The speed of 213.25 mph is the red car actually traveling along the road.
What is speed?
The definition of speed is the pace of movement of an object (covering a particular distance). It defines only the magnitude and not the direction, making it a scalar quantity.
The meter per second (m/s) unit of speed is taken from the SI.
let distance between the police and red cars = h
distance from the red car to a point horizontal to the police car = a
distance from from the road to the police car = b
=>[tex]h^2=a^2+b^2[/tex]
take the derivative with respect to time
=>hh' = aa' + bb' b'=0
=>174.64(75) = 90a'
=>a' = 174.64(75)/90 = 145.4ft/sec
=>145.4ft/sec = 145.4(5280)/60^2 = about 213.25 mph
Here ,1 mile = 5280 feet
=>1 hour = 60 minutes x 60 seconds = 3600 seconds
=>1 mile per hour = 5280 feet per 3600 seconds
=>1 foot per second = 5280/3600 mph = 1.4666...mph
=>145.4x 1.4666... = 213.25 mph
Hence 213.25 mph speed is the red car actually traveling along the road.
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Given that U={a,b,c,d,e,f} and X={a,b,c,d}, Y={c,d,e} and Z={b,d,f} , Find (XUY)U(XUZ)
A and B are two sets, and the set formula is given as n(AB) = n(A) + n(B) - n(AB), where n(AB) denotes the number of elements present in either A or B, and n(AB) is the number of elements present in both A and B.
How do you solve sets?Drawing Venn diagrams, as seen below, is the simplest method for solving set issues.
The total number of elements in any set A or B is n(AB).
The total number of elements in sets A and B is n(AB).
n(AB) is equal to n(A) + n(B) - n(AB)
U={a,b,c,d,e,f}
X={a,b,c,d},
Y={c,d,e}
Z={b,d,f}
(XUY) = (a,b,c,d,e)
(XUZ) =(a,b,c,d,f)
(XUY)U(XUZ) = (a,b,c,d,e,f)
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Quadrilateral EFGH is similar to quadrilateral IJKL. Find KL. Round your
answer to the nearest tenth if necessary. Figures are not drawn to scale.
59
H
13
E
27
F
G
I
L
X
K
Answer:
x=81
steps
From the concept of similarity
3EH = ILhence, 3HG = KL3(27) = KLKL = 8118. Which of the following are solutions to the equation 19.
-11x = 2x² +15? Select all that apply.
x²
a. -5
b. -3
c. -5/2
d. 5/2
e. 3
f. 5
The solutions to the given equation are -5/2 and -3. These answer can get after using quadratic formula.
How can find solution using quadratic formula ?The quadratic formula is a formula that offers a quadratic equation's solution. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.
In the literature, there are numerous ways to derive the quadratic formula. The common one uses the completing the square method in a straightforward manner.
The given equation is :
-11x = 2x² +15
Move terms to the left side
-11x -(2x^2 +15) =0
Rearrange terms
-2x^2 - 11x -15 = 0
Common factor
-(2x^2+ 11x +15) =0
Divide both sides by the same factor
2x^2 +11x +15 =0
Use the quadratic formula
x = -11 ± √11² - 4 * 2*15/2*2
x =-11±1/4
Solve
x = -5/2
x= -3
The value of x will be -5/2 or -3.
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Is this relation a function ?
in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.4 inches, and standard deviation of 1.2 inches. what is the probability that the height of a randomly chosen child is between 50.5 and 53.7 inches? do not round until you get your your final answer, and then round to 3 decimal places.
Answer:
0.591
Step-by-step explanation:
You want the probability that a height falls between 50.5 and 53.7 when the distribution of heights is normal with mean 53.4 and standard deviation 1.2. All measurements are in inches.
ProbabilityThe area under the normal distribution curve with mean 53.4 and standard deviation 1.2 can be found using a suitable calculator. The one in the attachment shows the area between 50.5 and 53.7 is about 0.591
P(50.5 < X < 53.7) ≈ 0.591
__
Additional comment
Any spreadsheet and most graphing calculators have the necessary probability functions. Many special-purpose apps also can answer this question. A calculator answer is shown in the second attachment.
Take 16 objects (pieces of paper, coins, plums, checkers) and put them in four
rows of 4 each. Remove 6, leaving an even number of objects in each row and each
column. (There are many solutions.)
There can be different possible ways in which we can remove the objects and can form possibilities within the rows and columns
What are rows and columns?
Rows and columns are used to properly distinguish categories, classifications, types, etc., when they occur in matrices, spreadsheets, etc. The usage of these words is a bit confusing for most. Rows are a group of cells arranged horizontally to provide uniformity. Columns are a group of cells aligned vertically, and they run from top to bottom. Although the main reason for both rows and columns is to bifurcate groups, categories, and so on,
In the question, It is given that:
There are 16 objects.
and Number of rows = 4;
Number of column = 4;
The task to do is to remove 6, leaving an even number of objects in each row.
So, we can do that in the following manner;
So, we can remove the 2nd object, 4th object, 6th object,8th object,10th object, and 12th object. when we are dealing with rows.
So, we can remove the 2nd object, 4th object, 6th object,8th object,10th object, and 12th object. when we are dealing with the column.
Hence,
There can be different possible ways in which we can remove the objects and can form possibilities.
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-2x+5=23 what is x i dont know how to find it
Answer:
x=-9
Step-by-step explanation:
-2x+5=23
-5 on both sides
-2x=18
/-2 on both sides
x=-9
PLEASE HELP I REAALLY NEED HELP!
The domain of the exponential function in this problem is given as follows:
0 ≤ n ≤ 5.
How to obtain the domain of the exponential function?The exponential function in this problem is defined by the rule presented as follows:
g(n) = 10(1.02)^n.
In which the variables are listed as follows:
n is the number of days.g(n) is the height of flower after n days.When the study was finished, the height of the flower was of 11.04 inches, hence the day at which the study was finished is obtained as follows:
10(1.02)^n = 11.04
(1.02)^n = 11.04/10
log[(1.02)^n] = log(11.04/10)
Applying the logarithm of power property, we have that:
nlog(1.02) = log(11.04/10)
n = log(11.04/10)/log(1.02)
n = 5.
The domain is the number of days for which the student was realized, hence:
0 ≤ n ≤ 5.
As the number of days cannot assume negative values.
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Q1 Q2 Logic puzzles
Solve the problems.
3 paintings are for sale.
Painting A is three times the
price of painting B.
Painting B is half the price of
painting C.
Painting C costs £368.
What are the prices of paintings
A and B?
Painting A = £ I
Painting B = £
Step-by-step explanation:
so basically, because Painting C costs £368 and Painting B is half that cost, Painting B costs £184. And Painting A is three times that amount Painting A costs £552.
You're Welcome ♡.
given a normal distribution with a mean of 50 and standard deviation of 5, what percent of the values are between 40 and 60? enter answer as a percent with no decimals.
For the given normal distribution, 95% of the values lie between 40 and 60.
Let the said distribution be X
Here it is given that X follows a normal distribution and it has a mean of 50 and a standard deviation of 5.
Therefore we can write X~ N(50, 25)
Now we need to find P(40< X< 60)
= P(40< X< 60) = P(X < 60) - P(X<40)
To find this we need to convert it into the form of a standard normal and then look up the p-values from the Z-table.
To do this we need to use the formula
P(X < x) = Φ[(x - μ) / σ]
where,
μ is the mean
σ is the standard deviation
Therefore we get
P(X < 60) - P(X<40) = Φ[(60 - 50) / 5] - Φ[(40 - 50) / 5]
= Φ[2] - Φ[-2]
Φ(-x) = 1 - Φ(x)
Therefore,
Φ[2] - Φ[-2]
= 2Φ(2) - 1
We get the p-value
2 X .97725 - 1
= 1.9545 - 1
= 0.9545
= 95% (approx)
Hence 95% of the values are between 40 to 60.
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you play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. for any given match you have a probability of 0.6 of winning. what is the probability that you win the next two matches?
Answer:
0, 6 * 0,6 = 0.36
Step-by-step explanation:
Keyword is AND.First AND second matches both. It means you need to use *.
The probability of winning both matches is 0.36 or 36%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Since the outcome of each match is independent, we can use the multiplication rule of probability to find the probability of winning the next two matches:
P(win both matches) = P(win first match) x P(win second match)
The probability of winning a single match is given as 0.6.
Therefore, the probability of winning the first match is 0.6.
Now, assuming you won the first match, you still have a probability of 0.6 of winning the second match.
Therefore, the probability of winning both matches is:
P(win both matches) = P(win first match) * P(win second match)
= 0.6 x 0.6
= 0.36
Therefore,
The probability of winning both matches is 0.36 or 36%.
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the larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean.
As sample size grows, sample variance (variation among observations) grows, while sample mean variance (standard error) decreases, and therefore precision grows.
Define the term normal approximation?The normal curve approximates the sample distribution of averages as well as proportions from just a large number of distinct experiments.
The population value corresponds to the assumption of a sample fraction or average.Because summing big values might be cumbersome or impossible with certain discrete distributions, such as the Binomial or Poisson distributions. The Normal Distribution, thankfully, provides us to approximation the probability for random variables which would otherwise be impossible to quantify.Thus, the better the normal approximation here to sampling distribution for sample mean, the greater the sample size.
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13 is 6 1/2% of what number?
Answer:
200
Step-by-step explanation:
Diana recorded the total number of people living in each of the homes of 8 classmates. Which of the following values could be the median of those 8 numbers?
I. 0.0
II. 3.0
III. 4.5
Answer:
The answer is III: 4.5
Step-by-step explanation:
It's not the first option since there has to be more than one person living in those houses. It's not the second since 3 is greater than 0, and median is in order from least to greatest. It's three since it's reasonable and is in order from least to greatest.
a medical device company knows that 11% of patients experience injection-site reactions with the current needle. if 4 people receive injections with this type of needle, what is the probability that none of the 4 people get an injection-site reaction?
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Given: The proportion of patients experience injection-site reactions with the current needle : p=0.11Sample size : n= 4Let x be a binomial random variable that represents the people get an injection-site reaction.Binomial probability formula: The required probability : P(x=0)learn more about probability click here:
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Help me, please!!!!!!!!!
Answer:
Step-by-step explanation:
firstv= block second one
secondblock third one
and so on
Jonathan‘s scout troop tie-dyed sweatshirts and T-shirts last year for a fundraiser. For every 20 sweatshirts they dyed 30 T-shirts. This year Jonathan scout troop will keep the same ratio of sweatshirts and T-shirts. They plan to tie-dye 60 sweatshirts.
How many T-shirts with Jonathan Scout troop dye this year?
Answer:90 t shirts
Step-by-step explanation: 20:30 is the ratio and if they make 60 sweatshirts, they would have to make 90 tshirts as well. this would keep the same ratio
I need help like asap !!!
only numbers and decimal points
Answer:
24.41
Step-by-step explanation:
a^2+b^2=c^2
14^2+20^2=c^2
196+400=596
14^2+20^2=24.41^2
Please can someone answer this question it would be much appreciated
Thanks so much :)
I need help too on this one
Answer:
you lowest tempeture in the mesosphere is -96
Step-by-step explanation:
Please help me solve as soon as possible
Using the given expression, the number of tiles Mr. Grants will need to buy is 48
Solving an expression to determine the number of tilesFrom the question, we are to use the given expression to determine the number of tiles Mr. Grant would have to buy
From the given information,
The given expression is,
27 ÷ s²
and
Mr. Grants decides to buy square tiles that have side lengths of 3/4 foot
That is,
s = 3/4
Now,
Using the given expression
27 ÷ s²
We get
27 ÷ (3/4)²
27 ÷ 9/16
= 27 × 16 / 9
= 3 × 16
= 48
Hence, he will need to buy 48 of the tiles
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Help Please!!!
Direct and Inverse Variations
aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given sequence is 5,9,13,17,21
Five comma nine comma thirteen comma seventeen comma twenty one.
We need to find the nth term of the sequence.
Firstly we need to find the sequence is AP or GP.
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.
so 9-5=4,
13-9=4
Hence the sequence is a Aritmetic sequence.
In arithmetic sequence the nth term can be find by using the formula
aₙ=a+(n-1)d
where a is first term and d is common difference.
Hence aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.
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which is a net for this triangular prism
Answer:
this One...............
Find the largest area for a rectangle that is inscribed in a semicircle with radius 4 inches.
Answer:
16 square inches
Step-by-step explanation:
You want the largest rectangle that can be inscribed in a semicircle with radius 4 inches.
AreaThe equation of a circle centered at the origin with radius 4 is ...
x² +y² = 16
The height (y) of a rectangle whose corner is on the circle will be ...
y = √(16 -x²)
The width of such a rectangle is 2x, so the area of it is ...
A = WH = (2x)√(16 -x²)
MaximumThe maximum area will be had when the derivative of the area with respect to x is zero.
A' = 2√(16 -x²) - 2x²/√(16 -x²) = 0
Multiplying by √(16 -x²)/2 gives ...
16 -x² -x² = 0
16 = 2x²
x = √(16/2) = 2√2
The corresponding area of the rectangle is ...
A = 2(2√2)√(16 -(2√2)²) = 16
The largest rectangle has an area of 16 square inches.
__
Additional comment
As is often the case with rectangle optimization problems, the largest rectangle that can be inscribed in the quarter circle in each quadrant is a square. It has a diagonal of 4 inches, so an area of 4²/2 = 8 square inches.
The attachment shows the cubic curve representing the area of that square as a function of its width. As above, the rectangle area is double this value.
-12a + -5b - 12c + 6a - 8b - (-4)
Answer:
-6a -13b - 12c + 4
Step-by-step explanation:
-12a + -5b - 12c + 6a - 8b - (-4)
-12a + -5b - 12c + 6a - 8b + 4 [a "- -" = +]
(-12a + 6a) -(5b -8b) - 12c + 4 [Group like terms.]
-6a -13b - 12c + 4
Find the solution of the system of equations.
−10x+2y=−32
-2x-2y=−16
The solution of the system of equations are x = 4 and y = 4.
What are the solutions?The system of equations would be solved using the elimination method.
−10x+2y=−32 equation 1
-2x-2y=−16 equation 2
In order to determine the value of x, take the following steps:
Add equation 2 and equation 1 together
-12x = - 48
Divide both sides of the equation by -12
x = -48 / - 12
x = 4
In order to determine the value of y, substitute for x in equation 1:
-(10 x 4) + 2y = -32
-40 + 2y = -32
Combine similar terms:
2y = -32 + 40
Add similar terms:
2y = 8
Divide both sides of the equation by 2
y = 8 / 2
y = 4
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the hire purchase price for a refrigerator is 6500 a deposit of 500 is made and the remainder is paid in equal monthly payments of $250 calculate the number of month that the payments must be made
If the remainder is paid in equal monthly payments of $250. the number of month that the payments must be made is 24.
How to find the monthly payment?First step is to find the remainder after down payment
Remainder = 6500-500
Remainder = 6000
Now let find the number of monthly payment
Number of monthly payment = Remainder / Monthly payment
Number of monthly payment = 6000 / 250
Number of monthly payment = 24
Therefore the monthly payment is 24.
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Noah runs a farm stand that sells bananas and raspberries. Each pound of bananas
sells for $3 and each pound of raspberries sells for $2.25. Noah made $72 from
selling a total of 28 pounds of bananas and raspberries. Graphically solve a system of
equations in order to determine the number of pounds of bananas sold, a, and the
number of pounds of raspberries sold, y.
There is no possible solution for the weight of raspberries sold, given that 28 pounds of banana were sold.
What is Co-ordinate Geometry?
Graphs and coordinates are utilised in coordinate geometry to discover information about various geometric figures. A description of the coordinate plane must be included in a definition of coordinate geometry. A coordinate plane, also known as a coordinate graph, is a grid system formed by the intersection of two number lines known as axes. The x-axis is the horizontal number line, and the y-axis is the vertical number line. These axes meet at a position known as the origin.
Solution:
let, the total weight of banana sold be x pounds
and total weight of raspberries soldd be y pounds.
From the data given in the question, the equation formed is
3x + 2.25y = 72
(See Graph)
at x = 28 we will get the value of y as -5.34
which is not a possible solution
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read.
The total number of pages that he read will be 210 pages.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Based on the equation given, the equation to represent Amir's information will be:
y = 35 × x
y = 35x
Jesse's equation will be:
y = 30(x + 1)
Then, we'll equate both equations together. This will be:
35x = 30(x + 1)
35x = 30x + 30
35x - 30x = 30
5x = 30
x = 30/5
x = 6
Therefore, the number of pages read will be:
y = 35x
y = 35 × 6
y = 210 pages.
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On a photograph an ant is enlarged at a scale 25:1. In the photo, the ants leg is 15 cm. What is the actual length of the ants leg?
Answer:
0.6cm
Step-by-step explanation:
25 : 1
1 : 0.04
15 : 0.6
11 student are in a waitlist for a course. two of the students in the list are named ed and ned. how many different ways are there for the students to be ordered in the list so that ed is higher in the list than ned?
The different ways that are there for the students to be ordered in the list so that Ed is higher on the list than Ned is 19,958,400
In the order, if Ned comes first on the list then Ed will not be on the list before Ned. (remember for Ed to be higher than Ned on the list, it should come after Ned on the list).
So if Ned is first on the list, then all the remaining (including Ed) can occur anywhere in the remaining list. Hence the total permutations will be 10!
Ned's corresponding choices: 1 109 8 7 6 5 4 3 -2 1
If Ned comes in the second position, then Ed can't come in the first position. Hence in the first position, there are only 9 choices.
*(excluding Ed) Ned * corresponding choices:
= 9*9!
*(including Ed (including Ed) Ned corresponding choices: *k
= 9*8*8!
Total combinations will be:
10! + 9*9! + 9*8*8! + 9*8*7*7! + 9*8*7*6*6! + 9*8*7*6*5*5! + 9*8*7*6*5*4*4! + 9*8*7*6*5*4*3*3! +9*8*7*6*5*4*3*2*2! + 9*8*7*6*5*4*3*2*1*1! .
= 19,958,400
We can directly compute it. Since there will be a total of 11! combinations in which 11!/2 times Ed comes after Ned and 11!/2 times Ed comes before Ned.
and 11!/2 = 39,916,800/2 = 19,958,400
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