On a map, Mary's house is located at (−3, 1) and the grocery store is located at (5, 7). Mary walks on a straight line from her house to the grocery store.
Which ordered pair represents the halfway point between Mary's home and the grocery store?
(−1, 4)
(−4, −3)
(4, 4)
(1, 4)
Answers
The ordered pair that represents the halfway point between Mary's home and the grocery store is (1, 4)
The midpoint (a, b) between two linear points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:
\(a=\frac{x_1+x_2}{2} \\\\b=\frac{y_1+y_2}{2}\)
On a map, Mary's house is located at (−3, 1) and the grocery store is located at (5, 7).
\(x_1=-3, y_1=1, x_2=5, y_2=7\)
Substitute these values into the mid-point formulae
\(a=\frac{-3+5}{2} \\\\a=\frac{2}{2}\\\\a=1\)
\(b=\frac{1+7}{2} \\\\b=\frac{8}{2}\\\\b=4\)
The ordered pair that represents the halfway point between Mary's home and the grocery store is (1, 4)
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Related Questions
Please help me in this! you get 30 points!
Answers
Answer:
y=3x-2
Step-by-step explanation:
You can verify it's not D because the y-intercept is at -2.
You can verify it's not A because that would mean the x-intercept is 2 despite it appearing to be closer to one.
You can verify it's not B because that would mean the x-intercept is 1.5
Convert 2,430 yards to km
Answers
Answer:
2.221992
Step-by-step explanation:
can i have the crown pls ૮ ♡ﻌ♡ა
Answer:
2.221
Step-by-step explanation:
You roll a 6-sided die. What is P(3)
Answers
The probability of rolling a 3 on a fair 6-sided die that P(3) is 0.17.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Since each side of the die is equally likely to land face up,
So the number of favorable outcomes n(E) = 1
And the total number of outcomes n(S) = 6
Thus, P(3) is the probability of rolling a 3 on a fair 6-sided die :
P(3) = n(E)/n(S)
P(3) = 1/6
P(3) = 0.17
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Find the sum.
(4x² + x − 4) + (2x² + 4x + 5) =
20 POINTS PEASE
Answers
Answer:
6x² + 5x + 1
Step-by-step explanation:
(4x² + x − 4) + (2x² + 4x + 5)
1. Expand the brackets to get
4x² + x − 4 + 2x² + 4x + 5
2. Group common terms (terms with same power as well as the constant)
4x² + 2x² + x + 4x - 4 + 5
3. Simplify
4x² + 2x² = 6x²
x + 4x = 5x
-4 + 5 = 1
4. Solution is
6x² + 5x + 1
While reviewing the previous day’s arrest report, a police sergeant notices that five suspects were arrested, all of whom had either one or two previous arrests. Including yesterday’s arrests, there were 12 total arrests among them. How many suspects had less than two prior arrests?
Answers
The number of suspects had less than two prior arrests are 3.
Given that, While reviewing the previous day’s arrest report.
Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.
Here, x+y=5 -----(i)
2x+3y=12 -----(ii)
From equation (i), x=5-y in equation (ii), we get
2(5-y)+3y=12
10-2y+3y=12
10+y=12
y=2
Substitute y=2 in equation (i), we get
x+2=5
x=3
Therefore, the number of suspects had less than two prior arrests are 3.
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Alice and Bob play a game by taking turns removing 1 or 2 stones from a pile that initially has n stones. The person that removes the last stone wins the game. Alice plays always first.
(a) Prove by induction that if n is a multiple of 3 then Bob has a wining strategy.
(b) Prove that if n is not a multiple of 3 then Alice has a wining strategy.
Answers
Answer:
Step-by-step explanation:
(a) We will prove by induction that if n is a multiple of 3 then Bob has a winning strategy.
Let n=3
It is given that Alice always plays first.
Then, for the first move, Alice has a choice of removing 1 or 2 stones.
Case 1:
Alice removes 1 stone. Then it is now Bob's turn. There are 2 stones left. Bob has the choice of removing 1 or 2 stones. Then Bob's winning strategy should be to remove 2 stones. Then Bob removes the last stone and wins.
Case 2:
Alice removes 2 stones. Then it is Bob's turn. There is exactly 1 stone left, which Bob removes in his turn. Since he removes the last stone, he wins.
Thus, in either case, for n=3, Bob has a winning strategy. ____ (A)
Now, let us assume that Bob has a winning strategy for n=3p.
We will now check if Bob has a winning strategy for n=3p+3
It is given that Alice plays first.
Case 1:
Alice starts the game by removing 1 stone. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 2 stones, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case Bob has a winning strategy.
Case 2:
Alice starts the game by removing 2 stones. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 1 stone, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is again exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case also, Bob has a winning strategy.
Thus, in either case Bob has a winning strategy for n=3p+3 if he has a winning strategy for n=3p. _______ (B)
Thus, from (A) & (B), using induction, we can say that Bob has a winning strategy if n is a multiple of 3.
(b) We will now prove that if n is not a multiple of 3, then Alice has a winning strategy.
If n is not a multiple of 3, then n can have either of the forms of 3m+1 or 3m+2, m ∈ W.
We will prove the given fact for both the forms simultaneously
Let m=0, i.e., n=1 or n=2
Since Alice starts first, she removes 1 stone, if n=1 or 2 stones if n=2 and thus wins. Thus Alice has a winning strategy if m=0. ______ (A)
Let us assume that Alice has a winning strategy for m=k, i.e., for n=3k+1 & n=3k+2
Now, we will check if Alice has a winning strategy for m=k+1, i.e., for n=3(k+1)+1=3k+4 or n=3(k+1)+2=3k+5
Let n=3k+4
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 2 stones and in turn Bob removes 2 stones, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 1 stone. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+4-1-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+4-1-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Let n=3k+5
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 1 stone and in turn Bob removes 1 stone, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 2 stones. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+5-2-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+5-2-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Then, we can say that Alice has a winning strategy for m=k+1 if she has a winning strategy for m=k. _____ (B)
Then, by induction, from (A) & (B), we can say that if n is not a multiple of 3, then Alice has a winning strategy.
Which of the following is a factor of 2x2 - x-6?
O (x+2)
O (2x - 3)
o (x – 3)
O (2x + 3)
Answers
A pharmacist receives a shipment of 21 bottles of a drug and has three of the bottles tested. If five of the 21 bottles are contaminated, what is the probability that less than two of the tested bottles are contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
The probability is 0.8722
Step-by-step explanation:
There are 21 bottles
5 of them are contaminated.
there are 21 - 5 = 16 non-contaminated bottles.
So, if we grab a bottle at random, the probability that this bottle is contaminated will be equal to the quotient between the number of contaminated bottles and the total number of bottles, this is:
p = 5/21
Now we want to find the probability that, for 3 tested bottles, that less than two (0 or 1 ) are contaminated.
Let's see each case on its own.
0 bottles:
The probability of getting a non-contaminated bottle in the first try is equal to the quotient between the number of non-contaminated bottles and the total number of bottles, this is:
p₁ = 16/21
For the second bottle is the same, but because one non-contaminated bottle was drawn before, now there are 15 non-contaminated bottles and 20 bottles in total, so now the probability is:
p₂ = 15/20
and similarly, for the third bottle the probability is:
p₃ = 14/19
The joint probability is the product of the individual probabilities, we get:
P = p₁*p₂*p₃ = (16/21)*(15/20)*(14/19) = 0.4211
Now the case that one bottle is contaminated.
Let's assume that the first one is contaminated.
The probability of getting a contaminated bottle in the first draw is equal to the quotient between the number of contaminated bottles and the total number of bottles, so:
p₁ = 5/21
For the second bottle, we want a non-contaminated one, there are 16 non-contaminated bottles and 20 bottles left, so here the probability is:
p₂ = 16/20
and for the third bottle we have the probability:
p₃ = 15/19
The joint probability is:
p = p₁*p₂*p₃ = (5/21)*(16/20)*(15/19)
Also notice that we only looked at the case where the first bottle is contaminated, we also have the case where the second one is contaminated and the case where the third one is contaminated, so there are 3 permutations, then the probability of having one contaminated bottle is:
Q = 3*p = 3*(5/21)*(16/20)*(15/19) = 0.4511
Then the probability of having less than two contaminated bottles is:
probability = P + Q = 0.4211 + 0.4511 = 0.8722
2+2=4\
whats yall qc (question cove)
Answers
Answer:
TrinityInfinity. and 4
Step-by-step explanation:
500,000 in expanded form
Answers
Answer:
500,000 =
5 × 100,000
+ 0 × 10,000
+ 0 × 1,000
+ 0 × 100
+ 0 × 10
+ 0 × 1
Step-by-step explanation:
there are more then one ways of writing this so here's another example
500,000 =
500,000
+ 0
+ 0
+ 0
+ 0
+ 0
Which expression represents the distance between 4.7 and −11.2 on the number line?
Drag and drop the correct expression into the box.
30 points to answer!
Answers
Answer:
Option A or 1 or |-11.2 -4.7|
Step-by-step explanation:
Calculate the distance :
distance =
| 4.7 - (- 11.2) | =
| 4.7 + 11.2 | =
| 15.9 | =
15.9.
Should help
Answer:
|-11.2 -4.7|
Step-by-step explanation:
You want the expression that represents the distance between 4.7 and -11.2 on a number line.
DistanceThe distance on a number line is the positive difference between the coordinates of the points. Here, that would be either of ...
|4.7 -(-11.2)|
or
|-11.2 -4.7| . . . . . . matches an answer choice
__
Additional comment
Note that when we subtract the left coordinate from the right coordinate, the difference is already positive, so no absolute value function is needed.
Pls help me plssss plsssss
Answers
Answer:
B
Step-by-step explanation:
how many 1/2's in 4? thats how many bows so 4 ÷ 1/2
Answer:
it's b.
debbie can make 8 bowls
FOR 20 POINTS!!!
(Look at picture)
Answers
Answer:
Kenyon could make a total of 7 bouquets.
Step-by-step explanation:
To find the greatest number of bouquets we need to find GCF.
We need to find GCF for 21 and 28.
The factors of 21 are: 1,3,7, and 21.
The factors of 28 are: 1,2,4,7,14, and 28
1 and 7 are the common factors between 21 and 28.
From the factors, the greatest common factor is 7.
Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.
Answers
if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
How to determine the monthly instalment price and instalment price that Daikin needs to pay.Calculating the loan amount for each brand by subtracting the down payment from the cash price:
Loan amount for Daewoo = RM1,899 - RM300 = RM1,599
Loan amount for Daikin = RM1,699 - RM300 = RM1,399
Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699
Calculating the interest charge for each brand:
Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96
Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96
Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96
To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:
Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22
Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89
Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72
Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
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5. Ángulos Un ángulo recto se divide en tres ángulos más pequeños. El más grande de
los tres mide el doble del más pequeño. El ángulo restante mide 10º más que el ángulo
más pequeño. Determine la medida de cada ángulo.
Answers
Answer:
Disculpe, ¿esta es la pregunta completa?
In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle. Let us read about the different parts of an angle.
Parts of an AngleThere are two main parts related to an angle - the arms and the vertex.
Arms of the AngleThe two rays which join at a common point to form the angle are called the arms of the angle.
given:
angle= 90
let the smaller angle is x
largest angle= 2x
and the third angle = x+ 10
Now
x+ (x +10) +2x= 90
4x + 10= 90
4x= 80
x= 20
So,
smallest angle= 20
second angle= x+10= 30
largest angle= 2x= 2*20 = 40
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The translation of the question is:
A right angle is divided into three smaller angles. The largest of
all three are twice the size of the smallest. The remaining angle measures 10º more than the angle.
smaller. Determine the measure of each angle.
Calculator Triangle ABC is similar totriangle DEF. The length of AC is 12 cm. The length of EF is 35 cm. The length of DF is 20 cm What is the length of BC ? Enter your answer in the box. cm
Answers
Answer:
BC = 21 cm
Step-by-step explanation:
In similar triangles the corresponding sides are in same proportion.
Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.
\(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)
\(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)
21 20 15 22 19 23 17 what is the median and range
Answers
The median would be 22:
Step-by-step explanation: The median is the number that is in the middle
Simply defined, the median is the number right in the middle of a set.
But before I get down to finding the median, I will order the numbers from least to greatest:
15, 17, 19, 20, 21, 22, 23
Now, the middle number is 20. So that's the median.
As for the range, it's the difference between the largest number and the smallest one:
Range = Greatest number - Smallest number
= 23 - 15
= 6
In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.
Triangle A B C is shown. The length of A C is 8 and the length of C B is a. Angle C A B is 45 degrees and angle A B C is 77 degrees.
Complete the work to determine the value of a.
Use the law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction.
Substitute: StartFraction sine (45 degrees) Over a EndFraction = StartFraction sine (77 degrees) Over 8 EndFraction .
Cross multiply: 8sin(45°) = asin(77°).
Solve for a and round to the nearest hundredth:
a ≈
.
Answers
Answer:
approximately 4.75 units
Step-by-step explanation:
Using the law of sines, we have:
sin(A)/a = sin(B)/b
Substituting the given values, we get:
sin(45°)/a = sin(77°)/8
Solving for 'a', we have:
a = sin(45°) * 8 / sin(77°)
a ≈ 4.75 (rounded to two decimal places)
Therefore, the length of CB is approximately 4.75 units
Answer:5.81
Step-by-step explanation: I'm doing the assignment rn and got it right.
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Answers
For example, suppose you have the Cartesian equation of a line in the form:
y = mx + b
and the equation of a plane in the form:
ax + by + cz + d = 0
To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.
Here's an example:
Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.
If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:
2(1) + 3(3) + 4z + 5 = 0
Solving for z, we find that z = -1.5.
Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.
If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.
A report states that the mean household income last year for a certain rural county was $46,200 and the median was $37,800. If a histogram were constructed for the incomes of all households in the county, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answers
Answer:
skewed to the right
Step-by-step explanation:
Given that
the mean household income for the last year was $46,200
And, the median was $37,800
In the case when the historgram is prepared so the income would be skewed to the right as the mean i..e $46,200 is more tha the median i.e. $37,800
So, the distribution would be right skewed
Hence, the same would be considered and relevant
What does 300,000÷700 Equal
Answers
Answer: 42.857142857142854
Step-by-step explanation:
Rounded to the nearest tenth: 42. 9 or 42.90
Rounded to the nearest hundred: 42. 86 or 42.860
Hope this help, take care.
I need help ASAP. Thank you.
Answers
Use a graph calculator.
A cake is made from the ingredients listed below.
500 g flour, 450 g butter, 470 g sugar,
1.8 kg mixed fruit, 4 eggs (70 g each)
The cake loses 12% of its mass during cooking.
What is its final mass?
Answers
To make a cake :-
Quantity of flour needed = 500 g
Quantity of butter needed = 450 g
Quantity of sugar needed = 470 g
Quantity of mixed fruit needed = 1.8 kg = 1000 g + 800 g
Quantity of eggs needed = 70 × 4 = 280 g
It's weight after adding all the ingredients =
=500 + 450 + 470 + 1000 + 800 + 280
= 3500 g
Mass that got lost while baking the cake :
= 12 % of 3500\( = \frac{12}{100} \: of \: 3500\)
\( = \frac{12}{100} \times 3500\)
\( =\frac{(12 \times 3500)}{100} \)
\( =\frac{42000}{100} \: g\)
\( = 420 \: g\)
Final mass = Initial mass - mass that got lost
\( = 3500 - 420 \: g\)
\( = 3080 \: g\)
∴ The final mass of the cake is 3080 g .
the circumference of a circular patio is 53 2/7 ft. what is the area of the patio. use 22/7 for pi. round to the nearest hundredth
Answers
Answer:
I think it is A≈225.77
Step-by-step explanation:
PLEASE HELP DUE NOW!!!
WILL MARK BRAINLIEST!!!
Answers
Answer:
(-4,6)
Step-by-step explanation:
Answer:
I can't help you
Step-by-step explanation:
but I recommend looking up videos to help you does not need to be the same problem but practice
1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
Answers
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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Tina is going on a 5 day trip. She has 1 blue shirt, 1 red shirt, 1 white shirt, 1 green shirt, and 1 grey shirt. What is the probability that Tina will wear blue on the first day of her trip and then wear grey on the second day of her trip?
Answers
Answer:
1/20
Step-by-step explanation:
1/5 chance she will wear the blue shirt on the first day and 1/4 chance she will wear a grey shirt on the second day.
1/5 X 1/4 = 1/20
Answer:
i got 1/20 as my answer
For the arithmetic sequence beginning with the terms {-1, 2, 5, 8, 11, 14...}, what is the sum of the first 16 terms?
Answers
Answer:
S₁₆ = 344
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then
S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]
= 8 (- 2 + 45)
= 8 × 43
= 344
Find P(AUB) of P(A)=2/5,P(B)=2/7 and A and B are Independent
Answers
P(A∪B)=24/35 when A and B are independent and P(A)=2/5,P(B)=2/7
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty. The greater the likelihood of an occurrence, the more likely it will occur.
Probability theory, which is widely used in domains such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these concepts axiomatic mathematical formalization.
Given,
P(A)=2/5
P(A)=2/7
P(A∪B)=?
And also given that A and B are independent then,
P(A∩B)=0
P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∪B)=(2/5)+(2/7)-0
P(A∪B)=(14+10)/35
P(A∪B)=24/35
Therefore, P(A∪B)=24/35 when A and B are independent.
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Drawing a number divisible by 3 then drawing a 1
Answers
Answer:
Step-by-step explanation:
The probability of drawing a number that is divisible by 3 is 1/3, since there are 3 numbers (3, 6, and 9) out of the 9 possible numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) that are divisible by 3.
The probability of drawing a 1 after drawing a number that is divisible by 3 is 1/10, since there is only one 1 among the 10 possible digits (0-9) that could be drawn after the first number.
To find the probability of both events happening together (drawing a number divisible by 3 and then drawing a 1), we need to multiply the probability of the first event by the probability of the second event. Therefore, the probability of drawing a number divisible by 3 and then drawing a 1 is:
(1/3) x (1/10) = 1/30
So the probability of drawing a number divisible by 3 and then drawing a 1 is 1/30, or approximately 0.0333, or about 3.33%
Answer:
If I understand this correctly you can draw a 9 and then draw the one if I'm wrong just delete this
Step-by-step explanation: