The experimental probability of the name Grace being chosen = 11/108
The theoretical probability of the name Grace being chosen = 1/6
We know that formula for the experimental probability of event A is :
P(A) = (Number of occurance of event A) / (Total number of trials)
Here, a name is chosen 108 times and the name Grace is chosen 11 times.
Let event A: the name Grace being chosen
the number of occurance of event A = 11
And the Total number of trials = 108
Using above formula the experimental probability would be,
P(A) = 11/108
Here, six different names were put into a hat.
This means that the number of possible outcomes n(S) = 6
And n(A) = 1
So, the theoretical probability would be,
P = n(A)/n(S)
P = 1/6
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A heptagon has perimeter 99 feet. Four of the sides are the same length, and the remaining sides are half as long. How long are the shorter sides? The shorter sides are how many feet
The shorter sides of heptagon as 9 feet each based on the relation, length of longer sides and total length.
Let the three shorter sides of heptagon (with seven sides) be of x feet. Hence, the remaining four sides will be of 2x feet. Now, sum of their lengths is stated thus, representing them as equation
(4 × 2x) + 3x = 99
Solving the bracket first
8x + 3x = 99
Adding the values on Left Hand Side of the equation
11x = 99
Rewriting the equation in terms of x
x = 99/11
Performing division on Right Hand Side of the equation
x = 9
Hence, the length of shorter sides is 9 feet each.
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Prove or disprove. show your work.
(a) for any integers n a and m: if both n and m are odd, then n - m² is even
(b) Vp Z: if p is prime, then p-2 is not prime.
(c) Vs R s is irrational s2 is irrational.
(d) There is two odd integers n and m such that n² m² - 1 is odd.
(a) The statement is false because we have found a case where n - m² is even.
(b) The statement holds true.
(c) The statement is false because we have found a case where s^2 is rational despite s being irrational.
(d) It is not possible to find two odd integers n and m such that n²m² - 1 is odd. Thus, the statement is false.
(a) The statement "for any integers n and m, if both n and m are odd, then n - m² is even" is incorrect. Let's consider a counterexample:
Take n = 3 and m = 1. Both n and m are odd.
n - m² = 3 - 1² = 3 - 1 = 2, which is an even number.
Therefore, the statement is false because we have found a case where n - m² is even.
(b) The statement "for any prime number p, p-2 is not prime" is generally true. Let's consider the cases:
If p is an odd prime greater than 2, then p-2 is an even number, and the only even prime number is 2. Therefore, p-2 cannot be prime in this case.
If p = 2, then p-2 = 0, which is not considered a prime number.
In both cases, p-2 is not a prime number. Therefore, the statement holds true.
(c) The statement "for any real number s, if s is irrational, then s^2 is irrational" is incorrect. Let's consider a counterexample:
Take s = √2. √2 is an irrational number.
s^2 = (√2)^2 = 2, which is a rational number.
Therefore, the statement is false because we have found a case where s^2 is rational despite s being irrational.
(d) The statement "There are two odd integers n and m such that n²m² - 1 is odd" is true. Let's consider the following example:
Take n = 1 and m = 1. Both n and m are odd.
n²m² - 1 = 1² * 1² - 1 = 1 * 1 - 1 = 0, which is an even number.
However, if we take n = 3 and m = 1, both n and m are still odd.
n²m² - 1 = 3² * 1² - 1 = 9 * 1 - 1 = 9 - 1 = 8, which is an even number.
Therefore, it is not possible to find two odd integers n and m such that n²m² - 1 is odd. Thus, the statement is false.
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DE≅AE ,BA∥CE , CB∥DA and m∠C=65∘
The measure of <BAE is 130 degree.
We have,
m <C = 65
As, opposite sides are parallel then ABCD is a parallelogram.
Then, opposite angles of a parallelogram are congruent
∠ BAD = ∠ BCD = 65°
∠ ADE = ∠ BAD = 65° ( alternate angles )
Since, DE = AE then Δ ADE is isosceles Triangle.
So, ∠ DAE = ∠ ADE = 65°
We can write,
∠ BAE = ∠ BAD + ∠ DAE = 65° + 65° = 130°
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Evaluate: summation from n equals 4 to 10 of 15 times 3 tenths to the n minus 1 power period Round to the nearest hundredth.
a
0.58
b
1.92
c
6.42
d
9.43
Answer:olution:. Given data:. Answer:. sum_(n=4)^10 15(3/10)^(n-1)= sum_(n=4)^10 15(0.3)^(n-1) = 15 [(0.3)^3 + (0.3)^4 + (0.3)^5+ (0.3)^6 + (0.3)^7+ (0.3)^8 + ...
Doesn’t include: 0.58 b 1.92 c 6.42 d 9.43
Evaluate: summation from n equals 4 to 10 of 15 times 3 tenths to the n minus 1 power period Round to the nearest hundredth.
Step-by-step explanation:Example
Evaluate X
4
r=1
r
3
.
Solution
This is the sum of all the r
3
terms from r = 1 to r = 4. So we take each value of r, work out
r
3
in each case, and add the results. Therefore
X
4
r=1
r
3 = 13 + 23 + 33 + 43
= 1 + 8 + 27 + 64
= 100 .
Example
Evaluate X
5
n=2
n
2
.
Solution
In this example we have used the letter n to represent the variable in the sum, rather than r.
Any letter can be used, and we find the answer in the same way as before:
X
5
n=2
n
2 = 22 + 32 + 42 + 52
= 4 + 9 + 16 + 25
= 54 .
Example
Evaluate X
5
k=0
2
k
.
A person paid by the hour works 25 hours a week and makes $539. How much would they make if they work 54 hours? Learn This: Multiply 25 with 539 and 54 Round your answer to 2 decimal places
Therefore, if the person works 54 hours, they would make $1,163.04. Rounded to 2 decimal places, the answer is $1,163.00.
The decimal system employs ten decimal digits, a decimal mark, and a minus sign ("-") for negative quantities when writing numbers. The decimal digits are 0 through 9, with the dot (".") serving as the decimal separator in many (mainly English-speaking) nations and the comma (",") in others.
The fractional portion of the number is represented by the place value that follows the decimal. The number 0.56, for instance, is composed of 5 tenths and 6 hundredths.
We can use proportionality to solve this problem. If the person works 25 hours and makes $539, then their hourly rate is:
$539 ÷ 25 hours = $21.56 per hour
They would make if they work 54 hours, we can multiply their hourly rate by the number of hours worked:
$21.56 per hour × 54 hours = $1,163.04
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You are conducting a research study. You give a group of participants an accelerometer. When you're analyzing this data, you realize that all participants had the highest levels of physical activity on Day 1. You decide to exclude this data. Excluding this data is an example of trying to avoid: Select one: a Rosenthal Effect b Getting a non significant statistical finding C Hawthorne Effect Od More data to sort through
Hawthorne Effect
You are conducting a research study and giving a group of participants an accelerometer. When analyzing the data, you notice that all participants had the highest levels of physical activity on Day 1. You decide to exclude this data. Excluding this data is an example of trying to avoid: Hawthorne Effect
The Hawthorne Effect refers to the phenomenon where participants modify their behavior in response to being observed or aware of being part of a study. By excluding the data from Day 1, you are trying to avoid the potential influence of this effect on the study results.
You collect your data by watching the employees during their work breaks. If employees are aware that you are observing them, this can affect your study's results. For example, you may record higher or lower smoking rates than are genuinely representative of the population under study.
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7. What is the radius of the circle?
The radius of the circle is 4 units
What is radius of a circle?A circle is simply a round shape that has no corners or line segments. The body of a circle is called the circumference and a cut out of circumference is called an arc.
The distance from the centre of a circle to any part of its circumference is called a radius. Twice of a radius is called the diameter.
In the circle, the distance between the center of the circle and it's circumference is ;
4-0 = 4 units
Therefore the radius of the circle is 4 units.
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Does anyone know how to solve this problem?
The coordinates of the original figure are (-2, 4), (4, 4), (-2, 1), and (4, 1).
The coordinates of the final transformed figure are (-1, 2), (2, 2), (-1, 0.5), and (-2, 0.5).
What is a dilation?In Mathematics and Geometry, a dilation simply refers to a type of transformation which typically changes the size of a geometric figure, but not its shape.
This ultimately implies that, the size of the geometric figure would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.
Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:
(-2, 4) → (-2 × 1/2, 4 × 1/2) = (-1, 2).
(4, 4) → (4 × 1/2, 4 × 1/2) = (2, 2).
(-2, 1) → (-2 × 1/2, 1 × 1/2) = (-1, 0.5).
(-4, 1) → (-4 × 1/2, 1 × 1/2) = (-2, 0.5).
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Which lists contain only rational numbers? Select all that apply.
The lists that contain only rational numbers is 4/3, -12/13 ,9/4 , -5/7 , 3/4
How can the rational numbersbe known?A rational number can be described as the number which can be expressed in the form of p/q where p and q are integers when writing this number, q must not equal to 0 .
Examples of rational numbers are , however in mathematics, a rational number i can be seen as one that can be expressed as the quotient or fraction which can involves two integers, wherby one will be the numerator p and a non-zero as well as the denominator q.
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Suppose you are using α = 0. 05 to test the claim that μ = 1620 using a P-value. You are given the sample statistics n-35, X_bar=1590 and σ=82. Find the P-value. State the answer only and no additional work. Make sure to use the tables from the book. Do not round the final answer
The P-value is 0.0107 for the sample statistics n-35 and the coefficient of standard deviation is 82.
α = 0. 05
μ = 1620
size (n)= 35
X_bar=1590
σ=82
From the given sample statistics, the test statistics will be calculated as:
t = (X_bar - μ) / (σ / sqrt(n))
t = (1590 - 1620) / (82 / sqrt(35))
t = (-2.5411)
Using the t-distribution table with 34 degrees of freedom, the critical value will be:
t_critical = -1.6909
Here the calculated test statistic is less than the critical value.
P - value = 2*P(-100< t < -1.9720, when df = 34)
P = tcf (-100,-2.4103,34)
P = 0.0107
Therefore we can conclude that the P-value is 0.0107.
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Use the table to identify values of p and q that can be used to factor
x2-4x-12
as (x + p)(x+q).
OA. -2 and 6
OB. 2 and -6
OC. 3 and -4
OD. -3 and 4
P
2-6 -4
qp+q
-2 6 4
-1
1
3-4
-3 4
Answer: Use the table to identify values of p and q that can be used to factor x2 + x – 12 as (x + p)(x + q).A. –2 and 6. B. 3 and –4. C. –3 and 4. D. 2 and –6.
Step-by-step explanation:
If n = 25, 4 = 20%, M = 10%, and s = 15%,
Use the drop-down menus to complete this sentence that reports the results. (Note: 'XXX' is put in place of the actual numbers so as to not give away what the correct values are for the previous
questions.)
There [8a. Select] a significant reduction in peoples over estimation of the line length, [8b. Select], p [8c. Select], with [8d. Select]
8a.
A. was
B. was not
8b.
A. t(df) = XXX
B. t = XXX with df = XXX
C. t-test with df = XXX
D. M = 10%
8c.
A. < 0.01 two-tailed
B. > 0.01 two-tailed
C. = 0.01
8d.
A. Cohen's d = XXX, M = 10%, 95% CI [XXX, XXX].
B. M = 10%, n = 25, s = 15%.
C. M = 10%, n = 25, s = 15%, Cohen's d = XXX , M = 10%, 95% CI [XXX, XXX].
D. the t-test showing that people did do better after training.
There was a significant reduction in peoples over estimation of the line length, t = XXX with df = XXX, p < 0.01 two-tailed, with M = 10%, n = 25, s = 15%, Cohen's d = XXX , M = 10%, 95% CI [XXX, XXX].
8a. A. was
8b. B. t = XXX with df = XXX
8c. A. < 0.01 two-tailed
8d. C. M = 10%, n = 25, s = 15%, Cohen's d = XXX , M = 10%, 95% CI [XXX, XXX].
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20) As noted on page 332, when the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that u1 = u2 and calculate how much difference should be expected between the two sample means.
One sample has n = 6 scores with SS = 500 and the second sample has n = 12 scores with SS = 524.
One sample has n = 6 scores with SS = 600 and the second sample has n = 12 scores with SS 5 696.
In Part b, the samples have larger variability (bigger SS values) than in Part a, but the sample sizes are unchanged. How does larger variability affect the magnitude of the standard error for the sample mean difference?
We can expect a difference of about 6.67 between the two sample means.
To calculate how much difference to expect between two sample means when the population means are equal, we need to compute the standard error of the difference between means (SED).
The formula for SED in the independent-measures t-test is:
SED = sqrt((s1^2/n1) + (s2^2/n2))
where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
a) For the first situation, we have:
s1^2 = SS1/(n1-1) = 500/(6-1) = 100
s2^2 = SS2/(n2-1) = 524/(12-1) = 49.45
Plugging these values into the formula, we get:
SED = sqrt((100/6) + (49.45/12)) = 5.76
Therefore, we can expect a difference of about 5.76 between the two sample means.
b) For the second situation, we have:
s1^2 = SS1/(n1-1) = 600/(6-1) = 120
s2^2 = SS2/(n2-1) = 696/(12-1) = 69.6
Plugging these values into the formula, we get:
SED = sqrt((120/6) + (69.6/12)) = 6.67
Therefore, we can expect a difference of about 6.67 between the two sample means.
When the samples have larger variability (bigger SS values), the standard error for the sample mean difference will increase. This is because larger variability means that the scores are more spread out around their respective means, which increases the amount of variability in the difference between the two sample means. In contrast, when the variability is smaller, the scores are more tightly clustered around their means, and the standard error for the sample mean difference will be smaller.
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CARD 4:
Zoe opens a savings account that
earns annual compound interest. If she
doesn't make any deposits or
withdrawals after her initial deposit,
the balance in the account after x
years can be represented by the
equation below.
b(x)=675(1.045)
Duncan says the
balance in the
account increases at
a rate of 45% each
year
Daniella says the
balance in the
account increases at
a rate of 4.5% each
year
Which is set is right
Answer:
Step-by-step explanation:
2
Cruz purchased a large pizza for $12.75. It serves 5 people. What is the cost per serving?
$2.55 per serving
$2.60 per serving
$3.15 per serving
$7.55 per serving
If cruz purchased a large pizza for $12.75. It serves 5 people, the cost per serving of the pizza is $2.55. So, correct option is A.
To find the cost per serving of the pizza, we need to divide the total cost of the pizza by the number of servings. In this case, the pizza costs $12.75 and serves 5 people.
Therefore, the cost per serving can be calculated as:
Cost per serving = Total cost of pizza / Number of servings
Cost per serving = $12.75 / 5
Cost per serving = $2.55
So, the cost per serving of the pizza is $2.55.
When working with fractions or dividing quantities, we need to pay attention to the units involved. In this case, the units of the cost and the servings must match for the division to be meaningful.
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Use the given information to find the minimum sample size required to estimate an unknown population mean .
22) How many women must be randomly selected to estimate the mean weight of women in one age
group. We want 90% confidence that the sample mean is within 3.4 lb of the population mean, and
the population standard deviation is known to be 25 lb.
A) 145
B) 147
C) 208
D) 148
The minimum sample size required to estimate an unknown population mean is 148. So, the correct option is D) 148.
To find the minimum sample size required to estimate an unknown population mean with 90% confidence, within 3.4 lb of the population mean, and a population standard deviation of 25 lb, follow these steps:
1. Identify the given values:
- Confidence level = 90%
- Margin of error (E) = 3.4 lb
- Population standard deviation (σ) = 25 lb
2. Find the corresponding z-score for the 90% confidence level. Using a standard normal distribution table or calculator, the z-score is 1.645.
3. Use the formula to find the sample size (n):
n = (z * σ / E)^2
n = (1.645 * 25 / 3.4)^2
4. Calculate the sample size:
n ≈ 147.267
Since we cannot have a fraction of a person, round up to the nearest whole number to ensure the required confidence level.
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Four times a number increased by 25 is 13 less than six times the number. Find the number
Answer:
19
Step-by-step explanation:
Let's call the number we're trying to find "x".
According to the problem:
4x + 25 = 6x - 13
To solve for x, we can start by isolating the x term on one side of the equation. Let's subtract 4x from both sides:
4x + 25 - 4x = 6x - 13 - 4x
25 = 2x - 13
Next, let's add 13 to both sides:
25 + 13 = 2x - 13 + 13
38 = 2x
Finally, we can divide both sides by 2 to solve for x:
38/2 = 2x/2
19 = x
Answer all boxes and read the questions
The area of the lateral face of cylinder = 75.4 in²
The area of the two bases of the cylinder = 25.13 in²
The total surface area of the cylinder = 100.53 in²
We know that the formula for the surface area of cylinder is:
A = 2πrh + 2πr²
where r is the radius of the cylinder
and h is the height of the cylinder
Here, r = 2 in and h = 6 in
The area of the lateral face of cylinder is given by,
A₁ = 2 × π × r × h
A₁ = 2 × π × 2 × 6
A₁ = 24 × π
A₁ = 75.4 sq. in.
And the area of two base is,
A₂ = 2πr²
A₂ = 2 × π × 2²
A₂ = 8 × π
A₂ = 25.13 sq. in.
The total surface area of cylinder would be,
A = A₁ + A₂
A = 75.4 + 25.13
A = 100.53 sq. in.
Therefore, the required area = 100.53 in²
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A. A rectangular loop of length 40 cm an width 10 cm with a 25 ohm light bulb is pulled from a large magnetic field (3. 5 T) very quickly (25 m/s). The light flashes as the circuit leaves the field. How long does the flash of light last in ms?
b. Which way does current flow as the loop exits the field? Why?
clock-wise
counter clock-wise
c. What is the power dissipated in the bulb during the flash in W?
a) The light flashes as the circuit leaves the field at a speed of 16 ms.
b) The current flow as the loop exits the field in the clockwise direction.
c) The power dissipated in the bulb during the flash is 0.04 W.
To reply to these questions, we will utilize Faraday's Law, which states that a changing attractive field actuates an electromotive drive (EMF) in a circuit, and the initiated EMF is rise to the rate of alter of attractive flux through the circuit.
a) The attractive flux through the circle is given by the item of the attractive field, region of the circle, and cosine of the point between the attractive field and the ordinary to the plane of the circle.
As the circle is pulled out of the attractive field, the magnetic flux through the circle diminishes, and thus, an EMF is actuated within the circle. This initiated EMF drives a current through the light bulb, causing it to light up.
The time term of the streak of light can be decided from the time taken by the circle to move out of the attractive field.
The removal voyage by the circle is 40 cm, and the speed is 25 m/s, so the time taken is:
t = d/v = 0.4 m / 25 m/s = 0.016 s = 16 ms
Subsequently, the streak of light endures for 16 ms.
b) Concurring to Lenz's Law, the course of the initiated current is such that it contradicts the alter within the attractive flux that produces it. As the circle is pulled out of the attractive field, the attractive flux through the circle diminishes.
Hence, the actuated current flows in a course that makes a magnetic field that restricts the initial attractive field. This could be accomplished by the induced current streaming clockwise as seen from above. Hence, the reply is clockwise.
c) The control scattered within the light bulb can be calculated utilizing the equation P = V²/R, where V is the voltage over the bulb and R is its resistance.
The voltage over the bulb is break even with to the initiated EMF, which can be calculated from Faraday's Law. The attractive flux through the circle changes at a rate of (40 cm) x (25 m/s) = 1 T.m²/s.
The region of the circle is (40 cm) x (10 cm) = 0.04 m². The cosine of the point between the attractive field and the ordinary plane of the circle is 1 (since the circle is opposite to the field). Subsequently, the induced EMF is:
EMF = -d(phi)/dt = -NA(dB/dt)
= -(1)(0.04 m²)(1 T.m²/s)/0.016 s
= -1 V
The negative sign indicates that the actuated EMF is within the inverse course of the current stream. Subsequently, the voltage over the light bulb is:
V = -EMF = 1 V
The power dissipated within the bulb is:
P = V²/R = (1 V)²/25 ohm = 0.04 W
Subsequently, the control scattered within the bulb during the streak is 0.04 W.
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please describes in two sentences for each graph if the discrimant is positive, negative, or 0.
1. The discriminant is positive, it has two real solutions
2. The discriminant is zero, it has a real solution
3. The discriminant is negative, it has no real solution
What is the discriminant of a graph?The discriminant of a graph is expressed as the part of the quadratic formula that is found under the square root symbol: b²-4ac.
It describes and gives information on whether there are two solutions, one solution, or no solutions.
It is important to note the following about discriminants;
If the discriminant is zero, then, the equation has real root valuesIf the discriminant is negative, then, the equation has no real root valuesIf the discriminant is positive, then, the equation has two different real root valuesLearn more about discriminants at: https://brainly.com/question/24730520
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18. Simplify -4-√-18
Answer:Step 1:
Enter the expression you want to simplify into the editor.
The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. The calculator works for both numbers and expressions containing variables.
Step-by-step explanation: I really hope this helps
At West High School, 10% of the students participate in sports. A student wants to simulate the act of randomly
selecting 20 students and counting the number of students in the sample who participate in sports. What is an
appropriate assignment of digits for this simulation?
O Let 0-8 = the student participates in sports. Let 9 = the student does not participate in sports.
Let 0 = the student participates in sports. Let 1-9 = the student does not participate in sports.
Let 0 and 1 = the student participates in sports. Let 2-9= the student does not participate in sports.
O Let 2-9 = the student participates in sports. Let 0 and 1 = the student does not participate in sports.
Let 0-1 represent students who participate in sports and let 2-9 represent students who do not participate in sports.
Let 0-9 represent students selected for the sample, with digits 0-8 representing students who participate in sports and digit 9 representing a student who does not participate in sports.
So, an appropriate assignment of digits for this simulation would be: Let 0-1 represent students who participate in sports and let 2-9 represent students who do not participate in sports.
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Find the probability of exactly one
successes in five trials of a binomial
experiment in which the probability of
success is 5%.
P = [? ]%
Round to the nearest tenth of a percent.
Enter
The probability of exactly one success in the binomial experiment would be 20. 4 %.
How to find the probability ?The probability that there is one success in a binomial probability which has a chance of success of 5 % can be found by the formula :
P ( X = 1) = (5 choose 1) x ( 0.05 ) x (0.95 ) ⁴
= ( 0.05 ) x ( 0. 95 ) ⁴
= 0.05 x 0.8145
= 0.040725
Multiplying both gives:
P(X = 1) = 5 x 0.040725
= 0.203625
In conclusion, the probability of one success is 0.203625 or 20. 4 %.
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A department store has an odd, but logical way of pricing their toys
A doll was $17
A kite was $14
A pair of skates was $24
using this logic, how much would Legos cost?
hint: it has to do with vowels and consonants
I can't figure it out
The cost of Legos, given that this is based on vowels and consonants would be $ 19.
How to find the cost ?The vowels and consonants can be arranged such that:
Doll - 1 vowel (o), 3 consonants ( d , l , l ) - $ 17
Kite - 2 vowels ( i, e ) , 2 consonants ( k, t) - $ 14
Skates - 2 vowels ( a, e ), 4 consonants ( s, k , t , s) - $24
Using this, we can solve for vowels and consonants such that cost per vowel is $2, and the cost per consonant is $5.
The cost of Legos is based on 2 vowels (e, o) and 3 consonants (L, g, s)
= ( 2 x 2 ) + ( 5 x 3 )
= $ 19
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Find an explicit formula for Fibonacci numbers, where the recurrence relation for In = {n-1 + fn-2, where fo = 0, fi = 1. 11. Solve the following recurrence relations (a) On=7an-1 -10am-2. (b) Qn=2
The solution to the recurrence relation is:
[tex]Qn = (1/2)(2^n) - (1/2)[/tex]
To find an explicit formula for the Fibonacci sequence, we first write out the first few terms:
[tex]f0 = 0[/tex]
[tex]f1 = 1[/tex]
[tex]f2 = 1[/tex]
[tex]f3 = 2[/tex]
[tex]f4 = 3[/tex]
[tex]f5 = 5[/tex]
[tex]f6 = 8[/tex]
...
We notice that each term is the sum of the two preceding terms. Therefore, we can write:
[tex]fn = fn-1 + fn-2[/tex]
Let's solve this recurrence relation to find an explicit formula for the nth term. First, we write out the first few terms in terms of f1 and f0:
[tex]f2 = f1 + f0[/tex]
[tex]f3 = f2 + f1 = f1 + f0 + f1 = 2f1 + f0[/tex]
[tex]f4 = f3 + f2 = 3f1 + 2f0[/tex]
[tex]f5 = f4 + f3 = 5f1 + 3f0[/tex]
[tex]f6 = f5 + f4 = 8f1 + 5f0[/tex]
We can see that the coefficients of f1 and f0 are the Fibonacci numbers themselves (1, 1, 2, 3, 5, 8, ...). Therefore, we can write the explicit formula:
[tex]fn = (1/√5) [(1+√5)/2]^n - (1/√5) [(1-√5)/2]^n[/tex]
(a) To solve the recurrence relation [tex]On = 7On-1 - 10On-2[/tex], we first find the roots of the characteristic equation:
[tex]r^2 = 7r - 10[/tex]
[tex]r = (7 ± √(7^2 + 40))/2[/tex]
[tex]r1 = 5, r2 = -2[/tex]
Therefore, the general solution to the recurrence relation is:
[tex]On = c1(5^n) + c2(-2^n)[/tex]
We can find the values of c1 and c2 by using the initial conditions:
[tex]O0 = 1, O1 = 5[/tex]
[tex]c1 + c2 = 1[/tex]
[tex]5c1 - 2c2 = 5[/tex]
Solving these equations, we get:
[tex]c1 = 1, c2 = -1/3[/tex]
Therefore, the solution to the recurrence relation is:
On = 5^n - (1/3)(-2)^n
(b) To solve the recurrence relation Qn [tex]= 2Qn-1 + 1[/tex], we first find the root of the characteristic equation:
[tex]r - 2 = 0[/tex]
[tex]r = 2[/tex]
Therefore, the general solution to the recurrence relation is:
Qn = c(2^n) + d
We can find the values of c and d using the initial conditions:
[tex]Q0 = 0, Q1 = 1[/tex]
[tex]c + d = 0[/tex]
[tex]2c + d = 1[/tex]
Solving these equations, we get:
[tex]c = 1/2, d = -1/2[/tex]
Therefore, the solution to the recurrence relation is:
Qn [tex]= (1/2)(2^n) - (1/2)[/tex]
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in a recent year, a hospital had 4126 births. Find the mean number of births per day, then use that result and the poisson distribution to find the probability that in a day, there are 14 births. Does it appear likely that on any given day, there will be exactly 14 births?
While it is not very likely that there will be exactly 14 births on any given day, it is still possible, and the probability of it happening is about 8.3%.
Let's start by calculating the mean or average number of births per day. To do this, we divide the total number of births in a year (4126) by the number of days in a year. Since there are 365 days in a year, the mean number of births per day is:
4126 / 365 = 11.3
This means that on average, there are about 11 to 12 births per day in this hospital.
In this case, the average rate of occurrence is 11.3 births per day. Using the Poisson distribution formula, we can calculate the probability of having 14 births in a day as follows:
P(X=14) = (e⁻¹¹°³) x (11.3¹⁴) / 14!
where e is the mathematical constant approximately equal to 2.71828, X is the random variable representing the number of births in a day, and ! represents the factorial function.
Using a calculator or a software tool, we get:
P(X=14) = 0.083
This means that the probability of having exactly 14 births in a day is about 8.3%.
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Bowling The time in which games are played determines the cost per game at Super Strike Bowling.
Games played from 1 pm to 4 pm cost $5
Games played after 4 pm and ending before 8 pm cost $6
Games played from 8 pm until the bowling alley closes at midnight cost $8
Write a step function that models the cost for one game where x represents the number of hours after 12 pm.
Kelly and two friends went bowling after school. They each played one game before 4 pm as well as one game after 4 pm. How much did it cost for all three to bowl?
As per the unitary method, it would cost $33 for Kelly and her two friends to bowl one game before 4 pm and one game after 4 pm each at Super Strike Bowling.
Bowling is a popular recreational activity enjoyed by many people around the world. Super Strike Bowling charges different rates for games played at different times of the day. To model the cost for one game, we can use a step function, where the value of x represents the number of hours after 12 pm. This function is defined as follows:
Cost per game (C) =
$5 if 1 pm ≤ x < 4 pm
$6 if 4 pm ≤ x < 8 pm
$8 if 8 pm ≤ x ≤ 12 am
Now, let's apply this step function to the scenario of Kelly and her two friends bowling. They each played one game before 4 pm, which cost $5 per game, and one game after 4 pm, which cost $6 per game. Therefore, the total cost for one person to play two games is:
Total cost = ($5 per game) + ($6 per game)
= $11
Since there were three people bowling, we can multiply the total cost by 3 to get the cost for all three to bowl:
Cost for all three to bowl = 3 × $11
= $33
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If you can’t see the question it’s f(x)=15^x+b
our environment is very sensitive to the amount of ozone in the upper atmosphere. the level of ozone normally found is 5.7 parts/million (ppm). a researcher believes that the current ozone level is not at a normal level. the mean of 8 samples is 6.1 ppm with a standard deviation of 0.7 . assume the population is normally distributed. a level of significance of 0.02 will be used. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is approximately 1.73.
To find the value of the test statistic, we can use a one-sample t-test.
The null hypothesis is that the true mean of the population is equal to the normal level of ozone, 5.7 ppm. The alternative hypothesis is that the true mean is not equal to 5.7 ppm.
We can calculate the t-value using the formula:
t = (sample mean - hypothesized mean) / (standard deviation / √(sample size))
Substituting in the given values:
t = (6.1 - 5.7) / (0.7 / √(8))
t = 1.73
To determine if this t-value is significant at a level of significance of 0.02, we need to compare it to the critical t-value from the t-distribution with 7 degrees of freedom (8 samples - 1). Using a t-table or calculator, the critical t-value is 2.998.
Since our calculated t-value of 1.73 is less than the critical t-value of 2.998, we fail to reject the null hypothesis. There is not enough evidence to conclude that the ozone level is not at a normal level.
Therefore, the value of the test statistic is t = 1.73.
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Jonty has a storage container in the shape of a cuboid
Jonty is correct as the original cost of paint is £196 which is less than £200 as said by him.
The area of part of cuboid to be painted will be the sum of all the unpainted areas. So, the area remaining to be painted will be = (2 × 3 × 2.5) + (2 × 3 × 12) + (12 × 2.5)
Remaining area = 15 + 72 + 30
Remaining area = 117 m²
Let us assume the original cost of paint be x. So,
x + 10%x = 26.95
110x = 26.95 × 100
110x = 2695
x = £24.5
Now, number of required tins = total unpainted area/area covered by one tin
Number of required tins = 117/15
Number of required tins = 7.8 tins
Taking it as 8 tins.
Previous cost of tins = 8 × 24.5
Previous cost = £196
Since the original cost is less than £200, Jonty is stating truth.
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