Given :
A bicycle wheel is 63 centimeters from top to bottom .
So, the diameter of the wheel = 63 cm
When the wheel goes all the way around one time , the bicycle travels 198 centimeters .
So, the circumference of the circle = 198 cm
The circumference of the circle of diameter = d will be :
[tex]\pi\cdot d[/tex]So,
[tex]\begin{gathered} \pi\cdot63=198 \\ \\ \pi=\frac{198}{63}=\frac{22}{7} \end{gathered}[/tex]PLEASE HELP! *not a test, just a math practice that I don't understand.
1) Let's analyze those statements according to the Parallelism Postulates/Theorems.
8) If m∠4 = 50º then m∠6 =50º
Angles ∠4 and ∠6 are Alternate Interior angles and Alternate Interior angles are always congruent
So m∠4 ≅ m∠6
9) If m∠4 = 50, then m∠8 =50º
Angles ∠4 and ∠8 are Corresponding angles and Corresponding angles are always congruent
10) If m∠4 = 50º, then m∠5 =130º
Angles ∠4 and ∠5 are Collateral angles and Collateral angles are always supplementary. So
≅
i inserted a picture of the question, could you please take the short way.
Recall the following property of exponents:
[tex](a\cdot b)^x=a^x\cdot b^x\text{.}[/tex]Therefore:
[tex](14\cdot(-58))^{16}=14^{16}\cdot(-58)^{16}\text{.}[/tex]Answer: Option A.
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
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decide whether the events are independent or dependent and explain your answer.-drawing a ball from a lottery machine, not replacing it, and then drawing a second ball.
If the probability of an event is unaffected by other events, it is called an independent event. If the probability of an event is affected by other events, then it is called a dependent event.
A ball is drawn from a lottery machine. Then, a second ball is drawn without replacing the first ball. Let T be the number of balls in the lottery machine initially. Before the first ball is drawn, the number of balls in the machine is T. At the time the second ball is drawn, the number of balls in the machine is T-1. From T-1 balls, the second ball is drawn. So, the event of drawing the second ball is affected by the event of drawing the first ball.
Therefore, the event of drawing a ball from a lottery machine, not replacing it, and then drawing a second ball is a dependent event.
Find the annual fixed expense for car insurance if John makes
six payments in a year at $174.45 each?
The annual fixed expense for car insurance is $ 1,046.70.
It is given in the question that John makes six payments in a year at $174.45 each.
We have to find the annual fixed expense for car insurance.
We know that,
The annual fixed expense for the car insurance will be 6 times the individual payment given in the question.
Hence, by simple multiplication, we can write,
Annual fixed expense for the car insurance = 6*174.45 = $ 1,046.70
Car insurance
Car insurance is a type of financial protection that covers the cost of another driver’s medical bills and repairs if you cause an accident with your car, or in case your car is stolen or damaged some other way.
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the x intercept of a functions is called?
In this case, the answer is very simple:
x
Simplify 6+ √-80.
06+16√5i
06+4√5
06+16/ √5
06+4√ √5i
Answer:
6 + 4[tex]\sqrt{5}[/tex]i
Step-by-step explanation:
The prime factorization of 80 is 2x2x2x2x5
6 + [tex]\sqrt{-2x2x2x2x5}[/tex] We can take out 2 pairs of 2 which would be 4 and [tex]\sqrt{-1}[/tex] is i
6 + 4[tex]\sqrt{5}[/tex] i
The equation of a line that is perpindicular to y=10x but passes through (1, -3)
The equation of line is y = -x/10 + -29/10.
Given,
The equation of a line that is perpendicular to y = 10x
and, passes through the (1, -3)
To find the equation of line.
Now, According to the question:
Find the slope of the line that is perpendicular to y = 10x;
m = - 1/10
We know that, Slope of line is ;
y = mx + c
m = -1/10
x = 1
y = -3
Substitute and calculate
- 3 = -1/10 + b
b = -29/10
Now, y = mx + b
Substitute all the values in above slope equation:
y = -x/10 + -29/10
Hence, The equation of line is y = -x/10 + -29/10.
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Find the y-coordinate of point P that lies 1/3 along segment CD, closer to C, where C (6, -5) and D (-3, 4).
SOLUTION:
The given ratio is:
[tex]1:3[/tex]• The given points are ,C(6, -5) and D (-3, 4).
Using the section formula, the coordinate of P is:
[tex]\begin{gathered} P=(\frac{1(-3)+3(6)}{1+3},\frac{1(4)+3(-5)}{1+3}) \\ P=(\frac{-3+18}{4},\frac{4-15}{4}) \\ P=(\frac{15}{4},\frac{-11}{4}) \end{gathered}[/tex]Therefore the coordiantes of P
[tex]P=(\frac{15}{4},\frac{-11}{4})[/tex]First use the Pythagorean theorem to find the exact length of the missing side. Then find the exact values of the six trigonometric functions for angle 0.
The trigonometric functions are given by the following formulas:
[tex]\begin{gathered} \sin \theta=\frac{a}{h} \\ \cos \theta=\frac{b}{h} \\ \tan \theta=\frac{a}{b} \\ \cot \theta=\frac{b}{a} \\ \sec \theta=\frac{h}{b} \\ \csc \theta=\frac{h}{a} \end{gathered}[/tex]Where we call a to the opposite leg to the angle θ (the side whose measure equals 20), b is the adjacent leg to angle θ (the side whose measure equals 21) and we call h to the hypotenuse (the larger side, whose measure equals 29).
By replacing 20 for a, 21 for b and 29 for h into the above formulas, we get:
[tex]\begin{gathered} \sin \theta=\frac{20}{29} \\ \cos \theta=\frac{21}{29} \\ \tan \theta=\frac{20}{21} \\ \csc \theta=\frac{29}{20} \\ \sec \theta=\frac{29}{21} \\ \cot \theta=\frac{21}{20} \end{gathered}[/tex]What is the value of x if x + 15 = 38 ? Enter answer below
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
Evaluate the function: g(x)=-x+4Find: g(b-3)
The given function is:
[tex]g(x)=-x+4[/tex]Value of :
[tex]g(b-3)=?[/tex][tex]\begin{gathered} g(x)=-x+4 \\ x=b-3 \\ g(b-3)=-(b-3)+4 \\ g(b-3)=-b+3+4 \\ g(b-3)=7-b \end{gathered}[/tex]so the g(b-3) is 7-b.
Find the component form of the sum of u and v with direction angles u and v.
We will have the following:
[tex]\begin{gathered} U_x=14cos(45) \\ \\ U_y=14sin(45) \\ \\ V_x=80cos(180) \\ \\ V_y=80sin(180) \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sum_x=\frac{14\sqrt{2}}{2}+(-80)\Rightarrow\sum=7\sqrt{2}-80 \\ \\ \sum_y=\frac{14\sqrt{2}}{2}+(0)\Rightarrow\sum=7\sqrt{2} \end{gathered}[/tex]So, the component form for the sum of the vectors will be:
[tex]u+v=(7\sqrt{2}-80)i+(7\sqrt{2})j[/tex]This figure shows two similar polygons; DEFG∼TUVS. Find the value of x.
According to the question, both polygons are similar. It means you can use proportions to find the value of x.
[tex]\frac{DE}{TU}=\frac{EF}{UV}[/tex]Replace for the given values in the picture
[tex]\begin{gathered} \frac{x}{6}=\frac{4}{12} \\ x=\frac{4}{12}\cdot6 \\ x=2 \end{gathered}[/tex]x has a value of 2.
What’s the correct answer answer asap for brainlist please
Answer:
A.it can't be endeavor.
Solve the following inequality for t. Write your answer in the simplest form.6t + 3 < 7t + 10
Therefore, the solution is t > -7.
Which of the following is not a valid way of starting the process of factoring60x² +84x +49?Choose the inappropriate beginning below.O A. (x )(60)OB. (2x (30%)O C. (6x X10x)OD. (2x (5x )
Given the equation:
60x^2 + 84x + 49
We are to determine among the options which is not a process of factorizing.
In factorizing, you get factors of the given numbers of the equation that when they are being multiplied or added, they give the numbers in the equation.
So, looking at the options, the only option that does not satisfies the requirement for starting a factorization process is B, which is (2x (30%)
Therefore, the inappropriate process of starting factorization among the option is option B which is (2x (30%).
F(x)=x+1 and g(x)=x^3 -1Find (fg)(5)
Solution
[tex](fg)(x)=f(x)\times g(x)[/tex]So
[tex]\begin{gathered} f(5)=5+1=6 \\ g(5)=5^3-1=125-1=124 \end{gathered}[/tex]and
[tex]\begin{gathered} (fg)(5)=f(5)\times g(5) \\ (fg)(5)=6\times124=744 \end{gathered}[/tex]Answer: (fg)(5) = 744
write an equation in slope -intercept form for the line with y- intercept -1 and slope -3/2
The line equation in the slope -intercept form can be written as,
[tex]y=mx+b[/tex]Here, m is the slope and b is the y intercept.
Given,
m = -3/2 and b = -1, therefore we can write the equation as,
[tex]y=-\frac{3}{2}x-1[/tex]The equation is, y =(-3/2)x-1.
A boutique in Lanberry specializes in leather goods for men. Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This month, they sold 94 wallets and 22 belts, for a total of $3,230. How much does the boutique charge for each item?
Let w represent the cost of each wallet.
Let b represent the cost of each belt.
Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that
56w + 63b = 3920
This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that
94w + 22b = 3230
We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be
5264w + 5922b = 368480
5264w + 1232b = 180880
Subtracting the second equation from the first, we have
5264w - 5264w + 5922b - 1232b = 368480 - 180880
4690b = 187600
b = 187600/4690
b = 40
Substituting b = 40 into 56w + 63b = 3920, we have
56w + 63(40) = 3920
56w + 2520 = 3920
56w = 3920 - 2520 = 1400
w = 1400/56
w = 25
Thus, the boutique charges $25 for each wallet and $40 for each belt
If triangle ABC with C =90°,if C = 31MM & B equals 57° then a equals
SOLUTION
Step1; Draw the Triangle and locate the angles
We are to obtain the value of a that is the side |BC|
Applying trigonometry ratios we have
[tex]\begin{gathered} \text{hypotenuse}=c=31 \\ \text{Adjacent}=a \\ \theta=57^0 \end{gathered}[/tex][tex]\begin{gathered} \cos \theta=\frac{adjacent}{Hypotenuse} \\ \cos 57^0=\frac{a}{31}\ldots.\text{ cross multiply} \\ a=31\times cos57^0 \end{gathered}[/tex][tex]\begin{gathered} a=31\times0.8999 \\ a=27.89 \end{gathered}[/tex]Then the value of a = 28mm to the nearest whole number
Type the correct answer in each box use numerals instead of words What are the values of the function
Given the following function:
[tex]h(x)=\begin{cases}{3x-4;x<0} \\ {2x^2-3x+10;0\leq x<4} \\ {2^x};x\ge4\end{cases}[/tex]We will find the value of the function when x = 0 and when x = 4
First, when x = 0, the function will be equal to the second deifinition
So, h(0) will be as follows:
[tex]h(0)=2(0)^2-3(0)+10=10[/tex]Second, when x = 4, the function will be equal to the third definition
So, h(4) will be as follows:
[tex]h(4)=2^4=16[/tex]So, the answer will be:
[tex]\begin{gathered} h(0)=10 \\ h(4)=16 \end{gathered}[/tex]An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away. A group of scientists has designed a spaceship that can travel at the speed of 7 x 108 kilometers per year. How many years will the spaceship take to reach the extrasolar planet?
Speed is the time rate at which an object is moving along a path. Then 0.6×10-8 years will the spaceship take to reach the extrasolar planet.
What is Speed?Speed is the time rate at which an object is moving along a path.
The formula for speed is distance/time
Given that
An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away.
Distance= 4.2 x 10°
A group of scientists has designed a spaceship that can travel at the speed of 7 x 10⁸ kilometers per year
Speed = 7 x 10⁸
Time we need to calculate
Time =Distance/speed
Time = 4.2 x 10°/7 x 10⁸
=0.6×10⁻⁸
Hence 0.6×10-8 years will the spaceship take to reach the extrasolar planet.
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A board game that normally costs $30 is on sale for 25 percent off. What is the sale price of the game?
$22.50
$27.50
$32.50
$37.50
Rewrite the fallowing as an exponential expression in simplest form.
SOLUTION
[tex]\begin{gathered} 5x\sqrt[]{x} \\ 5x\times\sqrt[]{x} \\ 5x^1\times x^{\frac{1}{2}} \\ 5x^{1+\frac{1}{2}} \\ 5x^{\frac{3}{2}} \\ \end{gathered}[/tex]which expression could be substituted for x in the second equation to find the value of y?
Substitution
We have the system of equations:
x + 2y = 20
2x - 3y = -1
To solve it with the substitution method, we need to solve the first equation for x and substitute it in the second equation.
Subtracting 2y to the first equation:
x = -2y + 20
This expression corresponds to choice B.
Y=1/3x+2 standard form
3y - x = 6 is standard form for the given equation
What is standard form of linear equation ?The typical form for linear equations with two variables is Ax+By=C.For instance, the linear equation 2x+3y=5 is in standard form. Finding both intercepts of an equation in this style is quite easy (x and y).This form is also very useful when trying to solve systems of two linear equations.Calculationy = 1/3x + 2
3y = x + 6
3y - x = 6 is standard form
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find the equation of the circle with the given center and radius:center (-1,-6), and radius = 6
ANSWER:
[tex](x+1)^2+(y+6)^2=36^{}[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where (h, k) is the center and r is the radius } \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} (x-(-1))^2+(y-(-6))^2=6^2 \\ (x+1)^2+(y+6)^2=36^{} \end{gathered}[/tex]Cindy eats 12 oz of candy in 4 days how long will it take her to eat 1 pound of candy
We should know that:
1 pound = 16 oz
given Cindy eats 12 oz in 4 days
She will eat 1 pound in x days
So, we need to find the number of days to eat 1 pound which is equal to 16 oz
Using the ratio and proportion
12 : 4 = 16 : x
[tex]\begin{gathered} 12\colon4=16\colon x \\ \frac{12}{4}=\frac{16}{x} \\ x=\frac{4\cdot16}{12}=\frac{16}{3}=5\frac{1}{3} \end{gathered}[/tex]so, the number of days = 5 1/3
A radio announcer asked her listeners which type of music they preferred. The results are below. which answer choice lists the results from greatest to least perefence?F. 0.10, 25%, 0.20, 45/100G. 25%, 45/100, 0.20, 0.10H. 0.10, 0.20, 25%, 45/100J. 45/100, 25%, 0.20, 0.10
To compare the preferences is best to express them using the same form, for example, express all values as decimal values:
To express 25% as a decimal value you have to divide it by 100:
[tex]\frac{25}{100}=0.25[/tex]To express the fraction 45/100 as a decimal value you have to divide 45 by 100
[tex]45\div100=0.45[/tex]So, the observations expressed as decimal values are:
Rap 0.25
Norteno 0.45
Kazz 0.20
Tejano 0.10
Now that all numbers are on the same form you can order them from greatest to least. To do so, you have to compare the digit on the first decimal place, if the first digit is equal, you have to compare the digit on the second decimal place.
The number with the greatest decimal value is 0.45
Then you have 0.20 and 0.25 both have the same first digit, so you have to compare the second digits. "0" is less than "5" so, 0.20 is less than 0.25.
The least value is 0.10.
So ordered from greatest to least the values are:
[tex]\begin{gathered} 0.45;0.25;0.20;0.10= \\ \frac{45}{100};25\%,0.20;0.10 \end{gathered}[/tex]The correct option is J.