Answer:
33.51 cm
Step-by-step explanation:
240/360 = 2/3 (Arc length is 2/3 of the total circumference)
C = 2[tex]\pi[/tex]r ( Calculate the total circumference)
C = 2(8)[tex]\pi[/tex]
C = 50.265
2/3(50.265) (Take 2/3 of the circumference. times 2 divide by 3)
33.51
Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.
The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
The arc length in approximate form is 33.49 radians.
What is the formula for arc length?[tex]s = r\times \theta[/tex]
where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.
How to convert angle from degrees to radians?Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]
For given question,
We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.
[tex]r=8~cm,~\theta=240^{\circ}[/tex]
First we convert angle in radians.
[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]
Using the formula of the arc length,
[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]
The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]
Substitute the value of [tex]\pi = 3.14[/tex]
So, the arc length would be,
[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians
Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
the arc length in approximate form is 33.49 radians.
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How does the sample size affect the validity of an empirical argument? A. The larger the sample size the better. B. The smaller the sample size the better. C. The sample size is not relevant if it is greater than 30. D. The sample size is not relevant if it is greater than 50.
Answer:
A. The larger the sample size the better.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have to look at the standard error, which is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
This means that an increase in the sample size reduces the standard error, and thus, the larger the sample size the better, and the correct answer is given by option a.
Use the graph to find the y-intercept and axis of symmetry
Answer: (a) and (d)
Step-by-step explanation:
From the graph, vertex is at
Graph is same about the point [tex]x=2[/tex] . Therefore, axis of symmetry is the line [tex]x=2[/tex]
Y intercept is the place where curve intersect the Y-axis that is [tex](0,2)[/tex]
Option (a) and (d) are correct.
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW!!!
9. Suppose y varies inversely with x, and y = 49 when x = 1/7. What is the value of x when y = 7?
a. 14
b. 2
c. 1
d. 7
10. Suppose y varies inversely with x, and y = 5 when x = 3. What is the inverse variation equation that relates x and y?
a. y = 3/x
b. y = 5/x
c. y = 15/x
d. y = 15x
9514 1404 393
Answer:
9. c. 1
10. c. y = 15/x
Step-by-step explanation:
The equation for inverse variation can be written as ...
y = k/x
The value of k can be determined from given values of x and y. Multiply by x to get ...
k = xy
Solving for x, you get ...
x = k/y
___
9. k = (1/7)(49) = 7
x = k/y = 7/7
x = 1
__
10. k = (3)(5) = 15
y = 15/x
What is 70% less than 55?
Answer:
100-70=30 so
55*0.3=16.5
Hope This Helps!!!
Answer:
Answer :
70% less than 55 is
16.5
You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?
$550 in 4%, $450 in 6%
$300 in 4%, $700 in 6%
$700 in 4%, $300 in 6%
$150 in 4%, $850 in 6%
9514 1404 393
Answer:
$150 in 4%, $850 in 6%
Step-by-step explanation:
The fraction that must earn the highest rate is ...
(5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85
That is 0.85 × $1000 = $850 must be invested at 6%. Matches the last choice.
_____
If you let x represent the amount that must earn 6%, then the total interest earned must be ...
x·6% +(1000 -x)·4% = 1000·5.7%
x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000
x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above
If a person high jumps 6 feet 2 inches, how many inches is the jump?
Answer:
74 inches
Step-by-step explanation:
1 foot is 12 inches, so 6 x 12 = 72, and just add the other 2 inches to get 74 inches.
Answer:
74 inches.
Step-by-step explanation:
Each foot has 12 inches, so multiply 6 by 12 to get 72 inches. Then add the remaining two inches to get a total of 74 inches.
I need help with this math problem not sure what to do?
Answer:
B. 14
Step-by-step explanation:
It's asking for function f + function g. Then it wants you to use 2 as the x value. So you have:
(f+g)(x) = 2x^2 + 3x + x - 2
(f+g)(x) = 2x^2 + 4x -2
Then using 2 as x:
(f+g)(2) = 2(2^2) + 4* 2 -2
(f+g)(2) = 8 + 8 - 2
(f+g)(2) = 14
Hope that helps, and let me know if I did any of that wrong.
What is this expression in simplified form?
Answer:
16 √(3)
and then the decimal form if needed is: 27.7128129211
Step-by-step explanation:
Need answer urgently
Answer:
x = -2; y = 1
Step-by-step explanation:
See picture below.
We are told matrices B is the inverse of matrix A.
The product of a matrix and its inverse is the identity matrix.
Ivan is playing a skee-ball game. Different points are awarded depending on which hole the ball goes through. When the ball goes in the smallest hole, it is worth 100 points. When it goes in the bigger hole, it is worth 10 points, and when it does not go in either hole, it is worth 1 point. Ivan earned 352 points in the last game.
Which combination will result in a score greater than his current score?
2 balls in the smallest hole, and 8 balls in the bigger hole
4 balls in the smallest hole, and 6 balls in neither hole
3 balls in the smallest hole, 4 balls in the bigger hole, and 3 balls in neither hole
3 balls in the smallest hole, 3 balls in the bigger hole, and 4 balls in neither hole
Answer:
B.
Step-by-step explanation:
I don't know for a fact but i think its B. Sorry if I got it wrong.
A car and a motorcycle whose average rates are in the ratio of 4:5 travel a distance of 160 miles. If the motorcycle
travels 1/2 hour less than the car, find the average rate of each.
Answer:
Step-by-step explanation:
I always advise my students to make a table of information for these story problems because trying to keep track of the information otherwise is a nightmare. The table will look like this:
d = r * t
m
c
m is motorcycle and c is car.
First thing we are told is that the ratio of m's speed to c's speed is 5:4; that means that we can divide 5/4 to find out how many times faster m is going than c.
5/4 = 1.25 so we have a couple of values to put into the table right away, along with the fact that they are both traveling the same distance of 160 miles.
d = r * t
m 160 = 1.25r
c 160 = r
The last thing we have to fill in is the time. If m travels a half hour less than c, c is driving a half hour more than m, right? Filling that in:
d = r * t
m 160 = 1.25r * t
c 160 = r * t + .5
Now we have our 2 equations. Looking at the top row of the table gives us the formula we need to solve this problem. It tells us, in other words, what we are going to be doing with these columns of numbers. Distance equals the rate times the time. For the motorcycle, the equation is:
160 = (1.25r)t and that seems pretty useless since we still have 2 unknowns in there and you can only have 1 unknown in 1 equation. Let's see what the equation for the car is.
160 = (t + .5)r Same problem.
Let's go back to the equation for the motorcycle and since we are looking for the rates of each, let's solve that equation for time in terms of rate (solve it for t):
[tex]t=\frac{160}{1.25r}[/tex] and sub that into the car's equation in place of t:
[tex]160=r(\frac{160}{1.25r})+.5r[/tex] and simplify. The r's to the left of the plus sign cancel out leaving us with:
[tex]160=(\frac{160}{1.25})+.5r[/tex] and divide those numbers inside the parenthesis to get:
160 = 128 + .5r and subtract 128 from both sides to get:
32 = .5r and finally divide by .5 to get
r = 64 miles/hour
The car goes 64 mph and the motorcycle goes 1.25 times that so,
m = 1.25(64) and
m = 80 mph
A family eats out at a restaurant and the total for their meals is $73.89. They also pay sales tax of 5.8% and leave a tip for their server. If the family leaves a total of $93, which of the following might be a description of the service they received?
a.
They left a 10% tip, so the service was probably below average.
b.
They left a 15% tip, so the service was probably average.
c.
They left a 20% tip, so the service was probably above average.
d.
They left a 25% tip, so the service was probably outstanding.
The answer is They left a 20% tip, so the service was probably above average.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
First step is to the amount of the sales tax.
If 100% is $73.89,
5.8% will be x (tax):
100% : $73.89 = 5.8% : x.
x = $73.89 * 5.8% : 100%.
x = $4.28.
Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:
$93.00 - $73.89 - $4.28 = $14.83.
So, the tip is $14.83.
Let represent it as percent.
If $73.89 is 100%, $14.83 will be x.
$73.89 : 100% = $14.83 : x.
x = $14.83 * 100% : $73.89.
x = 20%.
So, they left a 20% tip, so the service was probably above average.
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The expansion of (x-2)(x+2) is …..
Answer:
x2-4
Step-by-step explanation:
Answer:
(x+2)(x-2)(x²-2²)(x²-4)hope it helps
stay safe healthy and happy...Describe how the graph of y = |x - 2| - 5 is a transformation of the graph of y = |x|. Use terms such as "shifted", "reflected", "stretched", or "compressed".
Answer:
The original graph was shifted 2 units to the left and 5 units down.
Step-by-step explanation:
y = |x|
From this, we go to: y = |x - 2|.
When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.
y = |x - 2|.
From this, we go to: y = |x - 2| - 5.
Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.
5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D
Answer: just had this problem! X = 11
why no one helping me please help please please please please please
Answer:
a) A
b) C and E
c) C, D and F
d) two
e) Equal
Question 1 of 10
The triangles shown below may not be congruent.
66V
100
100
00
2017
A. True
B. False
SUBMIT
Answer:
A. TRUE
Step-by-step explanation:
To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.
The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.
Solve the equation −96=3(8x)^(5/3).
Answer:
x= - 1
Step-by-step explanation:
Consignment Sale. Just Between Friends is the leading pop-up consignment sales event franchise in North America. The Des Moines event for Just Between Friends takes place each year at the Iowa State Fairgrounds for one week in the spring and one week in the fall. Families can earn money on gently used baby clothes, baby gear, maternity items, kids' clothes, shoes, toys, and books. Families sign-up as consignors and then price and tag their own items. At the end of the sale, consignors are given a check based on their item sales. Using historical records, the Des Moines event organizers advertise that their consignor check amounts follow a bell-shaped distribution (symmetric and unimodal) with a mean of $480 and a standard deviation of $110. Use the Empirical Rule: What percentage of consignors receive a check for more than $370
Answer:
Just Between Friends
The percentage of consignors who receive a check for more than $370 is:
= 16%.
Step-by-step explanation:
Mean of consignor check, μ = $480
Standard deviation, σ = $110
Value of check received, x > $370
Solution: find the z-score to determine the percentage of consignors who receive a check for more than $370:
z = (x-μ)/σ
z= ($370 - $480)/$110
z = -$110/$110
z = -1.00
Percentage of consignors who receive a check for more than $370
= 0.15866
= 0.16
= 16%
One hundred sixty people were surveyed and asked if believed in ufos, ghosts, and bigfoot. 42 believed in ufos 45 believed in ghosts 21 believed in bigfoot 11 believed in ufos and ghosts 6 believed in ghosts and bigfoot 4 believed in ufos and bigfoot 2 believed in all three how many people surveyed believed in at least one of these ?
Answer:
[tex]P(A\cup B \cup C)=89[/tex]
Step-by-step explanation:
From the question we are told that:
Believed in UFO's [tex]A=42[/tex]
Believed in Ghosts [tex]B=45[/tex]
Believed in Bigfoot [tex]C=21[/tex]
Believed in UFO's & Ghosts [tex]A&B=11[/tex]
Believed in Ghosts & Bigfoot [tex]B&C=6[/tex]
Believed in UFO's & Bigfoot [tex]A&B=4[/tex]
Believed in ALL [tex]A&B&C=2[/tex]
Generally with a well detailed Set diagram of the Number of People that that believed in at least one of them is mathematically given by
[tex]P(A\cup B \cup C)=n(A\cap C)-n(B\cap C) +n(A\cap B \cap C)[/tex]
[tex]P(A\cup B \cup C)=42+45+21-11-6-4+2[/tex]
[tex]P(A\cup B \cup C)=89[/tex]
The foot of a ladder is placed 9 feet away from a wall. If the top of the ladder rests 13 feet up on the wall, find the length of the ladder.
4 feet
15.81 feet
8.81 feet
13 feet
Answer:
15.81 ft .
Step-by-step explanation:
This question is based on " Pythagoras Theorem " . If we imagine the given situation as a right angled triangle , then the base will be " 9ft " , and the perpendicular will be " 13 ft" . And the length of the ladder will be equal to hypontenuse of the triangle.
Using Pythagoras Theorem :-
[tex]\implies\rm h^2= p^2+b^2 \\\\\implies\rm h^2 = (9ft)^2+(13ft)^2 \\\\\implies\rm h^2 = 81 ft^2 + 169 ft^2 \\\\\implies\rm h^2 = 250ft^2 \\\\\implies \boxed{ \rm Ladder's \ Length = 15.81 \ ft }[/tex]
Hence the length of the ladder is 15.81 ft.
Question 1 of 10
Estimate the difference of the decimals below by rounding to the nearest
whole number. Enter your answer in the space provided.
46.327
-4.801
Answer:
Step-by-step explanation:
46.327=46 ( neaarest whole number)
-4.801=-5 (nearest whole number)
46-(-5)=46+5=51
Assigned Media
Use integers to represent the values in the following statement.
Jon Applebee deposited $619 in his savings account. He later withdrew $230.
The integer that represents the amount Jon Applebee deposited is
Answer:
Jon Applebe withdrew 37.15% of the amount he initially deposited.
Step-by-step explanation:
Given that Jon Applebee deposited $ 619 in his savings account, and I have later withdrew $ 230, to determine the integer that represents the amount Jon Applebee deposited the following calculation must be performed:
619 = 100
230 = X
230 x 100/619 = X
23,000 / 619 = X
37.15 = X
Therefore, Jon Applebe withdrew 37.15% of the amount he initially deposited.
What is the area of a parallelogram if the length is 4+ x and it's height is x+3
Answer:
[tex]x^{2}[/tex] + 7x + 12
Step-by-step explanation:
The area of a parallelogram is A = bh, where the base is the length.
To solve this, you have to multiply 4 + x and x + 3.
(4 + x)(x + 3)
If you factor this more, it should be equal to:
[tex]x^{2}[/tex] + 3x + 4x + 12.
This simplified is equal to:
[tex]x^{2}[/tex] + 7x + 12.
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir
bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
ОА.
3.25x + 13.50 S 40
OB.
3.25x + 13.50 240
Oc.
13.50x +3.25 S 40
OD.
13.50x +3.25 2 40
Answer:
A. 3.25x + 13.50 ≤ 40
The number of bracelets is x. It's a variable.
The 13.50 is a constant.
The total needs to be less than or equal to 40 because that's all the money he has.
Answer:
3.25x + 13.50 ≤ 40
Step-by-step explanation:
For this problem, you have to directly make the equation. Using the givens, it shows that he has only 40 dollars, and wants to buy only one hat for 13. 50. He wants to buy his friends braclets 3.25, but since you dont know how many friends its for, you will leave it as x.
There is only 40 dollars so you will use: ≤
The answer will be:
3.25x + 13.50 ≤ 40
Hope this helps.
The park is 18 miles east of my home. The library is 12 miles north of the park. How far is my home from the library?
35 miles
21.6 miles
8.2 miles
18.6 miles
Answer:
21.6 miles
Step-by-step explanation:
If you draw, it'll be a right triangle with legs 12 miles and 18 miles, we need to find the hypotenuse.
So,
[tex] \sqrt{ {12}^{2} + 18^{2} } [/tex]
[tex] = \sqrt{144 + 324} [/tex]
[tex] = \sqrt{468} [/tex]
[tex] = 6\sqrt{13} [/tex]
6√13 ≈ 21.6
Answered by GAUTHMATH
Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Answer:
240
Step-by-step explanation:
minus how much u sold them and how much it cost to make
3-1=2
times 2 and 120
2(120)
240
870,640 rounded to the nearest ten thousand
Answer: 870,000
Step-by-step explanation: First find the digit in the rounding place
which in this case is the 7 in the ten thousands place.
Next, we look at the digit to the right of the 7, which is 0.
According to the rules of rounding, if the digit to the right
of the rounding place is less than 5, we round down.
So the 7 in the rounding place stays the same
and all digits to the right of the become 0.
So 870,640 rounded to the nearest ten thousand is 870,000.
Escreva a matriz A = (aij) do tipo 3x4 sabendo que aij = 3i – 2j.
Answer:
[tex]A = \left[\begin{array}{cccc}1&-1&-3&-5\\4&2&0&-2\\7&5&3&1\end{array}\right][/tex]
Step-by-step explanation:
A = (aij)
i representa a linha e j a coluna.
Tipo 3x4
Isto implica que a matriz tem 3 linhas e 4 colunas.
aij = 3i – 2j.
Primeira linha:
[tex]a_{1,1} = 3(1) - 2(1) = 1[/tex]
[tex]a_{1,2} = 3(1) - 2(2) = -1[/tex]
[tex]a_{1,3} = 3(1) - 2(3) = -3[/tex]
[tex]a_{1,4} = 3(1) - 2(4) = -5[/tex]
Segunda linha:
[tex]a_{2,1} = 3(2) - 2(1) = 4[/tex]
[tex]a_{2,2} = 3(2) - 2(2) = 2[/tex]
[tex]a_{2,3} = 3(2) - 2(3) = 0[/tex]
[tex]a_{2,4} = 3(2) - 2(4) = -2[/tex]
Terceira linha:
[tex]a_{3,1} = 3(3) - 2(1) = 7[/tex]
[tex]a_{3,2} = 3(3) - 2(2) = 5[/tex]
[tex]a_{3,3} = 3(3) - 2(3) = 3[/tex]
[tex]a_{3,4} = 3(3) - 2(4) = 1[/tex]
Matriz:
A matriz é dada por:
[tex]A = \left[\begin{array}{cccc}1&-1&-3&-5\\4&2&0&-2\\7&5&3&1\end{array}\right][/tex]
A manufacturer inspects a sample of 500 smart phones and finds that 496 of them have no defects. The manufacturer sent a shipment of 2000 smartphones to a distributor. Predict the number of smartphones in the shipment that are likely to have no dects.
Answer:
1984
Step-by-step explanation:
