In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Bicycle wheel:
diameter = 26 in
circumference = ?
Step 02:
Circumference
C = π d
C = π * (26 in) = 81.68 in
The answer is:
C = 82 in
Answer:
82 inches.
Step-by-step explanation:
diameter = 26 inches
radius = 13 inches
circumference = 2πr
π = 22÷7 or 3.142
... 2 × 22÷7 × 13 = 81.714
(to nearest inch) = 82inches.
Hello, may I please have help with this problem. Thank you.
Hello! We can solve this exercise using proportionality.
Let's look at the triangles:
In the smallest, there are two sides with measurement which equals 16.
In the biggest, there are the same sides but with another measurement: 20.
Knowing that we know that the biggest triangle follows the same structure as the smallest, but a teeny bit bigger, right?
So, as we can say that they follow the same proportionality, let's equal them:
[tex]\begin{gathered} \frac{16}{20}=\frac{24}{n} \\ \\ \text{multiplying accross, we will get:} \\ 16.n=24.20 \\ 16n=480 \\ n=\frac{480}{16} \\ n=30 \end{gathered}[/tex]So, n = 30.
Another way:
we know that the same side before measured 16 and now measures 20, so we can write the proportion: 16/20.
If we simplify this fraction we will get 4/5, or in decimal, 0.8.
Now, we will divide the previous measure of the long side by this obtained proportion:
[tex]\frac{24}{0.8}=30[/tex]Given: Circle HHKJK is best described as aof Circle H.JK is best described as a
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.
Answer:
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.
Step-by-step explanation:
here is some formula of understandable things. [tex] {14471}^{2852} \times 1 + 2 - {1666}^{3} \div 145663 \times \frac{5}{3} + \sqrt{86} \tan(5) + \pi0.14 = [/tex]
here is the session with equation in question
Simplify the following polynomials. All final answers must be in standard form!-3x(4x + 12)
Given the expression:
[tex]-3x(4x\text{ + 12)}[/tex]Let's simplify the expression by multiplying -3x to each of the terms inside the parenthesis.
We get,
[tex]-3x(4x\text{ + 12)}[/tex][tex](-3x)(4x)\text{ + (12)}(-3x)[/tex][tex](-12x^2)\text{ + (-36x)}[/tex][tex]-12x^2\text{ - 36x}[/tex]Therefore, the simplified form of the given expression is -12x^2 - 36x.
In a canoe race, Team A is traveling 6 miles per hour and is 2 miles ahead of Team B. Team B is also traveling 6 miles per hour. The teams continue traveling at their current rates for the remainder of the race. Using d for distance (in miles) and t for time (in hours), write a system of linear equations that represent this situation.Equation for Team A:Equation for Team B:Will team B catch up to Team Ao Yeso No
First of all, we need to remember the equation of the speed and time:
distance = speed x time
Now, for the first team (team A):
[tex]\begin{gathered} x=6\frac{miles}{hour}\cdot t+2; \\ x\text{ - distance} \\ t\text{ - time} \end{gathered}[/tex]After that, for the second team (team B):
[tex]x=6\frac{miles}{hour}\cdot t[/tex]Finally, the team B never catch up to team A!
I need help on question 13 for a b and c
b) We have to calculate the probability that a group of 25 men exceeds the average allowed weight per passenger.
As the water taxi has a load limit of 3500 lb, the maximum average weight per passenger is 3500/25 = 140 lb.
Then, we can calculate the probability that the mean of a sample of size n = 25 is greater than 140 lb.
The population distribution from where the sample is taken has a mean of 189 lb and a standard deviation of 39 lb.
We can calculate the z-score for M = 140 lb for this sample as:z
[tex]z=\frac{M-\mu}{\sigma\/\sqrt{n}}=\frac{140-189}{39\/\sqrt{25}}=\frac{-49}{39\/5}\approx-6.28[/tex]Then, the probabilitty can be expressed as:
[tex]P(M>140)=P(Z>-6.28)\approx1[/tex]It is almost certain that the sample mean will be greater than 140 lb.
c) We now have to calculate the probability that a sample of size n = 20 has a mean that is greater than 175 lb, the new load limit per passenger.
We can repeat the procedure calculating the z-score with this new values (M = 175 and n = 20):
[tex]z=\frac{M-\mu}{\sigma\/\sqrt{n}}=\frac{175-189}{39\/\sqrt{20}}\approx\frac{-14}{8.721}\approx-1.6[/tex]Then, we can look up the probability for the standard normal distribution when z = -1.6 and obtain:
We can express this as:
[tex]P(M>175)=P(z>-1.6)=0.9452[/tex]d) As the probabilty of exceeding the load limit per passenger is too high, we can consider that 20 passengers is still not safe enough.
Answer:
b) P(M > 140) = 1
c) P(M > 175) = 0.9452
d) Not safe
"10 more than one-fourteenth of some number, w" can be expressed algebraically as
To express the statement algebraically, we will break down the sentence into phrases or words we can interprete numerically:
the unknown number = w
one fourteenth = 1/14
one fourteenth of some number w:
[tex]\begin{gathered} =\frac{1}{14}\times w \\ =\text{ }\frac{w}{14} \end{gathered}[/tex]10 more: it means we will be adding 10 to the algebraic expression after
10 more than one-fourteenth of some number w will be:
[tex]=10\text{ + }\frac{w}{14}[/tex]Find the length of the guy wire. If necessary, round to the nearest tenth foot.
We are given a diagram showing a pole with a guy wire attached to the top of it and anchored into the ground.
From the base of the pole to the bottom end of the guy tower is given as a 20-feet distance. The pole itself is 24 feet tall. The guy wire from the top of the pole to the ground forms the hypotenuse of what we can describe as a right angled triangle.
We can now use the Pythagoras' theorem to solve for the missing side (hypotenuse).
The theorem states;
[tex]c^2=a^2+b^2[/tex]Where the variables are;
[tex]\begin{gathered} c=\text{hypotenuse} \\ a,b=\text{other sides} \end{gathered}[/tex]We can now substitute the values given;
[tex]c^2=24^2+20^2[/tex][tex]c^2=576+400[/tex][tex]c^2=976[/tex]Take the square root of both sides;
[tex]\sqrt[]{c^2}=\sqrt[]{976}[/tex][tex]c=31.240998\ldots[/tex]Rounded to the nearest tenth of a foot, the length of the guy wire is;
ANSWER:
Length = 31.2 ft
The second option is the correct answer.
I’m struggling with my homework assignment, can anyone help me?
We can find the inverse function writing f(x) as y in the original function and then changing x with y and isolating y again, so
[tex]y=\sqrt[]{x}-5[/tex]Changing y with x we have
[tex]x=\sqrt[]{y}-5[/tex]Now we must get y on one side of the equation again, then
[tex]\begin{gathered} x=\sqrt[]{y}-5 \\ x+5=\sqrt[]{y} \\ (\sqrt[]{y})^2=(x+5)^2 \\ y=(x+5)^2 \end{gathered}[/tex]The domain of the inverse function in the image of the original function f, the image of f is x ≥ -5, then the domain of the inverse of will be x ≥ -5, so our answer is
[tex]f^{-1}(x)=(x+5)^2,x\ge-5[/tex]Options for the first box: inverse and direct Options: 275, 50, 5,000, 13,750 Options for the third box: $275.00, $137.50, $550.00
• The proportional situation represents an Inverse Variation
,• The constant of variation, k = 13750
,• If all 100 students participate in the fundraiser, each will contribute $137.5
Explanation:From the given information, we notice that the more students involved in the fundraiser, the less the amount each student needs to contribute.
This is an INVERSE VARIATION
Let s represent the number of students who participated in the fundraiser, and t represents the amount needed to be contributed by each student, we have:
[tex]\begin{gathered} s\propto\frac{1}{t} \\ \\ \Rightarrow s=\frac{k}{t} \\ \\ OR \\ st=k \end{gathered}[/tex]To find k, we use the information that s = 50 when t = 275
So,
[tex]\begin{gathered} k=50\times275 \\ =13750 \end{gathered}[/tex]From the above, we have the formula:
[tex]st=13750[/tex]If 100 students participate in the fundraiser, we have:
[tex]\begin{gathered} 100t=13750 \\ t=\frac{13750}{100}=137.5 \end{gathered}[/tex]Each student needs to contribute $137.5
R=R¹+R² Solve for R²
Given that ;
R=R¹+R² -------- make R² the subject of the formula as;
Take R¹ to the left side of the equation as;
R-R¹ = R²
So;
Answer:
R² = R - R¹
Step-by-step explanation:
R = R¹ + R²
To make R² as the subject subtract R¹ from both sides.
R - R¹ = R²
Question 5Points 3A model rocket is projected straight upward from the ground level according to theheight equation h =-16f2 + 144t, t> 0, where h is the height in feet and t is the time inseconds. At what time is the height of the rocket maximum and what is that height?
Solution
Step 1:
Write the equation:
[tex]h\text{ = -16t}^2\text{ + 144t}[/tex]Step 2
[tex]At\text{ maximum height, }\frac{dh}{dt}\text{ = 0}[/tex]Step 3:
[tex]\begin{gathered} h\text{ = -16t}^2\text{ + 144t} \\ \\ \frac{dh}{dt}\text{ = -32t + 144} \\ \\ 32t\text{ = 144} \\ t\text{ = }\frac{144}{32} \\ t\text{ = 4.5} \end{gathered}[/tex]Step 4
Substitute t = 4.5 into the height equation.
[tex]\begin{gathered} h\text{ = -16 }\times\text{ 4.5}^2\text{ + 144 }\times\text{ 4.5} \\ h\text{ = -324 + 648} \\ \text{h = 324} \end{gathered}[/tex]THIS IS DUE TODAY PLEASE HELP ASAP AND PROVIDE AN EXPLANATION ILL GIVE YA 80 PONTS!!! Olivia has read 40 pages of a 70 page book, 60 pages of an 85 page book and 43 of a 65 page book. What is the percentage of pages Olivia has not read? PLEASE PROVIDE AN EXPLANATION
Answer: I believe 65%
Step-by-step explanation:
Add all the pages together from the books. Add all the pages they read. Lastly divide the pages they read by the pages there is in total. You get a decimal. move the decimal two numbers over.
Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 105 GB available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs. The cheapest memory cards she can find each hold 256 GB and cost $10. She wants to spend as little money as possible and still get the storage she needs. Let C represent the number of memory cards that Nancy buys. 1) Which inequality describes this scenario? Choose 1 answer: 105 + 100 < 1000 105 + 100 > 1000 105 + 2560 < 1000 105 + 256C 1000
The total GB is 1000
The available GB is 105 GB.
Each 256 GB and cost $10.
Let C be the number of memory cards, then we have,
[tex]105+256C\ge1000[/tex]Thus, option D is correct.
Find the slope of the line.
need help with a question
We can see than 300 is a constant, so mary has 300 stamps for sure.
Now, in that side of the equation, it is added 2x (variable). So that means she is collecting/adding 2stamps per week (where x is number of weeks).
Now, the other side is 10x, so that must be 10 stamps per week.
No constant means initial stamp is 0.
So, this must be Nick's.
Since both sides are equal and we can solve for x, that means:
when will their collection be equal (in what number of weeks).
Looking at the choices, A seems to be correct.
In ΔKLM, the measure of ∠M =90°, the measure of ∠K=,86°, and MK = 86 feet. Find the length of KL to the nearest tenth of a foot.
ΔKLM is a right triangle, the following measures are known:
∠M= 90º
∠K=86º
MK= 86 feet
The side KL is the hypotenuse of the right triangle. To determine its measure you have to apply the trigonometric ratios. In this case, we know one of the angles of the triangle and the length of the side next to the angle, the trigonometric ratio that relates the adjacent side and the hypotenuse is the cosine:
[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex]From this expression, you can calculate the measure of the hypotenuse.
[tex]\cos 86=\frac{86}{x}[/tex]-Multiply both sides of the expression by x to take the term out of the denominators place:
[tex]\begin{gathered} x\cos 86=x\cdot\frac{86}{x} \\ x\cos 86=86 \end{gathered}[/tex]-Divide both sides of the expression by cos 86 to reach the value of x:
[tex]\begin{gathered} x\cdot\frac{\cos86}{\cos86}=\frac{86}{\cos 86} \\ x=\frac{86}{\cos 86} \\ x=1232.86 \\ x\approx1232.9ft \end{gathered}[/tex]The length of KL is equal to 1232.9ft
Multiply. Write the result in standard form.(2 + 1)(3 − 5)
To multiply, we'll use all the terms in the 1st bracket and multiply all the terms in the 2nd bracket;
[tex](2x+1)(3x-5)=6x^2-10x+3x-5=6x^2-7x-5[/tex]So, the required expression is 6x^2 - 7x -5
the length of the longer leg of a right triangle is 3 ft more than three times the length of the shorter leg. the length of the hypotenuse is 4 ft more than three times the length of the shorter leg. find the side lengths of the triangle.
with the pythagorean theorem
[tex]\begin{gathered} (4+3x)^2=x^2+(3+3x)^2 \\ 16+24x+9x^2=x^2+9+18x+9x^2 \\ 16+24x+9x^2=10x^2+18x+9 \\ 16+24x+9x^2-9=10x^2+18x+9-9 \\ 9x^2+24x+7=10x^2+18x \\ 9x^2+24x+7-18x=10x^2+18x-18x \\ 9x^2+6x+7=10x^2 \\ 9x^2+6x+7-10x^2=10x^2-10x^2 \\ -x^2+6x+7=0 \end{gathered}[/tex]using the formula of the quadratic equation
[tex]\begin{gathered} x_{1,\: 2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x1=\frac{-6+\sqrt{6^2-4\left(-1\right)\cdot\:7}}{2\left(-1\right)}=-1 \\ x2=\frac{-6-\sqrt{6^2-4\left(-1\right)\cdot\:7}}{2\left(-1\right)}=7 \end{gathered}[/tex]the length cannot be negative, therefore x=7
length of the shorter leg is: 7ft
length of the longer leg is: 3+3(7)= 24ft
length of the hypotenuse is: 4+3(7)= 25ft
138°12 CSolve for the area of the sector, to the nearest tenth.14.528.90 173.4452.4
Given Data:
The central angle is, θ = 138.
The radius is, r = 12 cm.
The area of the sector can be calculated as,
[tex]A=\frac{\theta}{360}\times\pi\times r^2[/tex]Substituting the values, the area can be calculated as,
[tex]A=\frac{138}{360}\times3.14\times12^2=173.4[/tex]Solve for the height h in this right triangle. Show all steps and round your answer to thenearest hundredth.h39°875 feet
Step 1
Name all sides
Side facing given angle is the opposite = h
Side facing right angleis the hypotanuse
The other side is the adjacent = 875 feet
[tex]\begin{gathered} \tan \theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \theta\text{ = 39} \end{gathered}[/tex][tex]\begin{gathered} \tan 39\text{ = }\frac{h}{875} \\ 0.809\text{ = }\frac{h}{875} \\ \text{Cross multiple} \\ h\text{ = 0.809 x 875} \\ h\text{ = 708.561} \\ h\text{ = 708.56 } \end{gathered}[/tex]A county fair sells adult admission passes, child admission passes, and ride tickets. One family paid $29 for two adult passes,three child passes, and nine ride tickets. Another family paid $19 for one adult pass, two child passes, and eight ride tickets. A third family paid $51 for three adult passes,five child passes, and twenty one ride tickets. Find the individual costs of an adult pass,a child pass, and a ride ticket? Show all work
x= adult passes
y= child passes
z=ride tickets
the first family:
[tex]2x+3y+9z=29\text{ (1)}[/tex]the sencond family
[tex]x+2y+8z=19\text{ (2)}[/tex]third family
[tex]3x+5y+21z=51\text{ (3)}[/tex]now we have the 3 equations, and we can solve x, y and z
for the equation of the second family we have:
[tex]x=-2y-8z+19\text{ (4)}[/tex]reeplace the new equation(4) in (1), we have:
[tex]2(-2y-8z+19)+3y+9z=29[/tex][tex]-4y-16z+38+3y+9z=29[/tex][tex]y+7z=9\text{ (5)}[/tex]reeplace (4) in (3)
[tex]3(-2y-8z+19)+5y+21z=51[/tex][tex]-6y-24z+57+5y+21z=51[/tex][tex]-y-3z=-6[/tex][tex]y+3z=6\text{ (6)}[/tex]with 5 and 6, we have a 2x2 equation
that we can solve easier
solving 5 and 6, we have:
[tex]\begin{gathered} y+7z=9 \\ y=9-7z\text{ (7)} \end{gathered}[/tex]reeplace 7 in 6
[tex]\begin{gathered} 9-7z+3z=6 \\ 4z=3 \\ z=\frac{3}{4}=0.75 \end{gathered}[/tex]now we find y, reeplace z in (7)
[tex]\begin{gathered} y=9-7(0.75) \\ y=9-5.25 \\ y=3.75 \end{gathered}[/tex]and finally we can find x, reeplacing y and z in (4)
[tex]\begin{gathered} x=-2y-8z+19 \\ x=-2(3.75)-8(0.75)+19 \\ x=-7.5-6+19 \\ x=5.5 \end{gathered}[/tex]5.73×10^6 scientific notation or standard form
The number 5.73 10^6 is shown in scientific notation.
Its standard form is: 5,730,000 (five million 7 hundred thirty thousand)
The number 600 can be written in scientific notation by using the digit "6" followed by a product by 100: 6 * 100 and now writing the 100 in powers of ten:
100 = 10 * 10 = 10^2
then the scientific notation formof 600 is:
6 10^2 (6 times 10 to the power 2)
The number 0.24 is the same as the number 24 divided by 100 so notice that there is DIVISION by powers of ten now, and such division becomes a "negative" power of the base 10.
The way to quickly write 0.24 in scientific notation is:
1) count how many spaces you have to move the decimal point to the right in order to get to a number between 1 and something smaller than 10. In our case to get to 2.4.SO the decimal point has to move ONE space to the right. Now,that number of spaces you move to the right is going to becoma the exponent of the base 10:
2.4 10 ^(-1) (remember that since this is a division, the power is NEGATIVE.
The number 4.07369 is the same written in scientific notation and in standard form, because the number shown is in between 1 and something smaller than 10.
Your teacher may want tho to have yu write the exponent of 10 (you write it in this case as a zero):
4.07369 = 4.07369 10^0
Recall that 10^0 is 1, so there is no actual change to the number by multiplying by it.
The table below, from the Statistical Abstract of the United States, showsamusement park attendance at the top 15 amusement parks for given years. Findthe equation of the line that best fit the data.Year (x) | ,Amusement Park Attendance at Top 15 Amusement Parks (in thousands) (y)2009 | 107,3482010 | 109,3212011 | 112,5092012 | 116,4202013 | 119,951
Year (x) | Attendance (in thousands) (y)
2009 | 107,348
2010 | 109,321
2011 | 112,509
2012 | 116,420
2013 | 119,951
Using Excel the next equation is obtained:
[tex]y=3230.5x-6\cdot10^6[/tex]???can anyone please help???
Because he wants to mantain a constant rate over the first hours, we can see that on the first hour he should travel 26 miles.
How many miles should he travel in the first hour?The total race is 150 miles, if we discount the last 20 miles (that Jackson will bike as fast as he can) we get:
150mi - 20mi = 130mi
We know that he travels these 130 miles at a constant rate over 5 hours, so the distance that he moves each hour (an particularly the first hour) is given by the quotient between the distance and the time.
R = 130mi/5h = 26mi/h
So he should travel 26 miles in the first hour.
Learn more about constant rates:
https://brainly.com/question/25598021
#SPJ1
Sophie has eamed $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously write an equation to model this!
Step 1. The information we have is.
The initial amount of the investment which is called the principal P is:
[tex]P=3500[/tex]The interest rate is 7.05%, this will be r:
[tex]r=7.05\text{ percent}[/tex]We will need to represent the interest rate as a decimal number, for that, we divide by 100:
[tex]\begin{gathered} r=\frac{7.05}{100} \\ \downarrow \\ r=0.0705 \end{gathered}[/tex]As additional variables, we will have:
[tex]\begin{gathered} A\longrightarrow\text{Total amount} \\ t\longrightarrow\text{time of the investment} \end{gathered}[/tex]Step 2. Use the Continuous compounding formula:
[tex]A=Pe^{rt}[/tex]where A is the amount including interest, P is the principal amount of the investment, r is the interest rate, and t in years.
Also, e is a constant which is equal to:
[tex]e\approx2.783[/tex]But we will only represent it as e.
Step 3. Substitute P and r into the continuous compounding formula:
[tex]\boxed{A=3500e^{0.0705\times t}}[/tex]That is the equation that models the situation.
Answer:
[tex]\boxed{A=3500e^{0.0705\times t}}[/tex]Unsure of this one, I need it explained with the answer
ANSWER
k = 1 or 21
STEP-BY-STEP EXPLANATION:
According to the question, we were given the below trigonometric function
[tex]\sec ^2x\text{ - 22tanx + 20 = 0}[/tex]Recall that, we have trigonometric identity which is written below
[tex]\sin ^2\theta+cos^2\theta\text{ = 1}[/tex][tex]\text{Divide through by }\cos ^2\theta[/tex][tex]\begin{gathered} \frac{\sin^2\theta}{\cos^2\theta}\text{ + }\frac{cos^2\theta}{\cos^2\theta}\text{ =}\frac{1}{\cos ^2\theta} \\ \tan ^2\theta+1=sec^2\theta \\ \text{Let x = }\theta \\ \tan ^2x+1=sec^2x \end{gathered}[/tex]The next thing is to rewrite the equation
[tex]\begin{gathered} \text{ since sec}^2x=tan^2x\text{ + 1} \\ \text{Hence,} \\ \tan ^2x\text{ + 1 - 22tanx + 20 = 0} \\ \text{Let k = tanx} \\ k^2\text{ + 1 -22k + 20 = 0} \\ \text{Collect the like terms} \\ k^2\text{ - 22k + 21 = 0} \end{gathered}[/tex]The next thing is to find the value of P by factorizing the above equation.
Recall that, the standard form of the quadratic function is given as
[tex]ax^2\text{ + bx + c = 0}[/tex]Let
a = 1
b = -22
c = 21
The next thing is to find the value of ac
[tex]\begin{gathered} ac\text{ = 1 }\cdot\text{ 2}1 \\ ac\text{ = 2}1 \end{gathered}[/tex][tex]\begin{gathered} k^2\text{ - k -21k + 21 =0} \\ k(k\text{ -1) -21(}k\text{- 1) = 0} \\ (k\text{ -1) (k -21) = 0} \\ k\text{ -1 = 0 or =k - 21 = 0} \\ k\text{ = 1 or k = 22} \end{gathered}[/tex]Hence, the value of k is 1 or 21
evaluate the expression 3y+6÷2x
3y+6÷ 2x = 1/ 2x ( 3y + 6 )
Simplify: -12- (–17)
Given the expression:
[tex]-12-(-17)[/tex]You can simplify it as follows:
1. Multiply the signs applying the Sign Rules for Multiplication:
[tex]\begin{gathered} -\cdot-=+ \\ +\cdot-=- \\ +\cdot+=+ \\ -\cdot+=- \end{gathered}[/tex]Then:
[tex]=-12+17[/tex]2. Notice that the signs of the numbers are different. Therefore, you have to subtract them. The result will have the same sign of the number with the greatest absolute value (in this case, it will be positive:
[tex]=5[/tex]Hence, the answer is:
[tex]=5[/tex]find the slope of the line. (-3,0), (2,2), (7,4), (12,6)
find the slope of the line.
(-3,0), (2,2), (7,4), (12,6)
To find the slope we need two points
so
we take
(-3,0), (2,2)
so
m=(2-0)/(2+3)
m=2/5
Verify with the other two points
(7,4), (12,6)
m=(6-4)/(12-7)
m=2/5 ----> is ok
therefore
the slope is 2/5