Answer:
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
Step-by-step explanation:
Let the number of fit men is x.
Now,
we know
x = 12% of 200 men
x = [tex]\frac{12}{100}[/tex] ×200
x = 0.12 × 200
= 24 men.
Given,
The 60 people are fit to climb the Mount Shasta ,24 of them are men,
so there must be
60 - 24 = 36 women who are fit to climb the mountain.
The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,
P(male or fit) = P(male and fit) + P(female and fit)
P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)
P(male or fit) = ([tex]\frac{200}{500}[/tex]) ×([tex]\frac{24}{200}[/tex]) + ([tex]\frac{300}{500}[/tex]) × ([tex]\frac{36}{300}[/tex])
=.4 × .12 + .6 × .12
= 0.048 + 0.072
=.12
So,
P(male or fit) ≈ 0.12
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
Are square and rectangle similar
Answer:
no
Step-by-step explanation:
squares sides are all equal
rectangle only have 2 side alike
3/4 minus what equals 1/2
Answer:
W =1 1/4Step-by-step explanation: Let W = what. W - 1/2 = 3/4. Add 1/2 to each side. W -1/2 +1/2 = 3/4+1/2. W = 3/4+1/2.
Step-by-step explanation:
Please help me with this question
Answer:
m∠2=12°
Step-by-step explanation:
some of two angles is 90
90 -78=12
Help!!! Drag and drop an answer into each box to correctly complete the statement.
The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.
What precisely is dilation?
Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:
Properties of Rotation, Translation, Reflection, and Resizing
Dilation properties
The following are some features of shapes that remain constant with dilation changes:
The angles in the illustration are all the same.The figure's side midpoints remain the same as the dilated form's midpoint.The parallel and perpendicular lines in the illustration remain unchanged.Now,
As The image of A is made on line XY and the image will be A'
then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and
P is the midpoint of AA' because we know that AP and A'P are same in a image formation.
Hence,
Point P is midpoint of AA' and XY⊥AA'.
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This is a two-part question:
1. Jack's gasoline-powered model airplane travels in a circle while the cord is held. How far does it travel in 5 full circles if the cord is 15 ft.?
2. Last Saturday Jack flew his airplane 100 times around a circle with a cord of 50 ft. If Jack increases the length of the cord by 10 ft and fly it for 100 circles, how much further will the plane travel?
1. The plane travelled a distance of 471.239 ft
2. The plane would travel further by 6283.185 ft
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
If you move along a full circle of a radius 'r', the distance covered by you is equal to [tex]2\pi r[/tex]
Part 1:
Given that, Jack's aeroplane travels in a circle of a cord of length 15ft for 5 times
The total distance travelled by plane is [tex]15*2\pi *15[/tex]
[tex]=150\pi[/tex]
= 471.239 ft
Part 2:
Given that, Jack flew his aeroplane 100 times with a cord of 50 ft.
The total distance covered by the plane is 100 * (2*50*[tex]\pi[/tex])
If he increases the length by 10 ft, The cord will now be 60 ft.
The total distance it would cover then is 100 * (2*60*[tex]\pi[/tex])
Now,
100 * (2*60*[tex]\pi[/tex]) - 100 * (2*50*[tex]\pi[/tex])
= 100 * (2*(60-50))*[tex]\pi[/tex])
= 100 * 2 * 10 * [tex]\pi[/tex]
= 2000 * [tex]\pi[/tex]
= 6283.185 ft
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What is the rate of change for the equation y= 4x +40?
Answer:
4 would be the rate of change
Step-by-step explanation:
y=mx+b mx = slope
The slope represents the rate of change. Then the rate of change will be 4.
a square law has area 128ft squared what is the radius of the circle
Answer: 6.38
.................
Use the commutative and/or associative properties to simplify (17)(0.25)(4).
The solution is, (17)(0.25)(4) = 17.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
(17)(0.25)(4)
=(17)*1
=17
at first we have to multiply the last two terms i.e. (0.25) and (4), then, we multiply the result 1 with 17, and get the result 17.
Hence, The solution is, (17)(0.25)(4) = 17.
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If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.
The lowest common denominator of the fraction is 6
What is LCDThe lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.
The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.
In the fraction given;
x / 3 + x / 2 = 20
The lowest common denominator is 6
Using 6, we can divide through each of the fraction.
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Expression
9x - 2 + 16x + 8 - x + 10
What are the coefficients in this expression?
The coefficients in the expression "9x - 2 + 16x + 8 - x + 10" are the numerical values that multiply the variables. In this expression, the coefficients are 9, -2, 16, 8, -1, and 10.
So, the expression can be written as:
9x + 16x - x + 10 = 24x + 10
where 9, -2, 16, 8, -1, and 10 are the coefficients of the expression.
Answer:
The coefficients in this expression would be 10, -2, 8, -1, 10, 9, 16
Step-by-step explanation:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
Arturo purchased the tank below for his aquatic turtle. The tank has a length of 5.5 feet, a width of 4 feet, and a height of h feet. Arturo poured in 74.8 cubic feet of water in the tank to fill it half way. What is the value of h, the height of the tank, in feet?
Answer:
6.8 ft
Step-by-step explanation:
You want the height of a tank with a base of 5.5 ft by 4 ft if adding 74.8 ft³ of water fills it halfway.
VolumeThe volume of a rectangular prism is given by the formula ...
V = LWH
The filled volume of the tank h feet high is ...
74.8 ft³ = (5.5 ft)(4 ft)(h/2) . . . . . . the filled height is h/2
74.8 ft³/(11 ft²) = h ≈ 6.8 ft . . . . . . divide by the coefficient of h
The height of the tank is 6.8 feet.
An urn contains 3 white balls and 7 red balls. A second urn contains 7 white balls and 3 red balls. An urn is selected, and the probability of selecting the first urn is 0.3. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
Step-by-step explanation:
Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:
P(A and B) = P(A) * P(B|A)
where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.
First, let's find P(A):
P(A) = 0.3
Next, let's find P(B|A):
P(B|A) = (3/10) * (3/10) = 9/100
Finally, let's find P(A and B):
P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027
So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
The ratio of boys to girls at the park is 4 to 5. How many boys are at the park if there are 45 girls at the park.
Responses
A 30
B 36
C 42
D 48
Answer:
Step-by-step explanation:
B
Graphing Quadratic Functions 1. List a, b, and c. 4. What is the y-intercept? 5. Create a table and graph. X f(x) Quadratic Function f(x) = x² - 2x + 6 2. Find the axis of symmetry. F Y 10 9 8 7 6 5 4 3 2 1 -9-8-7-6-5-4-3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 3. Find the vertex. tx 1 2 3 4 5 6 7 8 9 10 X
The value of a, b, and c are 1, -2, and 6 respectively.
The y-intercept of this quadratic function is 6.
The axis of symmetry of this quadratic function is 1.
The vertex of this quadratic function is (1, 5).
How to calculate the axis of symmetry of a quadratic function?Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = x² - 2x + 6, we have:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(-2)/2(1)
Axis of symmetry, Xmax = 2/2 = 1.
Vertex (h, k) = (1, 5).
In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
y-intercept = 6.
Lastly, we would create a table and then graph the quadratic function as follows;
x y
0 6
2 2
5 11
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A tailor charges a basic fee of $20 plus $4 per letter to sew an athlete's name on the back of a jacket. Write a linear equation that will find the cost c to have a name containing x letters
The equation will be;
c = 20 + 4x
What are Linear Equations?Linear equations are equations of the first order. When a linear equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can also have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.
A linear equation that will find the cost c to have a name containing x letters will be;
c = $20 + 4x
where c = cost
$20 = basic fee
x = number of letters
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3. What is the volume of this complex figure?
3 m
4 m
6 m
4 m
7m
The volume of the rectangular prism is 140 cubic meters
What is the volume of the figureThe volume of a figure is a measure of the amount of space it occupies in three-dimensional space. It is a scalar quantity, meaning that it is a single numerical value with no direction.
The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.
This problem is a two rectangular prism joined together.
The volume can be calculated as;
V = l * w * h
v = (4 * 7 * 3) + (2 * 7 * 4)
v = 140m³
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Geometry!!! Please help due soon!!!!y
A boat heading out to sea starts out at Point A, at a horizontal distance of 1246 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 14°. At some later
time, the crew measures the angle of elevation from point B to be 5°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
Answer:2304.9
Step-by-step explanation:
Answer:
2304.9 ft
Step-by-step explanation:
You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.
TangentThe tangent relation for sides in a right triangle is ...
Tan = Opposite/Adjacent
In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:
tan(14°) = h/1246
tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B
SolutionSolving these equations for d, we have ...
h = 1246·tan(14°) = (1246+d)·tan(5°)
d·tan(5°) = 1246·(tan(14°) -tan(5°))
d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet
The distance from point A to point B is about 2304.9 feet.
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Wendy and Roger camped out at a state park, and then hiked back to their cars, which were
parked on opposite ends of the park. Wendy headed due north at 3 miles per hour, and Roger
hiked due south at 6 miles per hour. In how long were the two friends 2 miles apart?
If necessary, round your answer to the nearest minute.
In 30 minutes the two friends 2 miles apart.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.
We know that, Time= Distance/Speed
Now, T₁= 2/3
T₂= 2/6 =1/3
T=T₁-T₂
T=2/3+1/3
T=1/3
T=0.33 hours
= 30 minutes
Therefore, in 30 minutes the two friends 2 miles apart.
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What should be added to -7 mm + 2m ²+ 3n² to obtain 5m² +2mn-9n².
The expression to be added is 9mn +3m² - 12n²
What are algebraic expressions?These are expressions having terms, variables, coefficients, factors and constants.
They are also known to be composed of arithmetic operations, such as;
AdditionMultiplicationDivisionSubstraction BracketParenthesesFrom the information given, we have the expression;
-7 mm + 2m ²+ 3n²
To make it up to 5m² +2mn-9n²., we have
-7mn + 9mn + 2m² + 3m² + 3n² - 12n²
Hence, the expression is 9mn +3m² - 12n²
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)) Of the 90 people who attended the Baybridge Middle School Winter Formal, 18 are
not students at Baybridge.
4) Shade the grid to show the fraction of the people who attended the formal who are not
students at Baybridge.
) What percent of the people who attended the Winter Formal are not students at
Baybridge Middle School? You can use your model to help.
Answer:
Step-by-step explanation:
To find the percent of the people who attended the Baybridge Middle School Winter Formal who are not students at Baybridge, we can use the following steps:
Find the fraction of non-student attendees: 18 attendees out of 90 total attendees can be represented as 18/90.
Convert the fraction to a decimal: 18/90 = 0.20, which can be rounded to 0.2.
Convert the decimal to a percentage: 0.2 * 100 = 20%.
So, 20% of the people who attended the Baybridge Middle School Winter Formal are not students at Baybridge.
The vet says that raise puppy will grow to be at most 28 inches tall raise. Puppy is currently 1 foot tall how much more will the puppy grow?
Write an inequality to solve the problem
Answer:
16 inches
Step-by-step explanation:
28 - 12 = 16 inches
1 foot = 12 inches
20. A line passes through (4, 6) and (9, 9).
a. Write an equation for the line in slope-intercept
form.
y=3/5x+18/5?
b. Rewrite the equation in standard form using
integers.
Its 10/29 so its answers this
Explain how to find 20% of 160
Answer: 20% of 160 is 32.
Step-by-step explanation:
The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.
To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.
Let us now find the 20% of 160.
20% = 0.2
percentage = 160 × 0.2
= 32
PLS HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the solution to the equation given the replacement set?
25 - 3r = 10; {3, 4, 5, 6,}
Responses
3
4
5
6
Answer:
r = 5
Step-by-step explanation:
25 - 3r = 10 ( subtract 25 from both sides )
- 3r = - 15 ( divide both sides by - 3 )
r = 5
the solution from the replacement set is 5
help me with this please i need help because i dont get it <33
Answer:
C
Step-by-step explanation:
consider the coordinates of the same points on both figures
top left vertex of figure P (- 8, 8 )
top left vertex of figure Q (- 4, 4 )
note that both coordinates from Q are half the coordinates of P
then to obtain Q from P multiply each coordinate by [tex]\frac{1}{2}[/tex] , that is
(x, y ) → ([tex]\frac{1}{2}[/tex] x , [tex]\frac{1}{2}[/tex] y )
The following data represent the weights (in grams) of a
random sample of 50 candies
(a) Determine the sample standard deviation weight
SH gram
(Round to two decimal places as needed)
0.98
0.85
0.92
0.98
0.71
Part 1 of 6
0.88
0.86
0.75
0.85
0.85
0.86
0.78
0.75
0.75
0.74
Cm
0.82
0.85
0.91
0.78
0.72
O
081
0.81
0.81
0.81
0.84
Points: 0 of 4
087
0.85
0.89
0.77
0.85
0.97
0.74
0.89
0.82
0.86
0.82
084
0.91
0.87
0.94
0.85
0.71
0.83
0.87
0.94
0.81
0.81
0.78
0.77
0.85
The sample standard deviation weight of the 50 candies is, 0.07 grams.
What is standard deviation ?The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.
To find the sample standard deviation weight,
we can use the formula:
[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]
where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.
We can first find the sample mean weight:
[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50
[tex]\bar x[/tex] = 0.8456
Next, we can calculate the sample standard deviation:
s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))
s = sqrt(0.0045916)
s = 0.0678
Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.
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For the function
f(x)
given in the table, find the average rate of change over each specified interval.
x
0 2 2.5 3 3.8 4 5
f(x)
24 13 17 18 16 13 29
(a) [2, 5]
Incorrect: Your answer is incorrect.
(b) [3.8, 4]
The average rate of change over each specified interval is 8/3 and -10.
What is an average rate?The average rate shows the change in the function per unit, over an interval.
Given that, find the average rate of change over each specified interval.
The average rate of change is given by
f(b)-f(a) / b-a
a) [2, 5] :-
To find the average rate of change we will take the change in the function over the change in x,
f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3
Therefore, the average rate of change in interval [2, 5] is 8/3
b) [3.8, 4] :-
Similarly,
f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2
= -10
Therefore, the average rate of change in interval [3.8, 4] is -10
Hence, the average rate of change over each specified interval is 8/3 and -10.
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at a movie theater, tickets cost 15$ for adults and 8$ for children. a group of 28 movie goers cost 308$. how many adults and how many children are in the group?
The number of adult and children in the group is given as follows:
Adult: 12.Children: 16.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: number of adults.Variable y: number of children.There were a total of 28 people, hence:
x + y = 28
y = 28 - x.
They spent a total of $308, hence:
15x + 8y = 308.
Replacing the second equation into the first, the value of x is given as follows:
15x + 8(28 - x) = 308
7x = 84
x = 84/7
x = 12.
Then the value of y is given as follows:
y = 28 - x = 28 - 12 = 16.
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Rewrite in simplest terms: (5x + 5y) - (-x + 10y)
Answer:
6x - 5y
Step-by-step explanation:
( remove the unnecessary parentheses)
= 5x + 5y + x - 10y
= 6x + 5y - 10y
= 6x + 5y
