Answers
The student's questions relate to high school-level mathematics, such as using a graphing calculator for probability distribution calculations, the practice of mental arithmetic, and understanding significant figures and rounding. Some problems also touch on algebraic thinking and the application of mathematics in real-world contexts.
Explanation:The student is asking several questions that pertain to solving mathematical problems and making calculations, which fall within the subject of Mathematics. It's apparent that the questions involve using a graphing calculator, understanding probability distributions, mental arithmetic, and solving equations. This level of mathematics typically corresponds to High School curriculum.
For instance, the student mentions using a graphing calculator to find a probability with a binomial distribution (binompdf), which indicates a familiarity with statistical functions and probability theory. The second part of the series includes an arithmetic puzzle meant to encourage mental math skills by breaking down a problem into more manageable parts. Another problem gives insight into significant figures and decimal places, suggesting the topic of precision and rounding in measurements or calculated results.
Additional parts of the problems focus on making estimates and using ratios for time calculations, implying topics potentially from an algebra or pre-calculus course, with a touch on the real-world application of mathematics and the flexibility and multiple methods within the mathematical process.
Related Questions
On a blueprint, a wall that is 45 feet long is 6 inches long. How long should a girder appear on the blueprint if the girder is actually 30 feet long?
Answers
Answer:
4 inches
Step-by-step explanation:
1 foot = 12 inches
45 feet --- 6 inches
From this we can conclude that the scale of the Blueprint is:
1 foot in actual = 1/90 foot on blueprint
If the girder is actually 30 feet long, then
30 feet --- (1/90*30*12) inches
30 feet --- 4 inches
When creating a scatterplot, if the points are too close together to see the relationship, how could you adjust your graph?
A.
decrease your scale values
B.
increase your scale values
C.
plot more points
D.
plot fewer points
Answers
***ANSWER ASAP****
Use synthetic division to solve (x^3-x^2-17x-15)/(x-5)
Answers
5 | 1 -1 -17 -15
. | 5 20 15
- - - - - - - - - - - - - - - -
. | 1 4 3 0
which translates to
[tex]\dfrac{x^3-x^2-17x-15}{x-5}=x^2+4x+3[/tex]
Answer: [tex]1x^2+4x+3[/tex]
Step-by-step explanation: Given expression (x^3-x^2-17x-15)/(x-5).
We need to divide it x^3-x^2-17x-15 by x-5 using synthetic division .
In order to solve by synthetic division, we would write all the coefficients of given divisor polynomial:
And we divide them by 5 using synthetic division method.
______________
5 | 1 -1 -17 -15 Getting first number down.
| 5 20 -15 Multiplying each down number by
- - - - - - - - - - - - - - - - divisor 5.
1 4 3 0 5×1=5 , 5×2=20, 5×2=15
Subtracting those products from coefficients.
Now, writing the final polynomial degree 1 less than 3, that is 2.
So, [tex]1x^2+4x+3[/tex] would be our quotient.
WILL GIVE BRAINEST
use the elimination method to solve the system of equations.
2x+4y=10
3x-4y=5
a.(1,3)
b.(3,4)
c.(5,0)
d.(3,1)
Answers
Answer:
(3,1)
Step-by-step explanation:
Hi, to solve this problem:
[tex]2 x + 4y = 10\\ +\\3x-4y=5\\-----\\5x =15\\x = 15/5\\x= 3[/tex]
then, replacing the value of "x" in one equation.
2x (3) + 4 y = 10
6 +4y =10
4y= 10- 6
4 y = 4
y = 4/4
y =1
So, the correct option is d.(3,1).
Feel free to ask for more if it´s necessary or if you did not understand something.
The endpoints of line segment AB are A (9,4) and B (5,-4). Then endpoints of its image after dilation are A' (6,3) and B' (5,-4). Find the scale factor and explain
Answers
The length of AB is the distance from (9,4) to (5,-4).
Let's apply the distance formula:
AB = √ ((9-5)² + (4+4)²)
AB = √ (4² + 8²)
AB = √(16 + 64)
AB = √ (80)
AB = 4 √5
The length of AB is 4 √5.
Now for A'B':
A'B' = √ ((6-5)² + (3+4)²)
A'B' = √( 1 + 49)
A'B' = √ 50
A'B' = 5 √2
To find our scale factor k:
A'B' = k AB
5 √2 = 4 √5 * k Divide both sides by 4√5
5 √2 / (4 √5) = k To simplify, multiply the left side by (√5 / √5)
(5 *√5 * √2) / (4 *5) = k the 5's in the numerator and denominator cancel
√5 * √2 / 4 = k
√10 / 4 = k
To confirm, make sure AB * k = A'B', using the values that we've calculated.
Answer:To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).
Hope I helped
A contractor is building a circular swimming pool. The radius of the circle 12 feet. He needs to know the circumference in order to buy tile to put around the edge of the pool. What is the circumference if he uses =22/7 ?
Answers
Diameter is twice the radius so that would be 24 feet
C = Pi X 24
C = (22/7) X 24
C = 75.428 Feet.
Rafael walks 2.5 km every day. How far does he walk in 9 days?
Answers
All you have to do is multiply 2.5x9
Use the distributive property to create an equivalent expression to 54+18x
Answers
Just take out 18 from each term to get a binomial. Multiply what you factored out, 18, by the remaining binomial.
Answer:
An equivalent expression to 54+18x, using the distributive property is 18(3+x)
Step-by-step explanation:
In the problem we have the binomial (54+18x), and we are asked to use the distributive property, this means that we can find a factor wich is distributed in both terms of the binomial.
We know that any number, or in this case any polinomial (or binomial), can be multiplied times 1 and will stay the same number, and we only need to write this 1 in a way that could resolve our problem, in particular we can say that
[tex]1=\frac{18}{18}[/tex]
then we can distribute the denominator, so we calculate:
[tex](54+18x)=1(54+18x)=\frac{18}{18}(54+18x)=18(\frac{54}{18}+\frac{18x}{18})=18(3+x)[/tex]
And the equivalent expression to (54+18x) is 18(3+x).
Speed skiing takes place on a course that is 2/3 mile long. How many feet long is the course? Show work too
Answers
1 mile = 5280 feet
5280 * 2/3 =
5280 *2 = 10560
10560/3 = 3520
it is 3520 feet long
An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum values of I
Answers
[tex] - w \sin(wt) + \sqrt{8} w cos(wt)[/tex]
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
[tex]0 = -w \sin(wt) + \sqrt{8} w cos(wt)[/tex]
divide by w
[tex]0 =- \sin(wt) + \sqrt{8} cos(wt)[/tex]
we add sin(wt) to both sides
[tex]\sin(wt)= \sqrt{8} cos(wt)[/tex]
divide both sides by cos(wt)
[tex] \frac{sin(wt)}{cos(wt)}= \sqrt{8} \\ \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\ \\ wt=arctan(2 \sqrt{2)} [/tex] OR[tex] \\ [/tex] [tex]wt=arctan( { \frac{1}{ \sqrt{2} } ) [/tex]
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be
[tex]I=cos(2n \pi -2arctan( \sqrt{2} ))[/tex]
since 2npi is just the period of cos
[tex]cos(2arctan( \sqrt{2} ))= \frac{-1}{3} [/tex]
substituting our second soultion we get
[tex]I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))[/tex]
since 2npi is the period
[tex]I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3} [/tex]
so the maximum value =[tex] \frac{1}{3} [/tex]
minimum value =[tex]- \frac{1}{3} [/tex]
The maximum value of the electric current is [tex]I_{max}=\dfrac{1}{3}[/tex]
the minimum value of the electric current is [tex]I_{min}=-\dfrac{1}{3}[/tex]
The given expression for electric current is [tex]I=\cos(\omega t)+\sqrt{8}\sin(\omega t)[/tex] where [tex]\omega \neq 0[/tex].
Differentiate the given function with respect to [tex]t[/tex]-
[tex]\dfrac{dI}{dt}=\dfrac{d(\cos(\omega t)+\sqrt 8 \sin(\omega t))}{dt}\\\dfrac{dI}{dt}=-\omega \sin(\omega t)+\sqrt 8 \omega \cos(\omega t)[/tex]
Equate the derivative to 0-
[tex]\dfrac{dI}{dt}=0\\-\omega \sin(\omega t)+\sqrt 8 \omega \cos(\omega t)=0\\\sin(\omega t)=\sqrt 8 \cos (\omega t)\\\tan (\omega t)=\sqrt 8\\\omega t=\tan^{-1}\sqrt 8\\\omega t=2n\pi-2\tan^{-1}\sqrt 2}\\or,\\\omega t=2n\pi+2\tan^{-1}\sqrt {1/2}}[/tex]
[tex]2n\pi[/tex] is the period of sine and the cosine trigonometric function.
So, the maximum value of the electric current is
[tex]I_{max}=\cos(2\tan^{-1}\sqrt {1/2})\\I_{max}=\dfrac{1}{3}[/tex]
Also, the minimum value of the electric current is
[tex]I_{min}=\cos(2\tan^{-1}\sqrt {2})\\I_{min}=-\dfrac{1}{3}[/tex]
Learn more about maximum and minimum values of the functions here:
https://brainly.com/question/13581879?referrer=searchResults
y=0.6x–3;(–2,2) parallel lines
Answers
y=0.6x+a
plug (-2,2) into the equation
2= -2*0.6+a
2+1.2=a
a=3.2
function of the parallel line is y=0.6x+3.2
"is it possible for four consecutive even numbers to have a sum that is ten more than the sum of the smallest two numbers"
Answers
4 consecutive even numbers...x, x + 2, x + 4, x + 6
x + x + 2 + x + 4 + x + 6 = (x + x + 2) + 10
4x + 12 = 2x + 12
4x - 2x = 12 - 12
2x = 0
x = 0........no, it is not possible <==
A car company said that its top five models had the following fuel efficiency ratings: 26.3 mpg, 28.95 mpg, 33.6 mpg, 35 mpg, 38.24 mpg. What is the average mpg rating of these five models, recorded to the appropriate degree of precision? A. 32 mpg B. 32.0 mpg C. 32.4 mpg D. 32.42 mpg
Answers
The average fuel efficiency rating, calculated by adding the mpg ratings and dividing by five, is 32.418 mpg, rounded to the nearest hundredth as 32.42 mpg. The answer is D. 32.42 mpg.
To find the average fuel efficiency rating of the top five models, we need to calculate the mean mpg rating. To do this, we add up all the mpg ratings and then divide by the number of models:
Add the fuel efficiency ratings together: 26.3 + 28.95 + 33.6 + 35 + 38.24.
The sum is 162.09 mpg.
Divide this sum by the number of cars, which is 5: 162.09 ÷ 5.
The average is 32.418 mpg.
To record the average to the appropriate degree of precision, we consider the place values of the original data provided. The given ratings include mpg values recorded to the nearest hundredth, as in 28.95 mpg and 38.24 mpg. This means the average should also be recorded to the nearest hundredth: 32.42 mpg. Therefore, the correct answer is D. 32.42 mpg.
Pls help me with these three! Thanks!
Answers
What is the value of m?
13m+3−56m=−15
Answers
-43m = -18
43m = 18
m = 18/43 or about .4186
The value of m in the equation [tex]13m +3 -56m = -15[/tex] is [tex]\frac{18}{43}[/tex]
Given: [tex]13m +3 -56m = -15[/tex]
To find: value of m
To find the value of m we need to move all the terms containing variables on LHS and the constants on RHS. This can be done as follows:
[tex]13m +3 -56m = -15\\13m -56m =-15-3\\[/tex]
Now we can solve for m as follows:
[tex]13m-56m =-15-3\\-43m = -18\\[/tex]
The negative sign on both LHS and RHS will cancel out and it will give us:
[tex]m = \frac{18}{43}[/tex]
Since 18 and 43 do not have any common multiples so the fraction cant be simplified further. So, [tex]m = \frac{18}{43}[/tex]
A farmer estimates that he has 9,000 bees producing honey on his farm. The farmer becomes concerned when he realizes the population of bees seems to be decreasing steadily at a rate of 5% per year. If the number of bees in the population after x years is represented by f(x), which statements about the situation are true? Check all that apply. The function f(x) = 9,000(1.05)x represents the situation. The function f(x) = 9,000(0.95)x represents the situation. After 2 years, the farmer can estimate that there will be about 8,120 bees remaining. After 4 years, the farmer can estimate that there will be about 1,800 bees remaining. The domain values, in the context of the situation, are limited to whole numbers. The range values, in the context of the situation, are limited to whole numbers.
Answers
Answer:
Step-by-step explanation:
The function f(x) = 9,000(0.95)x represents the situation.
After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
The range values, in the context of the situation, are limited to whole numbers.
The true representation of the declining bee population is f(x) = 9,000(0.95)^x, accounting for a 5% annual decrease. The function and expected number of bees after 2 years are correct if rounded to approximately 8,120. The domain and range values are limited to whole numbers in this context.
Explanation:The given situation of the farmer noticing a decrease of bees in his population can be represented by a mathematical function that models the decline. This function is f(x) = 9,000(0.95)^x, which correctly represents a 5% annual decrease in the bee population.
After analyzing the situation:
The statement f(x) = 9,000(1.05)^x is false because it suggests a 5% increase rather than a decrease.The correct function, as mentioned before, is f(x) = 9,000(0.95)^x.After 2 years, the population of bees expected can be calculated: f(2) = 9,000(0.95)^2 ≈ 8,122.5, which, when rounded to a whole number due to the context, is about 8,123 bees remaining, making this statement true if it refers to approximately 8,120 bees.After 4 years, using the function, the statement that there will be about 1,800 bees remaining is false; the correct calculation would yield a higher number.The domain values are limited to whole numbers since you cannot have a fraction of a year.The range values are also limited to whole numbers as you cannot have a fraction of a bee.Learn more about Exponential Decay here:https://brainly.com/question/2193799
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Kathryn, a college student, works part time at a coffee house. She worked 5 StartFraction 7 Over 20 EndFraction hours on Monday, 4 and one half on Tuesday, 6 and three fourths on Wednesday, 3 and one fourth on Thursday, and 7 on Friday. How many hours did she work altogether? She worked nothing hours altogether.
Answers
5 + 4 + 6 + 3 + 7 = 25
7/20 + 1/2 + 3/4 + 1/4 = 7/20 + 10/20 + 15/20 + 5/20 = 37/20 = 1 17/20
25 + 1 17/20 =
26 17/20 <====
Answer: I’m just adding this to verify that the other answer was correct
Where a is the frontal area of the ball (πd2/4), and cd is the drag coefficient (0.47 for a sphere). what is the drag force on the ball?
Answers
a quarterback made 345 pass completions during one football season. if this was 60% of his attempts,how many passes did he attempt?
Answers
divide completions by percentage
345 / 0.60 = 575 pass attempts
0.60x = 345
x = 345 / 0.60
x = 575 <== total attempts
7-4.9t=15+7.6t solve for t
Answers
Start with adding 4.9t to both sides to get 7=15+12.5t
Then subtract 15 from both sides to get -8=12.5t
Divide both sides by 12.5t so you will get -0.64=t.
Plug this back in to the equation to check your work.
7-4.9(-.64)=10.136
15+7.6(-.64)=10.136
Show the tens fact you used. Show the difference.
14-6=
10-?=?
Answers
(b) In this item, we are to find out or determine the number that when subtracted from 10, will yield the same number. If we let x be this number then,
10 - x = x
Simplifying the equation,
10 = 2x
Dividing both sides by 2 will give us an answer of 5.
ANSWERS: (a) 8
(b) 5
Question 1:
14 - 6 = ?
Further ExplanationTo determine the difference between 14 and 6 is the same is 14 – 6. In other words, the different is the result we get if we subtract both values.
Therefore, the difference between 14 and 6 is 8.
14 – 6
= 8.
There is always three parts in any subtraction equation and these include:
The number that is being subtracted from also called minuendThe number that is being subtracted from the minuend, also called subtrahendThe differences, which is the result you get from subtracting the subtrahend from minuendQuestion 2:
10 - ? = ?
Further ExplanationThe given question means you should for a number that when being subtracted from 10 will give the same number.
Therefore, to solve the question, let the missing be X
10 – X = X
If you simplify the equation, then you should have:
10 = X + X
10 = 2X (divide both side by 2)
[tex]\frac{10}{2}[/tex] = [tex]\frac{2x}{2}[/tex]
5 = X
X = 5
Therefore, the answer for question 1 and 2 are 8 and 5 respectively
LEARN MORE:
Show the tens fact you used write the difference 14 https://brainly.com/question/13620963Show the tens fact you used. Write the difference. https://brainly.com/question/1904682KEYWORDS:
differencetens factsubtractionequationminuendA rectangular board is 18 feet by 24 feet. How far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board?
a. 7.94 ft
b. 4.06 ft
c. 15 ft
d. 15.9 ft
Answers
x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b
Center (0, 0):
h = 0
k = 0
a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:
General : (x - h)² / a² + (y - k)² / b² = 1
(x - 0)² / (12)² + (y - 0)² / (9)² = 1
x² / 144 + y² / 81 = 1
Focus = c:
_____
c = √a² - b²
_______
c = √(12)² - (9)²
______
c = √144 - 81 = sqrt63 = 7.9372
Focus : ( -7.9372, 0) and ( 7.9372, 0)
The correct answer is: a. 7.94 ft
Step 1
To find the distance from the center of the board to the foci of the ellipse that will result in the largest possible elliptical tabletop, we can use the formula:
[tex]\[ c = \sqrt{a^2 - b^2} \][/tex]
where:
- a is half the length of the major axis (which is half of the longer side of the rectangle)
- b is half the length of the minor axis (which is half of the shorter side of the rectangle)
Step 2
Given that the rectangle is 18 feet by 24 feet, [tex]\( a = \frac{24}{2} = 12 \)[/tex] feet and [tex]\( b = \frac{18}{2} = 9 \)[/tex] feet.
Step 2
Now, we can substitute these values into the formula:
[tex]\[ c = \sqrt{12^2 - 9^2} \]\[ c = \sqrt{144 - 81} \]\[ c = \sqrt{63} \][/tex]
Taking the square root of 63 gives us approximately 7.94 feet.
What is the area of a circle with a radius of 7 cm? (Use 3.14 for pi and round to the nearest tenth.)
Answers
Radius = 7cm
Area of circle = [tex] \pi r^2[/tex]
= [tex]3.14*7*7[/tex]
= [tex]153.94 cm^2[/tex]
[tex]153.94[/tex] rounded to the nearest tenth = [tex]153.9cm^2[/tex]
Hope I helped (:
Have a great day!
Answer:
[tex]153.9\ cm^{2}[/tex]
Step-by-step explanation:
Hello, thanks for asking this question here at Brainly, I think I can help you with this
the area of circle is given by:
[tex]Area=\pi * radius^{2} \\[/tex]
Step one
Let
[tex]\pi =3.14\\and\\r= 7 cm[/tex]
Step two
put the values into the equation
[tex]Area=\pi * radius^{2} \\Area=3.14* (7 cm)^{2}\\ Area=3.14* 49\ cm^{2} \\Area=153.9\ cm^{2} \\[/tex]
Hence, the area of a circle with radius 7 cm is 153.9 cm2
I hope it helps,do not hesitage in asking me anything about this, have a great day
Write 96 39/40 as a decimal
Answers
[tex] 96\frac{39}{40} = \frac{3,879}{40} = 96.975 \\ \\ Answer: 96.975[/tex]
How I got my result: Solve the mixed fraction: [tex] 96\frac{39}{40} [/tex] by multiplying the outer number ( [tex]96[/tex] ) by the denominator ([tex]40[/tex] ) then whatever [tex]96(40)[/tex] equals we add the numerator ([tex]39[/tex] ) to it, then get the answer and keep the denominator the same. Lastly, divide our new number by [tex]40[/tex] and it'll give you your result
Anyhow!
Good luck on your assignment and enjoy your day!
~[tex]MeIsKaitlyn:)[/tex]
To solve 49^3x = 343^2x+1, write each side of the equation in terms of base ____
Answers
Each side of [tex]49^{3x} = 343^{2x + 1}[/tex], expressed in terms of their bases, is: [tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex].
Solving Equations by Expressing Equations in Terms of their BasesTo solve an equation, the bases can be made equivalent and cancelled out by creating exponents.
Given:
[tex]49^{3x} = 343^{2x + 1}[/tex]
First, express each side by simplifying their bases and make them equivalent. Let the base be 7.
Thus:
[tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex]
To solve, cancel the bases to have, 2(3x) = 3(2x + 1) and solve for x.
Therefore, each side of [tex]49^{3x} = 343^{2x + 1}[/tex], expressed in terms of their bases, is: [tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex].
Learn more about bases on:
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Answer: 7 then B on edge
Step-by-step explanation:
Answer: it’s
Step-by-step explanation:
Joseph needs to find the quotient of 3216 divided by 8. In which place is the first digit of the quotient?
Answers
If 7.02 is subtracted 43.8 the correct answer will be
Answers
hope this helped!
The graph shows a line and two similar triangles.
Answers
The equation of the line will be y = 4/3x + 3. The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
From the given graph the slope will be calculated as:-
Rise = 4
Run = 3
Slope = Rise / Run = 4 / 3
The y-intercept is 3.
The equation can be written as:-
y = mx + c
y = 4/3x + 3
Therefore, the equation of the line is y = 4/3x +3.
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write 60 as the product of two factors
Answers
Use the formula to evaluate the series -3+6-12+24-...-a7
Formula:Sn=a1(1-r^n)/1-r
In the formula for a finite series, a1 is the first term, r is the common ratio and n is the number of terms.
Answers
-3 , +6 , -12 , +24 ,.... <---- to get the next term's value, you multiply it by -2
thus, is a geometric sequence, and -2 is the "common difference", and the first term is -3 of course.
so... what's the sum of the first 7 terms?
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-3\\ r=-2\\ n=7 \end{cases}[/tex]
[tex]\bf S_7=\sum\limits_{i=1}^{7}\ -3\cdot (-2)^{i-1}\implies S_7=-3\left( \cfrac{1-(-2)^7}{1-(-2)} \right) \\\\\\ S_7=-3\left( \cfrac{1-(-128)}{1+2}\right)\implies S_7=-3\left( \cfrac{129}{3} \right)\implies S_7=-3(43) \\\\\\ S_7=-129[/tex]