
A is the closest one
Step-by-step explanation:
Remark
The general formula is
V = V_2 cones + V_cylinder.
Formula
That turns out to be
V = 2*(1/3)*pi*r^2*h1 + pi*r^2*h
Givens
r = 7 feet
h = 22 feet
h1 = 12 feet
pi = 3.14
Solution
V = 2*(1/3)*3.14 * 7^2*12 + 3.14* 7^2 * 22
V = 1231.5 ft^3 + 3384.92
V = 4616.42
Answer:
4618.1 ft3
Step-by-step explanation:
That's the exact correct answer :)
Kevin caught some fish. Of them 4/9 were herring, and 2/9 salmon. What was the total amount of fish, amount of herring and amount of salmon if there were 12 flounders?
There were 3 different fish caught, Salmon, Herring and Flounder.
4/9 were Herring, 2/9 were Salmon, 4/9 +2/9 = 6/9
This means 3/9 were Flounders ( 3/9 + 6/9 = 9/9 = 1)
3/9 can be reduced to 1/3.
1/3 of the fish were Flounders.
Divide the amount of flounders by the portion caught:
12 / 1/3 = 12 * 3/1 = 36 total fish.
Now you have total number of fish, multiply the total by each portion for each type of fish.
Total fish = 36
Herring = 4/9 x 36 = 16
Salmon = 2/9 x 36 = 8
Please help me with this
Answer:
8.4
Step-by-step explanation:
hope it helped
Can someone help with these 8 problems and show your work please.
Answer:
Part 1) option a. [tex]y=(x+1)^{2}[/tex]
Part 2) option c. [tex]y(x)=10x+1[/tex]
Part 3) option a. Yes , d=-2
Part 4) option b. [tex]y=2x+4[/tex]
Part 5) option b. [tex]m=-2[/tex]
Part 6) option c. [tex]y=4x+14[/tex]
Part 7) option c. [tex]y=4x+5[/tex]
Part 8) option a. y=2x-1 and y=x+1
Step-by-step explanation:
Part 1)
we know that
If a ordered pair satisfy a function, then the function pass through the ordered pair
Verify each function with the points (1,4), (2,9) and (3,16)
case a) we have
[tex]y=(x+1)^{2}[/tex]
For x=1, y=4
[tex]4=(1+1)^{2}[/tex]
[tex]4=4[/tex] ----> is true
For x=2, y=9
[tex]9=(2+1)^{2}[/tex]
[tex]9=9[/tex] ----> is true
For x=3, y=16
[tex]16=(3+1)^{2}[/tex]
[tex]16=16[/tex] ----> is true
therefore
The function pass through the three points
case b) we have
[tex]y=(x+3)^{2}[/tex]
For x=1, y=4
[tex]4=(1+3)^{2}[/tex]
[tex]4=16[/tex] ----> is not true
therefore
The function not pass through the three points
case c) we have
[tex]y=7x-5[/tex]
For x=1, y=4
[tex]4=7(1)-5[/tex]
[tex]4=2[/tex] ----> is not true
therefore
The function not pass through the three points
Part 2)
Let
y------> the number of laps
x-----> the number of hours
we know that
The linear equation that represent this situation is
[tex]y(x)=10x+1[/tex]
Part 3) we have
{4,2,0,-2,-4,-6,...}
Let
a1=-4
a2=2
a3=0
a4=-2
a5=-4
a6=-6
we know that
a2-a1=2-4=-2 -----> a2=a1-2
a3-a2=0-2=-2 ----> a3=a2-2
a4-a3=-2-0=-2 -----> a4=a3-2
a5-a4=-4-(-2)=-2----> a5=a4-2
a6-a5=-6-(-4)=-2----> a6=a5-2
therefore
Is an arithmetic sequence, the common difference is -2
Part 4) we know that
The y-intercept of the graph is (0,4)
The x-intercept of the graph is (-2,0)
therefore
the function is [tex]y=2x+4[/tex]
because
For x=0 -----> y=2(0)+4 -----> y=4
For y=0 ----> 0=2x+4 --------> x=-2
Part 5) we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(3,5)\ B(2,7)[/tex]
substitute the values
[tex]m=\frac{7-5}{2-3}[/tex]
[tex]m=-2[/tex]
Part 6) we know that
The equation of the line into slope point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=4[/tex]
[tex]point(-3,2)[/tex]
substitute the values
[tex]y-2=4(x+3)[/tex]
Convert to slope intercept form
[tex]y=4x+12+2[/tex]
[tex]y=4x+14[/tex]
Part 7) we know that
If two lines are parallel, then their slopes are the same
The equation of the given line is [tex]y=4x-2[/tex]
so
The slope of the given line is [tex]m=4[/tex]
therefore
The line [tex]y=4x+5[/tex] is parallel to the given line
Because the slope is equal to [tex]m=4[/tex]
Part 8) we know that
If a ordered pair is a solution of a system of equations, then the ordered pair must satisfy both equations of the system
Verify each case for (2,3)
case a)
y=2x-1 -----> equation 1
y=x+1 -----> equation 2
Substitute the value of x and the value of y in each equation and then compare the results
Verify equation 1
3=2(2)-1
3=3 -----> is true
Verify equation 2
3=2+1
3=3 -----> is true
therefore
The point (2,3) is a solution of the system of equations case a
case b)
y=2x+1 -----> equation 1
y=x-1 -----> equation 2
Substitute the value of x and the value of y in each equation and then compare the results
Verify equation 1
3=2(2)+1
3=5 -----> is not true
therefore
The point (2,3) is not a solution of the system of equations case b
case c)
y=4x-5 -----> equation 1
y=2x -----> equation 2
Substitute the value of x and the value of y in each equation and then compare the results
Verify equation 1
3=4(2)-5
3=3 -----> is true
Verify equation 2
3=2(2)
3=4 -----> is not true
therefore
The point (2,3) is not a solution of the system of equations case c
What is the recursive rule for the sequence?
Answer:
C
Step-by-step explanation:
Since we are dealing with recursive equations, we can use a simple format.
[tex]a_{1}=x \\ \\ a_{n}=a_{n-1}+y[/tex]
x is the starting value and y is the change.
We can see that the change is -5.6 since 5.6 is being subtracted from each term each time.
So the equation would be
[tex]a_n=a_{n-1}-5.6[/tex]
We can check this by plugging in the numbers.
Let's see if -8.3 works, which is the 2nd term in the equation.
[tex]a_2=a_{2-1}-5.6 \\ \\ -8.3=a_{1}-5.6 \\ \\ -8.3=-2.7-5.6 \\ \\ -8.3=-8.3[/tex]
Therefore, the recursive rule is the third one.
use the equation to answer the following question y=(x-3(x+2)/(x+4)(x-4)(x+2)
a. Find all points of discontinuity
b. Determine whether each point is removable(hole) or non-removable (vertical asymptote)
c.find the equation of the horizontal and vertical asymptotes for the rational function if any
Answer:
See below
Step-by-step explanation:
The given rational function is;
[tex]y=\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}[/tex]
The given function is not continuous where the denominator is equal to zero.
[tex](x+4)(x-4)(x+2)=0[/tex]
The function is discontinuous at [tex]x=-4,x=4,x=-2[/tex]
b) The point at x=-2 is a removable discontinuity(hole) because (x+2) is common to both the numerator and the denominator.
The point at x=-4 and x=4 are non-removable discontinuities(vertical asymptotes)
c) The equation of the vertical asymptotes are x=-4 and x=4
To find the equation of the horizontal asymptote, we take limit to infinity.
[tex]\lim_{x\to \infty}\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}=0[/tex]
The horizontal asymptote is y=0
Though it is true I enjoy your writing style, I don't agree with your main point of view about this one. I do delight in your website nevertheless. Gedefkkfdefd
Answer:
34.
Step-by-step explanation: