a) The probability that random guessing will lead to a passing score is of: 0%.
b) The probability that random guessing will lead to a perfect score is of: 3.35 x 10^-18.
c) The first version of the test is safer against examinees guessing to achieve a passing score.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item a, considering that for 50 questions, all are guessed among five answer, the values of these parameters are given as follows:
n = 50, p = 1/5 = 0.2.
The probability of passing is given as follows:
P(X ≥ 35).
Using a binomial distribution calculator, with the given parameters, we have that:
P(X ≥ 35) = 0%.
For item b, the parameters are given as follows:
n = 25, p = 1/4 = 0.2.
Hence the probability of a perfect score is given as follows:
P(X = 25) = 0.2^25 = 3.35 x 10^-18.
For item c, we have that the first version is safer against examinees guessing to achieve a passing score, as:
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2 1/2 divided by 1 3/4
Answer:
10/7 or 1 3/7
Step-by-step explanation:
1. change from mixed fraction to improper fraction, 5/2 and 7/4
2. instead of the dividing the fractions as is, multiply the reciprocal which would be 5/2 multiplied by 4/7. Then you cross multiply. 2 into 2, 1 and 2 into 4, 2. So now you're left with 5 and 2/7 since 5/1 is basically 1.
3. simplify to just 10/7
Answer:
10/7 or 1 3/7
I took a test with that question.
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what level of confidence (as a ) would accompany each of the following intervals? (Round your answers for parts (a), (b), and (c) to the nearest Integer and your answer for part(a) tsample proportion 1.96(b) sample proportion 1.645to sample proportion 2.576(d) sample proportion 3.0 S
The level of confidence as a would accompany each of the given intervals are a. 95%, b. 90%, c. 99%
what level of confidence?Instead of being expressed as a percentage, the confidence level is expressed as a proportion using the confidence coefficient. For instance, the confidence coefficient would be. 99 if you had a confidence level of 99%. In general, the greater the coefficient, the more confident you can be in the accuracy of your findings.
What are the 3 common confidence level?The most typical levels of confidence are 90%, 95%, and 99%. A summary of the values corresponding to these typical confidence levels can be seen in the following table. The "confidence coefficient" is simply the confidence level presented as a proportion .
for a:
Z1=a/2=1.96
1-a/2=0.975
a=0.05
so,
(1-a)x100
=95%
Hence, the level of confidence is 95%
for b:
Z1=a/2=1.645
1-a/2=0.95
a=10
so,
(1-a)x100
=90%
Hence, the level of confidence is 90%
for c:
Z1=a/2=2.576
1-a/2=0.995
a=0.01
so,
(1-a)x100
=99%
Hence, the level of confidence is 99%
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what is the measure of AB in O below?
The measure of AB in the figure is C. 100 degree
How to find the measure of ABThe measure of AB in the figure is the length of arc, this is given by the formula
given angle / 360 * 2πr
However, the measure in degree is equal to the angle given which is 100 degree.
The size or the measure of the angle is same at any point within same lines that formed the angel AB.
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Hello can you help me with this question
Part A: Without using a graphing calculator, which equation could be represented by the accompanying graph?
A) y= x^2-2
B) y =2^-x
C) y= -2^x
D) y= 2^x
Answer:
Step-by-step explanation:
A
if 25% of tolla's sallary is birr 135.75, what is the amount of his full salary?
If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.
Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.
This is the amount of Tolla's full salary.
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Which answer describes the type of sequence? 1, 6, 7, 13, ...
O arithmetic
O geometric
O neither arithmetic nor geometric
A series that is neither mathematical nor geometric is described by the provided sequence. Which is the proper response would be a choice (B).
What exactly is an algebraic sequence?A grouping of numbers in a specific order is known as an arithmetic sequence.
The following question gives the sequence as follows: 1, 6, 7, 13,...
We must determine the kind of the current sequence.
According to the question, we have 1, 6, 7, 13,...
For verification as an arithmetic series:
The usual deviation between 1 and 6 is given by d = 6 - 1 = 5.
Commonly, 6 and 7 differ by 1 when d = 7 - 6
It is not an arithmetic sequence since the common difference between subsequent terms is not the same.
In order to verify it as a geometric sequence:
r = 6/1 = 6 is a common ratio between 1 and 6.
r = 7/6 is a common ratio between 6 and 7.
It is not a geometric sequence since the common ratio between subsequent terms is not the same.
A series that is neither mathematical nor geometric is described by the provided sequence.
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write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence be determined.
By observation, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
It follows that the expression is a arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
The required expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the nth term is given by the expression; T (n) = 1 + 7 (n -1).
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What is the surface area of the cube shown below?
Answer:
150 in^2
Step-by-step explanation:
It is a cube...it has six equal sides
the surface area of one side is 5 x 5 = 25 in^2
there are six .... so 6 x 25 = 15o in^2
Edited: should be in^2 not cm^2 as originally posted...wrong units
Answer:
150
Step-by-step explanation:
To find the surface area of a cube, you do 6a^2. That would mean it is 150.
I need help thank you
It follows that someone who watches TV for 11 hours can complete 19 situps.
How to find the calculation?This information was provided to us by the question.
A linear equation in slope-intercept form is one with the formula y = ax + b.
Claim: A line with slope a contains the point (0,b) on the y-axis and the solutions of the equation y = ax + b (where a and b are numbers) form a line with slope a.
a=−1.077
b=30.98
r2=0.744769
r=−0.863
Where
X is the amount of situps.
Y is the quantity of television viewing hours.
X equals 11, so
Including this in the existing formula
Y = (-1.077)(11) + 30.98
Y = −11.847 + 30.98
Y = 19.133
which equals around 19
So, it follows that someone who watches TV for 11 hours can complete 19 situps.
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a) Work out the minimum number of dogs that could have a mass of more than 24 kg
b) Work out the maximum number of dogs that could have a mass of more than 24 kg}.
Mass(kg) Frequency
0≤x<10 2
10≤x<20 7
20≤x<30 12
30≤x<40 6
a) The minimum number of hikers who could have walker between 6 and 17 miles is of: 9.
b) The maximum number of hikers who could have walker between 6 and 17 miles is of: 19.
What is shown by the frequency table?The frequency table shows the number of times that each range was observed in this problem.
For the minimum number of hikers walking between 6 and 17 miles, we have that:
All the 2 hikers in the interval 5 < x < 10 walked less than 6 miles.All the 8 hikers in the interval 15 < 20 < 20 walked more than 17 miles.Hence the minimum number is of 9, all of which walked between 10 and 15 miles, which is between 6 and 17.
For the maximum number of hikers walking between 6 and 17 miles, we have that:
All the 2 hikers in the interval 5 < x < 10 walked more than 6 miles.All the 8 hikers in the interval 15 < 20 < 20 walked less than 17 miles.Hence the maximum number is of:
2 + 9 + 8 = 19.
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14. Find (f +g)(x) if f(x)=4 x²-5x and g(x)=3x²+6x-4.
(f +g)(x)=-x²+11x-4
(f +g)(x)=7x²+x-4
(f +g)(x)=x²-11x+4
(f +g)(x)=-x²-x⁴
Answer:
(f +g)(x)=7x²+x-4
Step by step:
first you have to add both f(x) and g(x) to find (f +g)(x)
A box of chocolates contains 24 chocolates. Ten of the chocolates have cherry centers. All chocolates appear the same.
Two chocolates are selected. Find the probability of each of the following. (Round your answers to four decimal places.)
(a) both have cherry centers
(b) one has a cherry center and one does not
The probability of selecting chocolate such that:
(a) both have cherry centers: 0.1630
(b) one has a cherry center and one does not: 0.507
In this question, we have been given a box of chocolates contains 24 chocolates.
n(S) = 24
Ten of the chocolates with cherry centers.
n(A) = 10
So, the number of chocolates with no cherry centers are:
n(B) = 14
We need to find the probability of selecting chocolate such that
(a) both have cherry centers
P = (10/24)(9/23)
P = 90/552
P = 15/92
P = 0.1630
(b) one has a cherry center and one does not
P = 2*(10/24)(14/23)
P = 0.507
Therefore, the probability of selecting chocolate:
(a) both have cherry centers
P = 0.1630
(b) one has a cherry center and one does not
P = 0.507
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MULTIPLE CHOICE PRACTICE
9. For the function defined by the equation y=2 x²-10, which of the following represents the output when the input is -3 ?
(1) 6
(3) -10
(2) 8
(4) -28
10. If a function is defined by the equation y=-5 x+1 and the domain is the set {-2,0,2,4\}, which set below represents the range of the function?
(1) {11,12,13,14}
(3) {-10,-1,9,19}
(2) {-19,-9,1,10}
(4) {51,53,55,57}
11. A function is given by the set: {(-6,2),(-4,7),(0,5),(2,-4),(5,2),(7,5)}. Which of the following gives a pair of inputs that have the same output?
(1) -6and -4
(3) -4 and 2
(2) 5 and 7
(4) 0 and 7
Answer:
answer for no.10 is {11,12,13,14}
Step-by-step explanation:
According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers
Select all the points of intersection between the graphs of the functions f(x)=(x+5)(x-2)and g(x)=(2x + 1)(x-2)
Select all that apply
a: (-5,0)
b: (-1/2,0)
c: (-2, -12)
d: (2,0)
e: (4, 18)
f: (5, 30)
The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.
What is a function?
A function is defined as a relation between a set of inputs having one output each.
We have,
f(x) = ( x + 5 ) ( x - 2 )
g(x) = ( 2x + 1 ) ( x - 2 )
To find the points of intersection between the two functions we must equal the function.
f(x) = g(x)
( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )
( x - 2 ) gets canceled
x + 5 = 2x + 1
5 - 1 = 2x - x
4 = x
x = 4
This means that at x =4 the function f(x) and g(x) intersect.
we can see that at x = 4 both the functions have the same value.
f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2
f(x) = 18
g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )
= 9 x 2
g(x) = 18
Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.
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Find 910−238 . Express your answer as a mixed number in simplest form.
By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].
What is a mixed number?A mixed number is one that includes both a whole number and a legal fraction. A number with both an integer (whole number) and a correct fraction is referred to as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).
Pretzels, peanuts, Cheerios, and of course rice and corn Chex make up this mixture, which is dubbed a "mix." Numerals with both an integer and a fraction included are known as mixed numerals. The term "mixed number" refers to the combination of these two types of numbers.
Given,
910/238 is an improper fraction.
Now by dividing both the numerator and denominator by 14, we get
(910/14)/(238/14)
=65/17
Now, 65/17 can be written as a mixed number as 3[tex]\frac{14}{17}[/tex].
Therefore, By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].
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The complete question is:
"Find 910/238. Express your answer as a mixed number in simplest form."
A travel agent is interested in the average price of a hotel room during the summer in a resort community. The agent randomly selects 18 hotels from the community and determines the price of a regular room with a king size bed. The average price of the room for the sample was $135 with a standard deviation of $25. Assume the prices are normally distributed. Construct an interval to estimate the true average price of a regular room with a king size bed in the resort community with 99% confidence. Round the endpoints to two decimal places, if necessary.
The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 ).
What is the confidence interval of an average?One method of determining the actual population mean is by using a confidence interval for the mean. A confidence interval provides a lower estimate and an upper estimate rather than just the mean.
A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.
x = mean;
99% confidence interval for μ is
(x - t * S) /√n < μ <( x + t * S) /√n;
(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;
14.74< μ< 48.89;
99% CI is ( 14.74, 48.89 ) ;
critical value at 0.01 significance level with 17 df = 2.898
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cos^2x+cost^2x cot^2x
Yes, by definition cotx=1tanx, and tanx=sinxcosx, so cotx=1sinx/cosx=cosxsinx.
Step-by-step explanation:Thus, squaring both sides of the equation, we obtain cot2x=cos2xsin2x.The formula of 1 – cos2x is 1 – cos2x = 2sin²x. Through this, you can identify trigonometric identities.They're very different and your example is not correct.2cosx is twice the cosine of angle x.[tex]osx2=cos(x2)=cos(x[/tex]×[tex]x) while cos2(x)=cos(x)[/tex]×[tex]cos(x)=(cos(x))2.[/tex]
[tex]cos^2xcot^2+cos^2x\\= cos^2x(cot^2x+1)\\= cos^2x csc^2x\\= cot^2x < ==Answer[/tex]
[tex]cos2x = 1 - 2 sin 2x.\\cos2x = (1 - tan 2x) / (1 + tan2x)[/tex]
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Joe flew his small airplane 1000 km in 4 hours flying with the wind. He flew 700 km against
the wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind.
Answer:
To solve this problem, we can set up the following system of equations:
Let x be the rate at which Joe flew in still air and y be the rate of the wind.
1000 km / 4 hours = x + y
700 km / 7 hours = x - y
Solving this system of equations using the elimination method, we get:
x + y = 250
x - y = 100
Adding these two equations together, we get 2x = 350, so x = 175 km/hour.
Subtracting the second equation from the first equation, we get 2y = 150, so y = 75 km/hour.
Therefore, the rate at which Joe flew in still air is 175 km/hour and the rate of the wind is 75 km/hour.
Step-by-step explanation:
There is 14 feet of fencing available to enclose a rectangular region. For what
The maximum area is 12.25 square feet
How to determine the maximum areaFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 14 feet
This means that
P = 2(l + w)
So, we have
2(l + w) = 14
Divide by 2
l + w = 7
Make l the subject
l = 7 - w
The area is calculated as
A = lw
So, we have
A = (7 - w)w
Expand
A = 7w - w²
Differentiate and set to 0
7 - 2w = 0
So, we have
w = 3.5
Substitute w = 3.5 in A = (7 - w)w
A = (7 - 3.5) * 3.5
Evaluate
A = 12.25
Hence, the area is 12.25 square feet
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Complete question
There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum
The average score of all golfers for a particular course has a mean of 80 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 81. Round to four decimal places.
The probability that the average score of golfers exceeded = 0.0228
What is standard deviation?A measurement of a data set's deviation from the mean is referred to as "standard deviation.". A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out.
According to the given information
We are given that,
[tex]& \mu=80 \\[/tex]
[tex]& \sigma=3.5 \\[/tex]
[tex]& n=49 \\& \mu \bar{x}=\mu=80 \\[/tex]
[tex]& \sigma \bar{x}=\sigma / \sqrt{n}=3.5 / \sqrt{ } 49=0.5 \\& P(\bar{x} > 81)=1-P(\bar{x} < 81) \\& =1-P[(\bar{x}-\mu \bar{x}) / \sigma \bar{x} < (81-80) / 0.5] \[/tex]
[tex]& =1-P(z < 2) \\&[/tex]
Using standard normal table
[tex]& =1-0.9772 \\& =0.0228[/tex]
Probability [tex]$=0.0228$[/tex]
The probability that the average score of golfers exceeded = 0.0228
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57% of all the town's residents own a dog and 61% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible) a. P(Own a Dog)b. P(Own a Cat)- c. P(Own a Cat and a Dog) d. P(Own a Dog GIVEN Own a Cat)
Among dog owners, 40% also keep cats.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured
According to our question-
27% of households only own dogs.
12 percent own a cat but no dog.
18% of people own both dogs and cats.
43% don't own either a dog or a cat.
18/45 dog owners also have cats.
*100% = 40%
Among dog owners, 40% also keep cats.
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Four identical trapeziums are placed on a coordinate grid as shown.
a) Write down algebraic expressions for the coordinates of point L.
b) M has coordinates (9,9).
N has coordinates (15,15).
Work out the value of a and the value of b
a) The algebraic expression for the coordinates of point L is (a-b,b).
b)The value of a is 9, and the value of b is 3
What are coordinate points?
A specific point on a grid referred to as a coordinate plane can be located using coordinates, which are two numbers. In a plane, a point is known to have specific coordinates. The coordinates are the ordered pairs of numbers (x, y) that describe the location of any point on a plane. In our everyday lives, we use coordinates for things like map location, classroom seating, and more.
a) Extending point L towards the y-axis, we see that it corresponds to the given coordinate, i.e., (0,b). Therefore the y coordinate is b.
Next, extending the point L towards the x-axis, we see that the point lands somewhere between the distance 'a' from the origin. As the height is 'b', and as the trapeziums are identical, we can say that the extended point of L lands at a point that is 'b' distance from 'a'. Hence the x coordinate is a-b.
Hence, the coordinates of point L are (a-b,b).
b) Given M(9,9) and N(15,15).
Extending the point M towards the x-axis, we get that it coincides with the point 'a', therefore we get the value of a=9.
Now extending point N towards the x-axis, we get that it lands at a distance of 15 from the origin. We got the value of a=9, so the remaining distance between the point (9,0) and (15,0) is 6 units.
Extending the point (9,0) upwards, we see that it cuts the uppermost trapezium giving us the distance of the trapezium excluding the small triangle formed. Now taking the same information, if we cut the bottom-most trapezium, we see that it cuts at point (6,0).
Now we know the height of the trapezium is 'b'. So, we get b=9-6 (as 9 is the distance of the entire trapezium, and 6 is from the above calculations).
We get b=3.
Hence we got the value of 'a'=9 and 'b'=3.
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Monique wants to rent online movies. Movies Plus charges a one-time free of $20 plus $5 per movie. Movies-To-Go charges $7 per movie. Write and solve an equation to determine m, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same.
__; m = __ movies
The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let the no. of movies be 'm' and the total cost is 'C'
Movies Plus charges a one-time fee of $20 plus $5 per movie
which is, C = 5m + 20.
Movies-To-Go charges $7 per movie
which is, C = 7m.
Now, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.
∴ 7m = 5m + 20.
2m = 20.
m = 10.
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Which relationships would most likely be causal? Check all that apply.
O a positive correlation between depth under water and pressure
a negative correlation between total distance run and the runner's height
a positive correlation between a puppy's age and weight
a negative correlation between temperature and snowboards sold
a positive correlation between the price of milk and the price of socks
The correlation of two pairs of data values tells about the degree of movement that can occur. The correct option is A, C, and D.
What is correlation?The degree of movement that can occur in one of the data values when another data value is increased or decreased is indicated by the correlation of two pairs of data values.
A.) There is a positive relationship between depth under water and pressure.
Because water pressure increases with depth, this is a casual relationship that can be observed while swimming in a deep swimming pool.
C.) A positive relationship between the age and weight of a puppy.
This is a casual relationship because the puppy's weight and size both increase as it grows.
D.) A negative relationship between temperature and the number of snowboards sold
This is a casual relationship because as the weather warms up, fewer people prefer to go snowboarding.
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Round off 878 to the nearest 10
Answer:
880 is the answer
Step-by-step explanation:
hope this helps
what is the perimeter of a rhombus when the diagonals are 42cm and 40cm
Answer:
Step-by-step explanation:
P = 4 a
a = √p^2 + q^2 / 2
P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm
∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm
find the volume of the Rectangular prism given below the length is is 10 cm the width is 3.2 cm and the height is 1.5 cm
Answer:
44.8
Step-by-step explanation:
Volume = Length * Height * Width
Volume = 10 * 1.5 * 3.2
Volume = 44.8cm
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times and the volume of the cone would be about 536 in^3.
What is cone and its formula?They develop as a result of lava pieces being blown into the air by ferocious eruptions, solidifying, and then falling as cinders surrounding the volcanic vent. These cinders, which are typically the size of pebbles, are packed with numerous small bubbles that the lava captured as it solidified. The height of a cinder cone can range from tens to hundreds of metres.A cone has no edges and just one face, which is its round base. A cone only has one vertex or apex point. The cone has a volume of 13 r2h. The cone's total surface area is equal to r(l + r). The cone's slant height is (r2+h2).A cone has a vertex that is not on the base and a single circular base.Explanation :
If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times, because Centre radius will reduced to point when it reaches its full height.
The volume of the cone would be about 536 in^3.
Volume of a cone = 1/3 π [tex]r^{2}[/tex] *h
= 1/3 x π x [tex]8^{2}[/tex] x 8 = 536
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Answer:
two134Step-by-step explanation:
You want to know how many times the volume of a cone 8 inches in diameter and 8 inches high will fit into the volume of a beachball that is 8 inches in diameter, and you want the approximate volume of the cone.
Sphere volumeThe equation for the volume of a sphere based on its diameter is ...
V = π/6d³
Cone volumeThe equation for the volume of a cone is usually written ...
V = 1/3πr²h
For the cone in this problem, with both diameter and height equal to that of the sphere, we can rewrite the volume equation as ...
V = 1/3π(d/2)²·d = π/12d³ . . . . . . where d=8 inches, the sphere diameter
Volume ratioThen the ratio of the sphere's volume to that of the cone is ...
Vs/Vc = ((π/6)d³)/((π/12)d³) = 12/6 = 2
The volume of the cone will fit into the volume of the sphere two (2) times.
Numerical volume valueThe volume of the cone is ...
V = (π/12)8³ = 128π/3 ≈ 134 . . . . cubic inches
The cone's volume is about 134 in³.
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Additional comment
Note that we have taken the wording "with the same radius" to mean that the radius of the cone is the same as the radius of the sphere.
Alternatively, it could mean the radius of the cone is the same as the dimension given for the diameter of the sphere. In that case, the volume of the cone is 4 times as great, so its volume of 536 in^3 will fit into the sphere 1/2 times.
Connor is driving to a concert and needs to pay for parking. There is an automatic fee
of $8 just to enter the parking lot, and when he leaves the lot. he will have to pay an
additional $2 for every hour he had his car in the lot. How much total money would
Connor have to pay for parking if he left his car in the lot for y hours? How much
vould Connor have to pay if he left his car in the lot for t hours?
The solution is
a) The amount Connor has to pay for parking if he left his car for y hours is given by the equation A = 8 + 2y where y is the number of hours
b) The amount Connor has to pay for parking if he left his car for t hours is given by the equation B = 8 + 2t where t is the number of hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Let the second equation be represented as B
Now , the value of A is
The automatic fee for parking = $ 8
The additional fee for parking every hour = $ 2
So , for x number of hour , the additional parking fee = 2x
And , the total parking fee including x hours = automatic fee for parking + additional parking fee
Substituting the values in the equation , we get
The total parking fee including x hours = 8 + 2x
Now , when x = y hours
The total parking fee including y hours A = 8 + 2y
And , when x = t hours
The total parking fee including t hours B = 8 + 2t
Hence , the equations are A = 8 + 2y and B = 8 + 2t where y and t are number of hours
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