A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both. 8. What is the probability a vacationer will visit at least one of these attractions
Answers
Answer:
0.55 or 55%
Step-by-step explanation:
Let A represent the event when a vacationer visits Yellowstone Park
Let B be represent the event where a vacationer visits the Tetons.
We are told that 50% visit Yellowstone Park. Thus; P(A) = 50% = 0.5
Also,that 40% visit the Tetons. Thus;
P(B) = 40% = 0.4
Also that 35% visit both.
Thus; P(A & B) = 0.35
Now, probability that they visit at least one of these attractions will be P(A or B)
Now, formula for P(A or B) is;
P(A or B) = P(A) + P(B) - P(A & B)
Thus;
P(A or B) = 0.5 + 0.4 - 0.35
P(A or B) = 0.55
The probability a vacationer will visit at least one would be "0.55".
According to the question,
Let,
Vacationer visits Yellowstone Park = AVacationer visits Tetons = BProbability:50% at Yellowstone park,
→ \(P(A) = 50 \ percent\)
\(= 0.5\)
40% at Tetons,
→ \(P(B) = 40 \ percent\)
\(= 0.4\)
35% visits both,
→ \(P(A \ and \ B) = 0.35\)
hence,
Visits at least one of these,
→ \(P(A \ or \ B) = P(A)+P(B) -P(A \ and \ B)\)
By substituting the values,
\(= 0.5+0.4-0.35\)
\(= 0.55\)
Thus the answer above is right.
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Related Questions
Determine that the value x=9 of the following expiration given x2+3x-5
Answers
Step-by-step explanation:
To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:
9^2 + 3(9) - 5 = 81 + 27 - 5 = 103
Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.
rate my answer, please.
what is the lcm of the rational algebraic equation 6/x+x-3/4=2
Answers
The lcm of the rational algebraic equation 6/x+x-3/4=2 be (24 -3x - 4x²) / 4x = 0.
What is LCM?The least common multiple is defined as the set of numbers with the least common multiple. The lowest positive integer with more than one factor in the set is HCF.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We must find the lcm of the rational algebraic equation.
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ \(\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}\)
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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What is the distance between the following points?
Answers
Answer:
7.615773105864
Step-by-step explanation:
\(\text{let A and B be the points of coordinates} \ A\left( 3,-9\right) \text{and} \ B\left( 6,-2\right)\)
\(AB=\sqrt{\left( 6-3\right)^{2} +\left( -2-(-9)\right)^{2} }\)
\(=\sqrt{\left( 3\right)^{2} +\left( 7\right)^{2} }\)
\(=\sqrt{58} =7.615773105864\)
If x + 1/x = 83, find the value of x^2 + 1/x^2
Answers
Answer:
6887
Step-by-step explanation:
given
x + \(\frac{1}{x}\) = 83 ( square both sides )
(x + \(\frac{1}{x}\) )² = 83² = 6889 ← expand factor on left using FOIL
x² + 2( x × \(\frac{1}{x}\) ) + \(\frac{1}{x^2}\) = 6889
x² + 2(1) + \(\frac{1}{x^2}\) = 6889 ( subtract 2 from both sides )
x² + \(\frac{1}{x^2}\) = 6887
Write a two column proof (Given: x is the midpoint of WY and VZ) (Prove: VW=ZY)
Answers
Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.
To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.
By simplifying the equation, we can see that the equation becomes:
6x - 5x = 17 - 2
Simplifying further, we have:
x = 15
Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.
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I run 3 miles in 20 minutes. What was my average speed in miles per hour?
Answers
Step by step
To get minutes to equal one hour, multiply by 3 ( 20 minutes x 3 = 60 minutes or 1 hour)
If you multiply 20 x 3, you will do the same to the miles
3 miles x 3 = 9 miles
Now we have 9 miles per 1 hour
Problem solved
Proportionality yes or no - show work
X y
____ ____
6 -2
7 -1
8 0
9 1
Answers
No, the relationship on the table is not proportional
How to determine if the relationship is proportionalFrom the question, we have the following parameters that can be used in our computation:
x y
____ ____
6 -2
7 -1
8 0
9 1
On the table of values, we can see that:
The values of x increase by 1 i.e. 6, then 7, then 8 and finally 9 As these values of x increase by 1, the values of y increase by 1 also i.e. -2, then -1, then 0 and finally 1Using the above as a guide, we have the following:
The relationship is not a proportional relationship
This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)
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what is the meaning of sequence in mathematic and
Answers
Answer:
A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.
Step-by-step explanation:
The table shows how a 3-square-foot shelf is split into 6 sections for storing art materials. How many square feet are there for storing paint?
Answers
The number of square feet that are there for storing paint is 1/2
How to determine the number of square feet are there for storing paint?From the question, we have the following parameters that can be used in our computation:
Area of the table = 3-square-foot
Number of sections = 6 sections
The number of square feet is there for storing paint is calculated as
The number of square feet = Area of the table/Number of sections
Substitute the known values in the above equation, so, we have the following representation
The number of square feet = 3-square-foot/6
Evaluate the quotient
The number of square feet = 1-square-foot/2
This gives
The number of square feet = 1/2 -square-foot
Hence, the square feet is 1/2
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Complete question
The table shows how a 3-square-foot shelf is split into 6 sections for storing art materials. How many square feet are there for storing paint?
Area (square feet) Sections
3 6
6 12
9 18
identify the description that matches this equation. x² + (y - 3)² = 16 O A a circle with center (0,0) and radius 5 o B. a circle with center (0,3) and radius 4 0 C. a circle with center (0,-3) and radius 4 0 D. a circle with center (3,0) and radius 16
Answers
Answer:
B. a circle with center (0,3) and radius 4
Explanation:
Given the equation of the circle:
\(x^2+(y-3)^2=16\)Compare it with the standard equation of a circle:
\((x-h)^2+(y-k)^2=r^2\)We see that:
\(\begin{gathered} x^{}=x-h\implies h=0 \\ y-3=y-k\implies k=3 \\ r^2=16\implies r=4 \end{gathered}\)The centre of the circle is:
\((h,k)=(0,3)\)Therefore, the correct description is:
B. a circle with center (0,3) and radius 4
During surgery, patient's circulatory system requires at least 50 milligrams of an anesthetic: The amount of anesthetic present hours after 70 milligrams of anesthetic administered given by the following T(t) 70(0.727)t (a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 30 minutes after the anesthetic is administered? (b) How long_ to the nearest minute can the operation last if the patient does not recelve additional anesthetic?
Answers
63 mg of anesthetic is present in the patient’s circulatory system.
The operation can last for 20 minutes.
During surgery, a patient’s circulatory system requires at least 50 mg of an anesthetic. The amount of anesthetic present t hours after 70 mg of anesthetic is administered is given by the following,
T(t) = 70 × (0.727) ^t
Time = 1/3 hours
T (1/3) = 70 × (0.727) ^1/3
= 70 × ∛ 0.727
= 70 × 0.899176
= 62.94232
To the nearest mg: 63mg
Now,
63 = 70 × (0.727) ^t
63/70 = (0.727) ^t
0.9 = (0.727) ^t
Log0.9 = log (0.727) ^t
Log0.9 = t × log (0.727)
T = log0.9 / log0.727
T = 0.330461
T = 0.330461 hours
= 20 minutes
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Graph the functions f(x)=−6x+14 and g(x)=−2x+6 on the same coordinate plane. What are the solutions of the equation −6x+14=−2x+6? Select each correct answer. Responses x = 0 x, = 0 x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3 x = 4
Answers
Both functions are equal to each other then the solution of the equation −6x+14=−2x+6 is 2.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Graph the functions f(x)=−6x+14 and g(x)=−2x+6 are on the same coordinate plane.
For the value of x, both the function are equal to each other so we have;
f(x) = g(x)
−6x+14=−2x+6
-4x = -8
x = 2
Thus, the value of x is 2.
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I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answers
To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:
y = 3 - 4
Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:
y = -1
Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.
Answer
\(\pink\sf{y=-1}\)
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
\(\sf{y=3-4}\)
And now we just simplify the last part:
\(\sf{y=-1}\)
∴ answer: y = -1
A line with slope 5/4 passes through the point (-3, 1). Enter an equation of the line.
Answers
Answer:
y= 5/4x + 4 1/4 or y=5/4x +4.75
Step-by-step explanation:
y= 5/4x +b
1=5/4 *-3 +b
1=-3 1/4 + 4 1/4
Example 4: In May 2006, Commonwealth Edison Company supplied electricity to residences for a
monthly customer charge of $7.58 plus $0.08275 per kilowatt-hour (kWhr) for the first 400 kWhr
supplied in the month, and $0.06208 per kWhr for all usage over 400 kWhr in the month. (a) What is the
charge for using 300 kWhr in a month? (b) What is the charge for using 700 kWhr in a month? (c) If Cis
the monthly charge for x kWhr, develop a model relating the monthly charge and kilowatt-hours used.
That is, express C as a function of x.
Answers
Answer: monthly customer charge of $7.58 plus $0.08275 per kilowatt-hour (kWhr) for the first 400 kWhr
Step-by-step explanation: I took this test before so I hope this helps gl on the test
a) The charge for using 300 kWhr in a month is $ 32.41
b) The charge for using 700 kWhr in a month is $ 59.30
c) The rule for computing C is
C ( x ) = { 7.58 + 0.08275x if 0 ≤ x ≤ 400
15.848 + 0.06208x if x > 400
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 ,
The monthly charge = $ 7.58
The monthly charge for per kWhr = $ 0.08275
The monthly charge per kWhr over 400 kWhr = $ 0.06208
So ,
The monthly charge for x kWhr is given by the equation = 7.58 + 0.08275x
The monthly charge for x kWhr which is more than 400 kWhr is given by the equation = 7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )
Now ,
a)
The charge for using 300 kWhr in a month is calculated by substituting the value of x as 300
So ,
The monthly charge for x kWhr is given by the equation = 7.58 + 0.08275x
The monthly charge for 300 kWhr = 7.58 + 0.08275 x 300
= 7.58 + 24.825
= $ 32.405
Therefore , The monthly charge for 300 kWhr is $ 32.41
b)
The charge for using 700 kWhr in a month is calculated by substituting the value for x as 700
The monthly charge for x kWhr which is more than 400 kWhr is given by the equation = 7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )
The monthly charge for 700 kWhr =
7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )
Substituting the value for x as 700 , we get
= 7.58 + 0.08275 ( 400 ) + 0.06208 ( 300 )
= 40.68 + 18.624
= $ 59.304
Therefore , The monthly charge for 700 kWhr is $ 59.304
c)
Let x represent the number of kWhr used and C be the monthly charge for x kWhr.
The model can be split into 2 parts of condition , where
For , 0 ≤ x ≤ 400
The function is 7.58 + 0.08275x
For , x > 400
The function is 15.848 + 0.06208x
Therefore ,
The rule for computing C is
C ( x ) = { 7.58 + 0.08275x if 0 ≤ x ≤ 400
15.848 + 0.06208x if x > 400
Hence , The monthly charge for 300 kWhr is $ 32.41 and the monthly charge for 700 kWhr is $ 59.304
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The approximate populations of Kentucky and North Dakota (as of 2019) are listed
below:
Kentucky: 4.47 × 106
North Dakota: 7.62 x 105
How many times greater was the population of Kentucky than the population of
North Dakota? Write your answer in standard notation, rounding to the nearest
tenth.
Answers
The population of Kentucky is nearly 5.9 times that of North Dakota.
How to determine How many times greater was the population of Kentucky than the population of North DakotaTo determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:
4.47 x 10^6 / 7.62 x 10^5
We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87
5.9, rounded to the closest tenth.
As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.
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I need help because im not sure if im supposed to square it
\(2 \sqrt{x} = x - 3\)
Answers
Step-by-step explanation:
\(2 \sqrt{x} = \: x - 3 \)
\( ({ 2 \sqrt{x} )}^{2} = \: {x}^{2} - {3}^{2} \)
\(4x = {x}^{2} - 9\)
\( {x}^{2} - 4x - 9 = 0\)
\(x = 5.60 \: and \: x = - 1.60\)
Look at the image below to figure out the problem
I will give brainiest to the correct answer and giving 15 points away
Answers
Answer:
54 cups
Step-by-step explanation:
2/9=12/?
12/2=6
6*9=54
A man wants to mesure the height of a nearby building. He places a 7ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building’s shadow is 162ft, the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot.
Answers
The height of the building is approximately 227 feet.
In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.
The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.
As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.
Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF
On substituting the values from the given data, we get:
AE/(EF + 5.5) = 7/5.5.... (1)
Similarly, we can write from the given data:
BD/DF = 162/5.5.... (2)
From equations (1) and (2), we can write:
AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)
On solving the above equation for AE, we get:
AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft
Therefore, the height of the building is approximately 227 feet.
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Which statement is true ?
- 4 is the domain of f(g)
- 4 isn’t in the domain of f(g)
Answers
The statement -4 is not in the domain of f(g) is true.
What is domain?The domain is defined by the set of values of independent variables. The set of inputs that a function will accept is known as the domain of the function in mathematics. The collection of all potential inputs for a function is known as its domain.
what is range?In a function for each domain, we get a possible output from dependent variable which is termed as range.
From the diagram shown -4 cannot be used as domain because the output might be an imaginary number.
So, -4 is not in the domain of f(g) is true
hence, -4 cannot be a domain of given function f(g)
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The statement -4 is not in the domain of f(g) is true.
What is domain?
The domain is defined by the set of values of independent variables. The set of inputs that a function will accept is known as the domain of the function in mathematics. The collection of all potential inputs for a function is known as its domain.
What is range?
In a function for each domain, we get a possible output from dependent variable which is termed as range.
From the diagram shown -4 cannot be used as domain because the output might be an imaginary number.
So, -4 is not in the domain of f(g) is true
hence, -4 cannot be a domain of given function f(g)
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If sin x= 1/2 and cos x= √3/2, the measure of angle x is equivalent to:
Answers
Answer:
s
if sin x= 1/2, cos x= root 3/2,
x = 30 degrees
After how many
months will
Workout 24 and
your Gym cost the
same?
Sam joined Workout 24 for fifteen months. How much did he pay total?
After how many months will Workout 24 and Ultra Club be the same?
Answers
200= 50+5x
150=5x
x=30
So it will take 30 months where both gyms will be the same price.
Next question: 200+55(15)=$1,025 that is how much Sam would pay in total .
Last question :
200+55x=20+65x
200= 20+10x
180=10x
x=18
So the answer to last question is it will take 18 for both gyms to be the same cost
After 30 months, Workout 24 and Your Gym will cost the same.Sam paid a total of $825 for Workout 24. After 18 months, Workout 24 and Ultra Club will cost the same.
To find the number of months when the costs are the same, we need to set up an equation and solve for the number of months (let's call it "x"):
Workout 24 cost: $200 + $55x
Your Gym cost: $50 + $60x
Setting them equal and solving for x:
\(200 + 55x = 50 + 60x \\200 - 50 = 60x - 55x \\150 = 5x\\ x = 30\)
So, after 30 months, Workout 24 and Your Gym will cost the same.
For Workout 24, the monthly cost is $55, and Sam joined for 15 months: Total cost = Monthly cost × Number of months
Total cost = $55 × 15 = $825
Sam paid a total of $825 for Workout 24.
Similar to the first question, we'll set up an equation for the costs of Workout 24 and Ultra Club (let's call the number of months "y"):
Workout 24 cost: $200 + $55y
Ultra Club cost: $20 + $65y
Setting them equal and solving for y:
\(200 + 55y = 20 + 65y \\200 - 20 = 65y - 55y\\180 = 10y \\y = 18\)
So, after 18 months, Workout 24 and Ultra Club will cost the same.
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A random sample of 500 people were classified by their ages into 3 age-groups: 29 years and younger, 30 to 64 years, and 65 years and older. Each person from the sample was surveyed about which of 4 major brands of cell phone they used. Their responses were compiled and displayed in a 3-by- 4 contingency table. A researcher will use the data to investigate whether there is an association between cell phone brand and age-group. Which of the following is the appropriate test for the investigation? A) A one-sample t-test for a population mean B) A two-sample t-test for a difference between means C) A chi-square goodness-of-fit test D) A chi-square test of homogeneity E) A chi-square test of
Answers
When investigating whether there is an association between cell phone brand and age-group, the appropriate test is a chi-square test of homogeneity.
When investigating whether there is an association between cell phone brand and age-group, the appropriate test is a chi-square test of homogeneity.
Chi-square test: The chi-square test is a statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is valid.
A chi-square test may be used to see if there is an association between two variables.
The chi-square test of homogeneity is a statistical hypothesis test that is used to evaluate whether two or more populations have the same distribution of frequencies.
It's used to see if there's a significant difference between the proportions of categorical data in two or more independent groups.
In the same way, a chi-square test can be used to compare the frequency distributions of categorical variables in one or more populations.
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ILL GIVE BRAINLY What is the surface area of the cube?
Drag and drop the correct surface area to match the cube.
Answers
Answer:
Below
Step-by-step explanation:
A cube has SIX sides of equal area
each side has area = L x W and L and W are the same = 4.5 m
so: Area = six X ( 4.5 X 4.5) = 6 * 4.5 * 4.5 = 121.5 m^2
Answer:
Hope the picture will help you...
Given are the functions f(x) = x ^ 2 and g(x) = (x - 2) ^ 2 + 1 How can the graph of g(x) be obtained from the graph of f(x) ?
Answers
Answer:
c because it's the opposite
Enlarge shape A by scale factor 2 with centre of enlargement (1, 4).
What are the coordinates of the vertices of the image?
Answers
Answer:
hacunamatata
Step-by-step explanation:
it means no worrys
I will mark you brainiest!
A square and a rhombus have the following in common except:
A) opposite pairs of sides are parallel.
B) opposite pairs of sides are congruent.
C) pairs of interior and exterior angles are supplementary.
D) all interior angles are 90º.
Answers
Answer: D.All interior angles are 90 degrees
Im dum on this but smart on other things look at points too...
Answers
Step-by-step explanation:
Whole numbers = Natural numbers + "0"
Integers = Whole numbers + Negative counterparts
Since the set do contains negative numbers, only Rational numbers and Integers are correct. (D)
What is the equation of the line in standard form?
A. x-2y=4
B. x+2y=4
C. 2x+y=2
D. 2r-y-2
Answers
Answer:
D. 2x -y = 2
Step-by-step explanation:
You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.
Intercept formThe graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...
x/a +y/b = 1
x/1 +y/(-2) = 1
Standard formMultiplying this equation by 2 gives ...
2x -y = 2 . . . . the standard form equation for the line
__
Additional comment
The standard form equation can also be developed from the coordinates of points on the line:
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
(2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)
6x -3y = -6 +12
Dividing by 3 gives the standard form equation ...
2x -y = 2
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
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