Pythagorean Theorem POSSIBLE POINTS : 13:33 Two joggers run 12 miles north and then 8 miles west. What is the shortest distance to reach their starting point? It irrational round to the nearest tenth of a mile.
Answers
Answer:
14.4 miles
Step-by-step explanation:
Given that :
Distance moved North = 12 miles
Distance moved West = 8 miles
Shortest distance to reach starting point :
Let shortest distance to reach starting point = d miles
Using the relation :
Longest side of a right angled triangle:
d = sqrt(8^2 + 12^2)
d = sqrt(64 + 144)
d = sqrt(208)
d = 14.422205
d = 14.4 miles (nearest tenth of a mile)
Related Questions
A function is initially defined by the set of coordinate pairs ((-3,7), (1,5), (4,13)). Which coordinate pair below, if added to this set, prevents the set from representing a function?
1) (2,5) 2) (5,0) 3) (-1,8) 4) (1,4)
Answers
Answer:
We conclude that if we add (1, 4) to this set, it prevents the set from representing a function.
Step-by-step explanation:
Given the initial function
{(-3, 7), (1, 5), (4, 13)}
We know that the given function indicates the relation in which each input has only one output.
i.e.
at x = -3, y = 7
at x = 1, y = 5
at x = 4,y = 13
Thus, it represents a function, becaus there is no repetitive inputs.
The only way the above function will no longer be a function we bring a point, adding of which makes the initial function having repetitive inputs.
i.e. if we add (1, 4) to the initial set, the relation will no longer be a function.
because induction of the point (1, 4) causes repetitive inputs because x = 1 is already present in the set.
so adding the point (1, 4)
{(-3, 7), (1, 4), (1, 5), (4, 13)}
Now, check the points (1, 4) and (1, 5).
It is clear that there are multiple outputs for x = 1. In other words, the input is no more a unique value as x=1 has been repeated multiple times.
Therefore, we conclude that if we add (1, 4) to this set, it prevents the set from representing a function.
I need G PLZZZZZZZZZZZZZZZ
Answers
The king who retains power by tradition of allegiance ensures that a religious doctrine is enforced as government policy. Which of the following accurately describes the type of government? (4 points)
a
This country has both a monarchy and a theocracy.
b
This country has both a dictatorship and a monarchy.
c
This country has both a democracy and a theocracy.
d
This country has both a democracy and a monarchy.
Answers
Answer:
The answer is C.This country has both a democracy and a theocracy
With domestic sources of building supplies running low several years ago, roughly 60,000 homes were built with imported Chinese drywall. According to an article federal investigators identified a strong association between chemicals in the drywall and electrical problems, and there is also strong evidence of respiratory difficulties due to the emission of hydrogen sulfide gas. An extensive examination of 58 homes found that 46 had such problems. Suppose these 58 were randomly sampled from the population of all homes having Chinese drywall.
(a) Does the data provide strong evidence for concluding that more than 50% of all homes with Chinese drywall have electrical/environmental problems? Carry out a test of hypotheses using a = 0.01.
Compute the test statistic value. Round your answer to two decimal places.
(b) Calculate a lower confidence bound using a confidence level of 99% for the percentage of all such homes that have electrical/environmental problems. (Round your answer to one decimal place.)
(c) If it is actually the case that 80% of all such homes have problems, how likely is it that the test of (a) would not conclude that more than 50% do? (Round your answer to four decimal places.)
Answers
Answer:
Step-by-step explanation:
Null hypothesis:
[tex]H_o : \mu = 0.50[/tex]
Alternative hypothesis:
[tex]H_a : \mu > 0.50[/tex]
The sample proportion [tex]\hat p = \dfrac{x}{n}[/tex]
[tex]\hat p = \dfrac{46}{58}[/tex]
[tex]\hat p = 0.7931[/tex]
The test statistics:
[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n} } }[/tex]
[tex]Z = \dfrac{0.7931 - 0.50}{\sqrt{\dfrac{0.5(1-0.5)}{58} } }[/tex]
[tex]Z = \dfrac{0.2931}{\sqrt{\dfrac{0.25}{58} } }[/tex]
[tex]Z = \dfrac{0.2931}{0.06565321643}[/tex]
Z = 4.46 (to two decimal places)
At 99% C.I
Level of significance is:
∝ = 1 - C.I
∝ = 1 - 0.99
∝ = 0.01
Thus, the lower confidence bound can be computed as:
[tex]= \hat p - Z_{\alpha} \sqrt{\dfrac{\hat p ( 1- \hat p )}{n} }[/tex]
Critical value of [tex]Z_{0.01/2} = 2.33[/tex]
[tex]= 0.7931 - 2.33 \sqrt{\dfrac{0.7931 (1-0.7931)}{58}}[/tex]
[tex]= 0.7931 - 2.33 (0.05319)[/tex]
= 0.7931 - 0.1239327
= 0.6691673
[tex]\simeq[/tex] 0.7 (to one decimal place)
(c)
Given:
[tex]P_o = 0.50[/tex] and [tex]\hat p = 0.80[/tex]
Then:
[tex]\beta (0.8) = \phi \Big [ \dfrac{p_o-\hat p + Z_{\alpha} \sqrt{\dfrac{p_o(1-p_o)}{n}}}{\sqrt{\dfrac{\hat p(1-\hat p)}{n} } } \Big][/tex]
[tex]\beta (0.8) = \phi \Big [ \dfrac{0.5-0.8 + 2.33 \sqrt{\dfrac{0.5(1-0.5)}{58}}}{\sqrt{\dfrac{0.8(1-0.8)}{58} }}\Big][/tex]
[tex]= \phi \Big [ \dfrac{-0.3+ 2.33 (0.06565)}{\sqrt{0.0027586 }} \Big][/tex]
[tex]= \phi \Big [ \dfrac{-0.3+ 0.1529645}{0.052522} \Big][/tex]
[tex]= \phi \Big [ \dfrac{-0.1470355}{0.052522 } \Big][/tex]
[tex]= \phi \Big [-2.799\Big][/tex]
= 0.0026 ( to four decimal place).
evaluate the expression. (120÷20)÷(2*3)
Answers
Answer: 9
Step-by-step explanation:
120/20/2 (3)
6/2 (3)
(3) (3)
= 9
Glad I could help!
A varsity boy's basketball team has ratio of seniors to juniors that is 7:4. The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors?
Answers
Answer:
Girl's basketball team has more seniors
Step-by-step explanation:
A varsity boy's basketball team has ratio of seniors to juniors that is 7:4.
Let there are 7x seniors and 4x juniors in boy's basketball team.
ATQ,
7x+4x = 12
11x = 12
x = 12/11
Seniors = [tex]7\times \dfrac{12}{11}=7.63[/tex]
The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2.
Let there are 7x seniors and 4x juniors in girl's basketball team.
3x+2x = 12
5x = 12
x = 12/5
Seniors = [tex]7\times \dfrac{12}{5}=16.8[/tex]
As we can see that girl's basketball team has more seniors as compared to the boy's team.
Need pleas ok need today
Answers
Answer:
90
Step-by-step explanation:
You need to simply add all the given numbers together and enter the missing number that'll make the total 0. So:
-75 + (-25) = -100
-100 + 10 = -90
-90 + 90 = 0
Thus, adding a 90 in the empty box will make it 0.
Answer:
90
Step-by-step explanation:
This is the answer because:
1) -75 + (-25) = -100
2) -100 + 10 = -90
3) -90 + 90 = 0
Therefore, the answer is 90 because whenever a negative number is added with the same poitive number, it beomes a 0.
Hope this helps! :D
1) A school has 1600 students and they are going to vote as to whether they will completely convert the school completely off fossil fuels. How many students would you have to poll to be 95% confident of the outcome within /- 2% of the vote
Answers
Answer:
Standard deviation of the students = 0.408
The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote
= 0.408 X 1600
= 652.8
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 1600
95% confidence interval of the margin error is determined by
[tex]M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
Given Margin of error = 2% = 0.02
[tex]M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }[/tex]
[tex]0.02 = \frac{1.96 X S.D}{\sqrt{1600} }[/tex]
0.02 X √1600 = 1.96 X S.D
[tex]S.D = \frac{0.02X\sqrt{1600} }{1.96} = 0.408[/tex]
Standard deviation of the students = 0.408
The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote
= 0.408 X 1600
= 652.8
Using the z-distribution, it is found that you would have to poll 2401 students.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
There is no prior estimate, hence [tex]\pi = 0.5[/tex] is used.
The sample size is n for which M = 0.02, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \left(\frac{1.96(0.5)}{0.02}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.02}\right)^2[/tex]
[tex]n = 2401[/tex]
You would have to poll 2401 students.
To learn more about the z-distribution, you can take a look at https://brainly.com/question/12517818
The value of y is directly proportional to the value of x. If y = 35 when & = 140, what is the value of y when 3 = 70
answer choices -
17,5
280
70
35
Answers
help needed, fast! thank you :)
Answers
Answer:
x ≥ 16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
x - 4 ≥ 12
Step 2: Solve for x
Add 4 to both sides: x ≥ 16Here we see that any value x greater than or equal to 16 would work as a solution to the inequality.
Answer: x ≥ 16
Step-by-step explanation:
x−4≥12
Step 1: Add 4 to both sides.
x−4+4≥12+4
x≥16
Answer:
x≥16
If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, then what is the probability that an oil change job is completed in less than or equal to 22 minutes?
Answers
Answer:
The value is [tex]P(X \le 22) = 0.2[/tex]
Step-by-step explanation:
From the question we are told that
The lower limit of the interval is [tex]a = 20[/tex]
The upper limit of the interval is [tex]b = 30[/tex]
Generally the cumulative distribution function for uniform distribution is mathematically represented as
[tex]F(x) = \left \{ {{0 \ \ \ \ \ \ \ \ \ \ \ for x < a } \atop {\frac{x - a}{b-a} \ \ \ \ \ \ for a \le x \le b }} \atop { 1 \ \ \ \ \ \ \ \ \ \ \ for x > b}\right.[/tex]
Generally the probability that an oil change job is completed in less than or equal to 22 minutes is mathematically represented as
[tex]P(X \le 22) = \frac{22 - 20}{30 - 20 }[/tex]
=> [tex]P(X \le 22) = 0.2[/tex]
Considering only the factors of the form x - k, what is the relationship between the k values and the zeros?
Answers
Given:
Considering only the factors of the form x - k.
To find:
The relationship between the k values and the zeros?
Solution:
We know that, if (x-c) is a factor of a function f(x), then x=c is a zero of function f(x), i.e., f(c)=0, where, c is a constant.
It is given that, only the factors of the form x - k. Then by using the above theorem we can say that, k values are the zeros of the function.
The relationship between the k values and the zeros is defined as
k values = Zeros of the function
Therefore, the k values are to zeros of the function.
Complete the congruence statement by naming the corresponding angle or side.
50 points
Answers
Answer:
Step-by-step explanation:
B is correct..............
Step-by-step explanation:
Triangles HIJ and HCE are congruent
The letter I is the 2nd letter in HIJ. Similarly, the letter C is the 2nd letter in HCE.
Hence Angle I = Angle C (B).
What is the L.C.M OF 8,
5 AND 9
Answers
Answer:
What is the L.C.M OF 8,
5 AND 9
Step-by-step explanation:
A+b=30, a-b=20, a/b=?
Answers
Answer:
5
Step-by-step explanation:
a+b=30
a=30-b------1
&a-b=20
a=20+b-----2
From eqn 1 and 2, we get
30-b=20+b
or, 10=2b
b=5
Now, a=20+5
a=25
Therefore, a/b=25/5
=5
Using a system of equation, the value of a/b obtained from the values of a and b calculated is 5
The system of equations:
a + b = 30 - - - (1)a - b = 20 - - - (2)From (1) :
a = 30 - b - - - (3)
Substituting a = 30 - b into (2)
30 - b - b = 20
30 - 2b = 20
30 - 20 = 2b
10 = 2b
b = 5
From (3) :
a = 30 - 5
a = 25
Hence,
a/b = 25 / 5 = 5
Hence, the value of a/b is 5
Learn more : https://brainly.com/question/18796573
Find the sum of the interior
angles of a regular nonagon
(9-sided figure).
Answers
Answer:
1260°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Sum of Angles: 180(n - 2)Step-by-step explanation:
Step 1: Define
Number of sides n = 9
Step 2: Find
Substitute: 180(9 - 2)Subtract: 180(7)Multiply: 1260°
6. An ice cream costs 15 more than a cold drink. If the cost of
buying 5 ice creams is 125, find the price of a cold drink.
Answers
Answer:
The price of a cold drink is 10 dollars.
Step-by-step explanation:
We can use proportion.
[tex] \frac{5 \: ice \: creams}{125 \: dollars} = \frac{1 \: ice \: cream}{x} \\ \\ \frac{5x}{5} = \frac{125}{5} \\ \\ x = 25[/tex]
So we found out that one ice-cream costs $25.00.
The statement said, "An ice cream costs 15 more than a cold drink"
In other words, A cold drink costs 15 dollars less than an ice cream.
So we would subtract.
[tex]25 - 15 = 10[/tex]
So a cold drink costs $10.00.
A bag contains 120 marbles. Some are red and the rest are black. There are 17 red marbles for every 3 black marbles. How many red marbles are in the bag?
Answers
Given :
A bag contains 120 marbles. Some are red and the rest are black. There are 17 red marbles for every 3 black marbles.
To Find :
How many red marbles are in the bag.
Solution :
Let, number of red and black marbles are x and y respectively.
So, x + y = 120 ....1)
Now, it is given that there are 17 red marbles for every 3 black marbles.
So, 3x = 17y ....2)
Putting value of x from equation 2) to equation 1), we get :
[tex]\dfrac{17y}{3}+y = 120\\\\\dfrac{20y}{3}=120\\\\y = 18\\\\x = 120 - 18\\\\x = 102[/tex]
Therefore, the number of red and black marbles are 102 and 18 respectively.
What’s the formula for the sequence 9, 14, 19, 24, ...?
Answers
Answer:
add 5
Step-by-step explanation:
Answer:
+5
Step-by-step explanation:
It keeps adding five so,
14, 19, 24, 29, 34,39,44...
The cashier counts 80 bills, all with the same value. She gets a total of $800. What is the value of each bill?
help, help
Answers
Answer:
10 dollars
Step-by-step explanation:
Answer:
10!
Step-by-step explanation:
So the cashier counts 80 bills and if each bill was 10 dollars, then that would equal the total. ($800) Because 80 x 10 equals 800.
Hope this helps!. :)
Write the equation in POINT-SLOPE FORM of the line that passes throught (5,9) and has a slope of -7.
Answers
Answer:
The equation of line with slope -7 passing through (5,9) in point-slope form is:
[tex]y-9 = -7(x-5)[/tex]
Step-by-step explanation:
Given
Slope of line = m = -7
Point = (5,9)
The point slope form of equation is obtained from a point and slope. It is given by the equation:
[tex]y-y_1 = m(x-x_1)[/tex]
We know that (x1,y1) = (5,9)
Putting the values we get
[tex]y-9 = -7(x-5)[/tex]
Hence,
The equation of line with slope -7 passing through (5,9) in point-slope form is:
[tex]y-9 = -7(x-5)[/tex]
The net of a pyramid is shown below: The net of a square based pyramid, with bases labeled 7 inches and the height of the triangle labeled 14 inches. The surface area of the solid is square inches. (3 points)
Answers
Answer:
245 in²Step-by-step explanation:
The surface area is the sum of the areas of square base and triangle sides
S = 7² + 4*(1/2*7*14) = 49 + 196 = 245 in²Answer:
7 x 14 x 4 = 392
Step-by-step explanation:
The local high school is hosting the last soccer game. They charged adults, x, $5 to enter, and $3 for students, y. It costs the school $300 to pay the referees for the game. The school wants to make profit on the game, and 75 people attended. This is represented by the system:
5x +3y > 300
x+y = 75
which of the following points is a solution to the system?
(30,45)
(40,35)
(20,15)
(25,70)
Answers
Answer:
(40,35)
Step-by-step explanation:
Well we can immediacy eliminate 2 options for ow becuase if you add them up they don’t equal 75 and in the equation it asked for x+y=75.
Now we just test out each x and y possibility
We know 5x+3 > 300
So lets try the first one
30 is x
45 is Y
5*30=150
45*3=135
Now if you add them
285
285 is not greater than 300 so thats wrong
SO B is correct
But lets check just in case
5*40=200
3*35= 105
305 IS greater than 300
305 > 300
SO B is correct
The point (40,35)
How do you do this? is geometry please help this define my grade
Answers
Answer:
x = 21.287
Step-by-step explanation:
Use:
SOH CAH TOA
Cos(37) = 17.3/x
x = 21.287
Answer:
x = 21.287
Step-by-step explanation:
Use:
SOH CAH TOA
Cos(37) = 17.3/x
x = 21.287
3. For each literal, make a Venn diagram with three nonempty sets A; B and C, which satisfy simulta-
neously the given conditions:
a)A ⊂ B, C ⊂ B, A ∩ C = ∅ b)A ⊂ C, A 6= B, B ∩ C = ∅
c)A ⊂ B, C * B, A ∩ C 6= ∅ d)A ⊂ (B ∩ C), B ⊂ C, C 6= B, A 6= C.
Answers
Answer:
c is the right answer
Answer:
A
Step-by-step explanation:
I say a because it's supposed to bring the Venn diagram alone
To go on a summer trip, Ravi borrows $800. He makes no payments until the end of 3 years, when he pays off the entire loan. The lender charges simple interest at an annual rate of 5%. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Ravi have to pay? Х 5 ? s) (b) What will the total repayment amount be (including interest)?
Answers
Answer:
srry but search 12 z6xs
Step-by-step explanation:
(a) The total interest that Ravi will have to pay is $120. (b) The total repayment amount will be $920.
a) The interest rate is 5% per year, so Ravi will pay 5% * 800 = $40 per year in interest.
Since he borrowed the money for 3 years, he will pay a total of 3 * 40 = $120 in interest.
b) The total repayment amount will be the principal amount of $800 plus the interest of $120, for a total of 800 + 120 = $920.
Simple interest formula: I = P * r * t
Where:
I is the interest
P is the principal amount
r is the interest rate
t is the time in years
Interest per year: 5% * 800 = $40
Total interest: 3 * 40 = $120
Total repayment amount: 800 + 120 = $920
To learn more about interest here:
https://brainly.com/question/31135293
#SPJ2
PLZZ HELP!?!?Graph the linear equation −5x+y=−10. Then identify the x-intercept.
WILL BRAINLIEST IF RIGHT!?!?!?
Answers
Answer:
there is no x-intercept because the equation is
[tex]y = - 5[/tex]
there is only a y-intercept
I inserted an image of the graph. It's a straight line across -5.
Simplify the expression:
9g - 9g
Answers
Answer:
0
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
480
33°
*
Answers
PLZ HELP! WILL GIVE BRAINLIEST!! PLZ SOLVE QUICK!!
Find the value of x by filling in the blanks in the provided statement - reason solution.
I NEED THE WHOLE STATEMENT REASON CHART FILLED OUT!! THANK YOU SO MUCH IF YOU HELP!
Answers
Answer/Step-by-step explanation:
1. m<UTV = m<RTS = 85°
Reason: Definition of vertical angles.
Vertical angles are congruent to each other. m<UTV and m<RTS are vertical angles pair.
2. m<R + m<S + m<RTS = 180°
Reason: sum of interior angles of a ∆.
3. 3x + 2x + 85° = 180°
Reason: Substitution
4. x = 19
Reason: Algebra
Solving the equation algebraically, we would have the following:
3x + 2x + 85° = 180°
Add like terms
5x + 85 = 180
5x = 180 - 85 (subtraction property of equality)
5x = 95
Divide both sides by 5
x = 19