Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one
baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has
no effect, so the probability of a girl is 0.5. Assume that the groups consist of 45 couples. Complete parts (a) through (c)
below.
Answers
a) The value of the mean is μ = 22.5
The value of the standard deviation is σ = 3.5
b) The Value of 15 girls or fewer is significantly low.
The value of 30 girls or more is significantly high.
c) The result 36 is significantly high because 36 is greater than 30 girls. A result of 36 girls is not necessarily definitive proof of the method's effectiveness.
What is the standard deviation?The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.
According to the given informationa) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.
Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.
The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:
μ = np = 45 x 0.5 = 22.5
Therefore, we expect to see around 22-23 girls in a group of 45 couples.
The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:
σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535
Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.
b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.
Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.
Significantly high:
Mean + 2σ = 22.5 + 2(3.535) = 29.57
Significantly low:
Mean - 2σ = 22.5 - 2(3.535) = 15.43
c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.
Mean + 2σ = 22.5 + 2(3.535) = 29.57
Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.
This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.
It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.
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Related Questions
61. You plan to save some money based on the following criteria. On day 1, you save $2, on day 2 you save $22, and on day 3 you save $2³. If you continue along the same pattern for one week, how much do you save in all?
Answers
You would save a total of $272 in one week if you continued along the same pattern.
What is pattern?
A pattern is a repeating or predictable sequence of events, numbers, shapes, or objects. In the context of the question you asked earlier, the pattern is the sequence of the amounts saved on each day, which follows a predictable rule: the amount saved doubles each day, starting with $2 on day 1. So the pattern is: $2, $22, $2³, $2⁴, $2⁵, $2⁶, $2⁷. Recognizing and understanding patterns is an important skill in many areas of life, from mathematics and science to language and music.
Based on the given pattern, on day 4, the amount saved would be $2⁴ = $16. On day 5, the amount saved would be $2⁵ = $32. On day 6, the amount saved would be $2⁶ = $64. And on day 7, the amount saved would be $2⁷ = $128.
To calculate the total amount saved for the week, we simply add up the amounts saved on each day:
Total amount saved = $2 + $22 + $2³ + $16 + $32 + $64 + $128
= $2 + $22 + $8 + $16 + $32 + $64 + $128
= $272
Therefore, you would save a total of $272 in one week if you continued along the same pattern.
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there are n people seated at a round table.
Answers
Step-by-step explanation:
circular permutations of n objects =(n-1)!
Find the accumulated value of an investment of $15,000 for 5 years at an interest rate of 6.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly d. compounded continuously. Round answers to the nearest cent.
Answers
Answer:
a. Compounded semiannually: $19,216.67
b. Compounded quarterly: $19,338.56
c. Compounded monthly: $19,416.32
d. Compounded continuously: $19,451.08
Step-by-step explanation:
The formula for the accumulated value (A) of an investment with an initial principal (P), an interest rate (r) and a compounding period (n) for a number of years (t) is:
A = P(1 + r/n)^(n*t)
Using this formula, we can calculate the accumulated value for each of the compounding periods given:
a. Compounded semiannually:
A = $15,000(1 + 0.065/2)^(2*5) = $19,216.67
b. Compounded quarterly:
A = $15,000(1 + 0.065/4)^(4*5) = $19,338.56
c. Compounded monthly:
A = $15,000(1 + 0.065/12)^(12*5) = $19,416.32
d. Compounded continuously:
A = $15,000e^(0.0655) = $19,451.08
Therefore, the accumulated value of the investment varies depending on the compounding period, with more frequent compounding resulting in a higher accumulated value.
A two-day environmental clean up started at 9AM on the first day. The number of workers fluctuated as shown in the following figure.
graph of number of workers vs. time; between t=0 hours and t=8 hours the graph behaves as a sine curve with centerline 30, amplitude 10 and period 16; between t=12 and t=20, the graph is constant at 20. Then, at t=20 the graph becomes a sine curve again, starting at its minimum and completing one period between t=20 and t=36. The graph is then constant at 20 until t=44, before increasing as a sine again until t=48.
Suppose that the workers were paid 15 dollars per hour for work during the time period 9 am to 5 pm and were paid 22.5 dollars per hour for work during the rest of the day. What would the total personnel costs of the clean up have been under these conditions?
total cost =
dollars
Answers
The total personnel costs of the cleanup would be $8,625.
How to determine?Between 9AM and 5PM, a total of 8 hours, the workers are present during the interval t=0 to t=8. During this interval, the number of workers is given by:
f(t) = 30 + 10sin((2π/16)t)
We can calculate the number of workers for each hour using this formula:
f(0) = 30 + 10sin(0) = 30
f(1) = 30 + 10sin(π/8) ≈ 38.66
f(2) = 30 + 10sin(π/4) = 40
f(3) = 30 + 10sin(3π/8) ≈ 38.66
f(4) = 30 + 10sin(π/2) = 40
f(5) = 30 + 10sin(5π/8) ≈ 38.66
f(6) = 30 + 10sin(3π/4) = 30
f(7) = 30 + 10sin(7π/8) ≈ 21.34
f(8) = 30 + 10sin(π) = 20
So, during the first 8 hours, the number of workers fluctuates between 20 and 40.
Between 5PM and 9AM the next day, a total of 16 hours, the workers are present during the intervals t=8 to t=12, t=20 to t=36, and t=44 to t=48. During these intervals, the number of workers is given by:
Between t=8 and t=12, the number of workers is decreasing from 40 to 20. We can approximate this by a linear function:
f(t) = 40 - 5t
Between t=20 and t=36, the number of workers is constant at 20.
Between t=44 and t=48, the number of workers is increasing from 20 to 40. We can use the same linear function as before, but with t shifted by 44:
f(t) = 40 - 5(t-44)
We can now calculate the total personnel costs by multiplying the number of workers at each time interval by the appropriate hourly rate:
From 9AM to 5PM (8 hours): 30 workers on average, at a rate of $15 per hour:
8 × 30 × 15 = $3,600
From 5PM to 9AM the next day (16 hours):
From t=8 to t=12 (4 hours): average of 30 workers, at a rate of $22.5 per hour:
4 × 30 × 22.5 = $2,700
From t=20 to t=36 (16 hours): constant 20 workers, at a rate of $22.5 per hour:
16 × 20 × 22.5 = $7,200
From t=44 to t=48 (4 hours): average of 30 workers, at a rate of $22.5 per hour:
4 × 30 × 22.5 = $2,700
The total cost is the sum of the costs for each time interval:
$3,600 + $2,700 + $7,200 + $2,700 = $16,200
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Select the correct answer. Which statement best describes the zeros of the function h(x) = (x + 9)(x2 − 10x + 25)? A. The function has three complex zeros. B. The function has three distinct real zeros. C. The function has one real zero and two complex zeros. D. The function has two distinct real zeros.
Answers
All the zeroes of the function are,
x = - 9, 5, 5
Given that;
The function is,
h (x) = (x + 9) (x² - 10x + 25)
Now, We can find all the zeroes of the function as;
h (x) = (x + 9) (x² - 10x + 25)
h (x) = (x + 9) (x² - 5x - 5x + 25)
h (x) = (x + 9) ((x - 5) - 5 (x - 5))
h (x) = (x + 9) (x - 5) (x - 5)
Thus, All the zeroes of the function are,
x + 9 = 0
x = - 9
(x - 5)² = 0
x = 5, 5
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A company needs to deliver product to each of their 5 stores around the Dallas, TX area. Driving distances between the stores are shown below. Find a route for the driver to follow, returning to the distribution center in Fort Worth:
a. Using Nearest Neighbor starting in Fort Worth
b. Using Repeated Nearest Neighbor
Answers
Using Nearest Neighbor starting in Fort Worth, the route will have a total path length of 183.
How to calculate the valueUsing Nearest Neighbor starting in
Foethliceth:
We take the cheapest way to travel,
19 38 41 D42 F
d+ F A 43 M
Total path length = 19 +43 +38 +41 +42 = 183
Using Repeated Nearest. Neighbor:
The repetitive nearest algorithm says. to tey each veetex as starting point I then choose the best answer.
Feam Fort Worth:
F 19 A 43 M 38 p 4D 42 F
Total path length. = 183
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Ayuda porfavor , cuadros magicos de tal manera que al sumarlos horizontal y vertical den el resultado
Answers
hola te hice tres los otros no tuve tiempo espero te sirvan de ayuda :)
Each of P, Q and R had a certain amount of money. P gave some money to Q and R in such a way that the amounts with them were doubled. Now Q gave some money to P and R such that the amounts with them were doubled. Finally R also gave some money with him to P and Q such that the amounts with them were doubled. At this stage, each of them had 240.What was the initial amount with P?
Answers
The initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.
What is amount?Amount is the sum of money or quantity of something. It is usually measured in numerical values such as dollars, pounds, or euros. It is used to describe the total of something, such as how much money is in a bank account or the total cost of a purchase. Amount can also be used to describe a quantity of something such as the amount of time spent on a project or the amount of people present at an event.
Let us denote the initial amount of money with P, Q and R as P0, Q0 and R0 respectively. We know that P gave some money to Q and R such that their amounts were doubled, which implies that P0 = 2(Q0 + R0). Similarly, Q gave some money to P and R such that their amounts were doubled, which implies that Q0 = 2(P0 + R0). Finally, R gave some money to P and Q such that their amounts were doubled, which implies that R0 = 2(P0 + Q0). Substituting the value of P0 from the first equation in the third equation, we get:
2(Q0 + R0) = 2(P0 + Q0)
2Q0 + 2R0 = 2P0 + 2Q0
R0 = P0
Substituting the value of R0 in the first equation, we get:
P0 = 2(Q0 + R0)
P0 = 2(Q0 + P0)
P0 = 2Q0 + P0
P0 = 2Q0
Finally, substituting the value of P0 in the second equation, we get:
Q0 = 2(P0 + R0)
Q0 = 2(2Q0 + R0)
Q0 = 4Q0 + R0
R0 = 3Q0
Therefore, the initial amount of money with P, Q and R can be calculated as follows:
P0 = 2Q0
Q0 = 3Q0
R0 = 3Q0
Therefore, the initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.
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The volume of a cone is 678.24 cubic inches. What is the height of the cone?
Answers
The height of the cone is 18 inches.
How to find the height of a cone?The height of the cone can be found as follows:
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 6 inches
volume of the cone = 678.24
h = ?
Hence,
678.24 = 1 / 3 × 3.14 × 6² × h
678.24 = 1 / 3 × 3.14 × 36 × h
37.68h = 678.24
divide both sides of the equation by 37.68
h = 678.24 / 37.68
h = 18 inches
Therefore,
height of the cone = 18 inches
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
4x + 3y = 18
4x - 2y = 18
Answers
Answer:
To solve the system of linear equations:
4x + 3y = 18
4x - 2y = 18
we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the equations in a way that eliminates one of the variables. Here's how we can do it:
Multiply the first equation by 2, and the second equation by 3 to eliminate x:
8x + 6y = 36
12x - 6y = 54
Now, subtract the second equation from the first:
8x + 6y - (12x - 6y) = 36 - 54
8x + 6y - 12x + 6y = -18
-4x + 12y = -18
Divide both sides by -4 to isolate x:
-4x/(-4) + 12y/(-4) = -18/(-4)
x - 3y = 4.5
Now, we can substitute this value of x into one of the original equations, let's use the first equation:
4(4.5) + 3y = 18
18 + 3y = 18
3y = 18 - 18
3y = 0
y = 0
So, the solution to the system of equations is x = 4.5 and y = 0.
Method 2: Substitution
In this method, we solve one of the equations for one variable and then substitute that expression into the other equation to solve for the other variable. Here's how we can do it:
Solve the first equation for x:
4x + 3y = 18
4x = 18 - 3y
x = (18 - 3y)/4
Now, substitute this expression for x into the second equation:
4[(18 - 3y)/4] - 2y = 18
18 - 3y - 2y = 18
-5y = 18 - 18
-5y = 0
y = 0
Now, substitute this value of y back into the expression for x:
x = (18 - 3(0))/4
x = 18/4
x = 4.5
So, the solution to the system of equations is x = 4.5 and y = 0, which is consistent with the solution obtained using the elimination method.
Answer:
(4.5,0)
Step-by-step explanation:
The point that makes this system of equations true is (4.5,0.
When x=4.5, and y=0 both of these equations equal each other.
You can find this point either by using your calculator, or graphing the equations and seeing where they intersect.
Calculate the circumference, given the following diameters. Use T[= 22 7 I. 30 cm 2. 15 m 3. 40 ft 4. 20 cm 5. 8 m 6. 12 cm 7. 22 in. 8. 34 m 9. 10m 10. 34 cm
Answers
Required circumference of the given diameters are 94.29 cm, 471.43 m, 377.14 ft, 62.86 cm, 251.43 m, 37.71 cm, 69.71 in, 1068.57 m, 314.29 m, 106.86 cm respectively.
What is circumference of circle?
The circumference of a circle is the distance around the edge or boundary of the circle. It is a fundamental geometric property of a circle and is defined as the product of the circle's diameter and pi (π), which is a mathematical constant approximately equal to 3.14.
The formula to calculate the circumference of a circle is C = 2πr or C = πd
where C represents the circumference, r represents the radius, and d represents the diameter of the circle,
1. Diameter = 30 cm
Circumference = π x Diameter
= 22/7 x 30
= 94.29 cm
2. Diameter = 15 m
Circumference = π x Diameter
= 22/7 x 15 x 100
= 471.43 m
3. Diameter = 40 ft
Circumference = π x Diameter
= 22/7 x 40 x 12
= 377.14 ft
4. Diameter = 20 cm
Circumference = π x Diameter
= 22/7 x 20
= 62.86 cm
5. Diameter = 8 m
Circumference = π x Diameter
= 22/7 x 8 x 100
= 251.43 m
6. Diameter = 12 cm
Circumference = π x Diameter
= 22/7 x 12
= 37.71 cm
7. Diameter = 22 in
Circumference = π x Diameter
= 22/7 x 22
= 69.71 in
8. Diameter = 34 m
Circumference = π x Diameter
= 22/7 x 34 x 100
= 1068.57 m
9. Diameter = 10 m
Circumference = π x Diameter
= 22/7 x 10 x 100
= 314.29 m
10. Diameter = 34 cm
Circumference = π x Diameter
= 22/7 x 34
= 106.86 cm
Therefore, the circumference of the given diameters are 94.29 cm, 471.43 m, 377.14 ft, 62.86 cm, 251.43 m, 37.71 cm, 69.71 in, 1068.57 m, 314.29 m, 106.86 cm.
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Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log3 3/8
Answers
The expression "log₃(3/8)" can be expressed in the form of "difference-of-logarithms" is log₃(3) - log₃(8), and it's simplified value is -0.89278.
The "Quotient-Property" states that logarithm of quotient of "two-numbers" is equal to the difference of logarithms of individual numbers. It is expressed as : logₐ(b/c) = logₐ(b) - logₐ(c);
Using the quotient property, we can write log₃(3/8) as:
⇒ log₃(3) - log₃(8)
We know that log₃(3) = and log₃(8) = ,
So, ⇒ log₃(3) - log₃(8),
⇒ 1 - 1.89278
⇒ -0.89278,
Therefore, the value of log₃(3/8) is -0.89278.
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The given question is incomplete, the complete question is
Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log₃(3/8).
The life time of a certain device has CDF
F (x) = 1 − e^−λx2 x > 0; λ > 0
Derive the pdf of X and determine its mean, mode, median and variance.
Answers
The probability density function (pdf) of the lifetime of a certain device is expressed as: f (x) = 2λxe^−λx² ; x > 0; λ > 0
Mean: E(x) = -2λ + C
Mode: x = 0
Median: x = ±√(-ln(0.5)/λ)
Variance: Var(x) = 0
What is probability density function?Probability density function (PDF) describes the relative likelihood for a random variable to take on a given value. It is a continuous function that is used to represent the probability distribution of a continuous random variable.
The probability density function (pdf) of the lifetime of a certain device is expressed as:
f (x) = 2λxe^−λx² ; x > 0; λ > 0
Mean: The mean (or expected value) of the probability density function is given by:
E(x) = ∫x.f(x)dx = ∫x.2λxe^−λx²dx
= -2λe^−λx² + C
E(x) = -2λ + C
Mode: The mode of the probability density function is the value at which the maximum density occurs. This occurs at the point where the derivative of the function is equal to 0.
f′(x) = 2λxe^−λx²
= 0
x = 0
Therefore, the mode of the probability density function is 0.
Median: The median is the value of the random variable for which the cumulative distribution function is equal to 0.5.
F(x) = 1 − e^−λx² = 0.5
1 − e^−λx² = 0
e^−λx² = 0.5
−λx² = ln(0.5)
x² = -ln(0.5)/λ
x = ±√(-ln(0.5)/λ)
Therefore, the median of the probability density function is given by:
x = ±√(-ln(0.5)/λ)
Variance: The variance of the probability density function is given by:
Var(x) = E(x²) - (E(x))²
E(x²) = ∫x².f(x)dx
= ∫x^2.2λxe^−λx²dx
= -2λe^−λx² + C
E(x²) = -2λ + C
Var(x) = -2λ + C - (-2λ + C)²
= 0
Therefore, the variance of the probability density function is 0.
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Which graph shows the solution to the system of linear equations? y equals negative one third times x plus 1 y = −2x − 3 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma 0 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma 0 and another line that passes through the points 0 comma negative 3 and 1 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma negative 2 and another line that passes through the points 0 comma negative 2 and 1 comma negative 5
Answers
The graph of the system of linear equations can be seen in the image at the end.
Which is the graph of the system of linear equations?Here we have the following system of equations:
y = -(1/3)x + 1
y = -2x - 3
To graph the system of equations, we just need to graph both of these lines in the same coordinate axis. The point where the lines intercept are the solutions of the system.
In the image at the end we can see the graph of the system of equations, there we also can see that the solution is the point (-2.4, 1.8)
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Which graph shows the image of ABC after a rotation about the origin
Answers
Answer:
I need the rotation in degrees around the origin (flip around x axis, 90 degrees counter clockwise) or send all of the graph options
Step-by-step explanation:
Given the demand function D(p) = 400-4p².
Find the Elasticity of Demand at a price of $8.
At this price, we would say the demand is:
-Inelastic
-Elastic
-Unitary
Based on this, to increase revenue we should:
-Keep Prices Unchanged
-Lower Prices
-Raise Prices
Answers
The Elasticity of Demand at a price of $8 is 0.056.
Given the demand function,
D(p) = 400 - 4p²
The formula to find the elasticity of demand is,
e = p/D
Here p is the price and D is the quantity demanded.
When p = $8,
D = 400 - (4 × 8²) = 144
Elasticity of demand = 8 / 144 = 0.056
Hence the elasticity of demand is 0.056.
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The distance between Anaheim, CA and Sacramento, CA is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles.
Answers
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
Can someone help me with this thank you
Answers
Answer:
1. 4 tens 2 ones
2. 6 tens 5 ones
3. 3 tens 7 ones
4. 2 tens 6 ones
5. 7 tens 4 ones
6. 5 tens 9 ones
7. 8 tens 1 ones
8. 9 tens 9 ones
9. 1 tens 3 ones
Step-by-step explanation:
not sure if I did it right, lmk if im wrong. Think ur just suppsoed to count the number of boxes that make 10, and those that dont count up to 10, depending on the number, are seen as "ones".
The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 3 to 5.
Check
M(-6,-3)
N (?.?)
P (26,13)
Coordinates of N:
4D
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Answers
The coordinates of point N that divides the line segment formed joining points M(-6,-3) and P(26,13) in the ratio 3:5, evaluated using section-formula is (14,7)
What is section-formula?
The coordinates of the point that splits a specific line segment into two halves are given by the section formula. The line may be split at the point either internally or externally. Their lengths are divided in a way that keeps them in the m: n ratio. The ratio in which the line segment is divided and the coordinates of the points connecting it allow us to calculate the coordinates.
According to section-formula:
(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex]) {where (x,y)are coordinates of point which divides & (a,b) ; (c,d) are coordinates of points forming line segment.
Given P=(a,b) = (26,13)
M=(c,d) = (-6.-3)
m:n = 3 : 5
N=(x,y) = ?
N=(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex])
= {[tex]\frac{(-6)(3)+(26)(5)}{3+5}[/tex] ; [tex]\frac{(-3)(3)+(13)(5)}{3+5}[/tex] }
={ [tex]\frac{-18+130}{8}[/tex] ; [tex]\frac{-9+65}{8}[/tex] }
= {[tex]\frac{112}{8}[/tex] , [tex]\frac{56}{8}[/tex] }
={14 , 7}
The coordinates of point N are (14,7) which divides line joining P(26,13) and M(-6,-3) in ratio 3:5.
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graph the function f(x)=x^2+6x+4 by starting with the graph of y=x^2 and using transformations
Answers
The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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Solve the right triangle using the information given. Round answers to two decimal places, if necessary. a = 4, b = 6; Find c, α, and β.
Answers
Step-by-step explanation:
first, remember Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle).
a and b are the legs.
so, in our case
c² = 4² + 6² = 16 + 36 = 52
c = sqrt(52) = 7.211102551... ≈ 7.21
and then remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the corresponding opposite angles (here also called alpha, beta. gamma would be the 90° angle).
so,
4/sin(alpha) = c/sin(90) = c
4 = c×sin(alpha)
sin(alpha) = 4/c = 4/7.211102551... = 0.554700196...
alpha = 33.69006753...° ≈ 33.69°
we don't need to do that much calculation for the third angle beta, as we know the sum of all angles in a triangle is always 180°.
so,
180 = alpha + beta + 90 = 33.69 + beta + 90
90 = 33.69 + beta
56.30993247... = beta ≈ 56.31°
What are the odds in favor of Dave selecting a gray t-shirt if he has 5 gray in his wardrobe of 16
Answers
Answer:
wouldn't it be 5/16
Step-by-step explanation:
honestly not sure but isn't this just a probability question?
Number of gray t-shirts = 5
Total number of t-shirts = 16
Odds in favor of gray t-shirt = Number of gray t-shirts / Total number of t-shirts
Odds in favor of gray t-shirt = 5/16
Therefore, the odds in favor of Dave selecting a gray t-shirt are 5/16.
Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected net winnings?
Answers
Answer:
Expected Value = -1(999/1000) + 499(1/1000) = -500/1000 = -50 cents
Step-by-step explanation:
15.3
21. A squirrel is standing on the branch of a tree. The angle of elevation from a point on the ground to the squirrel
is 48°. The ground distance from the point to the tree is 28ft. How high above the ground is the squirrel?
Round your answer to the nearest foot.
48⁰
28 ft
21
Answers
Answer:
The height of the squirrel is 31 feet.
Step-by-step explanation:
You need to know your Right Triangle Trigonometry to do this problem.
Rt Triangle trig is all about ratios. Angles and ratios.
In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.
tan Angle = opposite/adjacent
tan 48° = x/28
multiply both sides by 28
28•tan48° = x
You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"
Enter 28 × tan48° =
It will return 31.0971504152
Your question asks you to round to the nearest whole.
x = 31
The squirrel's height in the tree is 31ft.
One can of soda has a capacity of 355mL. How may liters of soda does 12.
Answers
12 cans of soda hold 4.26 liters of soda.
The process for determining the total volume of soda would be the same using the specific capacity and number of cans.
We need to determine how many milliliters of soda 12 cans hold. We can do this by multiplying the capacity of one can (355 mL) by the number of cans (12):
355 mL/can x 12 cans = 4,260 mL
Now we need to convert this amount to liters. We know that 1 liter is equal to 1,000 milliliters, so we can divide the total volume in milliliters by 1,000:
4,260 mL ÷ 1,000 mL/L = 4.26 L
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The garment factory plans to make 690 sets of garments. It has been done for 5 days, with an average of 75 sets per day. The rest needs to be completed in 2.5 days, how many sets are done on average per day (step-by-step answer)
Answers
The garment factory needs to produce an average of 126 sets per day in the next 2.5 days to complete the order of 690 sets.
We have,
The number of sets produced in the first 5 days.
= 5 x 75
= 375
The number of sets remaining.
= 690 - 375
= 315
The number of sets to be completed in the next 2.5 days.
= 315
The average number of sets to be completed per day.
= 315 / 2.5
= 126
Therefore,
The garment factory needs to produce an average of 126 sets per day in the next 2.5 days to complete the order of 690 sets.
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Suppose it takes John 18 minutes to run 2 miles. How long would it take him to run 5 kilometers? Round your answer to the nearest minute.
Answers
The required it would take John 26.3 minutes to run 5 kilometers.
Since there are 1.60934 kilometers in a mile, we can first convert 2 miles to kilometers:
2 miles = 2 * 1.60934 kilometers = 3.21869 kilometers
Now we can use the formula for speed:
speed = distance/time.
time = distance/speed
We know the distance (5 kilometers), and we can find the speed by dividing the distance by the time it takes to run 2 miles:
speed = 3.21869 kilometers / 18 minutes
speed ≈ 0.19 kilometers per minute
Now we can use this speed to find the time it would take to run 5 kilometers:
time = 5 kilometers / 0.19 kilometers per minute
time ≈ 26.3 minutes
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different equation dy÷dx+ytanx=secx
Answers
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
The sample space for tossing a coin 4 times is {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}. Determine P(at least 3 heads). 12.5% 25% 31.25% 68.75%
Answers
Answer: a
Step-by-step explanation:
Theres 5 times that we could get at least 3 heads and were tossing the coin 4 times so 5/4. 5 divided 4 = 1.25 x100 =12.5 percent
The probability of P(at least 3 heads) is 31.25%
How to determine the probabilityProbability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
From the information given, we have that;
{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.
Count the number of events with 3 H's
Now, to determine the P(at least 3 heads).
We get;
P(at least 3 heads) = 5/16 × 100/1
Divide the values, we get;
P(at least 3 heads) = 0.3125×100/1
Multiply the values we get;
P(at least 3 heads) = 31.25%
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