Answer:
Step-by-step explanation:
After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.
If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.
The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).
After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:
$1500 x (1 + 0.025)^40 = $4045.56
Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.
Hope that Helps :)
(x+5)/(x+8)=1+(6/(x+1))
Answer:
(x+10)/(x+8).
Step-by-step explanation:
(x+5)/(x+8) = (x+5)/(x+8) + (x+5)/(x+1)
= (x+5) + (x+5)/(x+1)
= (x+10)
The following letter cards are put in a bag.
REFLEX
A card is picked at random.
A
B
C
D +
E-
0
Which letter on the probability scale shows the probability of:
a) picking a card with an 'E' on it?
b)
picking a card that does not have an 'E' on it?
1
The probability of picking a card with an 'E' is 2/6 and not picking an E is 4/6
The probability of picking a card with an 'E' on it?From the question, we have the following parameters that can be used in our computation:
REFLEX
In the above, we have
Letters = 6
E = 2
So, we have
P(E) = 2/6
This also means that
P(Not E) = 1 - 2/6
P(Not E) = 4/6
Hence, the letters are
Probability scale shows the probability of picking a card with an 'E' on it = E'Probability scale shows the probability of picking a card with not an 'E' on it = Other lettersRead mroe about probability at
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Please help me solve questions 7,8, & 9!
7) The probability of not being dealt a queen is: 12/13
8) The probability of not being dealt a 9 is: 12/13
9) The probability of not being dealt a heart is: 3/4
How to find probability of selection of cards?7) We know that in a standard deck of cards, that we have:
(4 Aces, 4 Kings, 4 Queens, 4 jacks)
Thus, probability of not selecting a queen is:
48/52 = 12/13
8) There are 4 nines in a standard deck of 52 cards. The probability of selecting the first nine is thus: 4/52.
Probability of not being dealt a 9 is: 48/52 = 12/13
9) In a standard deck of 52 cards, we know that there are 4 suits (Clubs, Hearts, Diamonds, and Spades) and there are 13 cards in each suit (Clubs/Spades are black, Hearts/Diamonds are red)
Thus, probability of not being dealt a heart = (52 - 13)/52
= 39/52
= 3/4
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Need help finding how long it will take the object to reach 7 meters.
it should be from -4.9t^2 +29.8t+ 55 but I don't know what to do from there.
Step-by-step explanation:
7 m = - 4.9t^2 + 29.8t + 62 <====solve for 't'
0 = - 4.9t^2 + 29.8t + 56 <===== Use Quadrtatic Formula
with a = - 4.9 b = 29.8 c = 55
to find t = 7.57 seconds
Proration means what your paying monthly
What is proration?
It's when you only pay for part of something you used.
Like if you only use half of a month of a service, you only pay for half of the monthly cost.y cost.
When is proration used?
When you sign up for a service that you don't use for a full month.
When you change your service in the middle of a billing cycle.
Why is proration used?
To make sure people only pay for what they use.
To be fair and not overcharge people for services they didn't fully use.
chatgpt
Evaluate the function for f(2)
a. f(x) = 8x + 7
Answer:
23
Step-by-step explanation:
replace x with 2 8×2+7=23
Answer:23
Step-by-step explanation: its actually really simple, all you have to do is replace x for 2, giving you the equation: f(2) = 8x2 + 7 then all you have to do is solve, 8x2 is 16 and 16+7 is 23, and thats how you get the answer.
2 2/7 - 1
Must give complete and correct explanation
Answer:
1 2/7
Step-by-step explanation:
State that 1 = 7/7
2 2/7 - 7/7
Convert 2 2/7 into improper fraction
= 16/7
=16/7 - 7/7
16 - 7 = 9
= 9/7
Simplify back to mixed fraction
= 1 2/7
HELPPP PLSSSSSSSSSS
Decide the type or transformation and state the rule
The transformation rule used for the diagram is: Shift by 3 units upwards and a shift by 5 units to the left.
What is the transformation rule that was used?
There are different methods of transformation such as:
Reflection
Dilation
Rotation
Translation
Now, from the given graph, we see that both objects remain the same size and the object on the right was first if all shifted by 3 units upwards.
Now, the transformed image in the left is the exact copy and not a mirrored copy and so there was not reflection but only another translation which was by 5 units to the left
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with 3 to 4 paragraphs on your thoughts on the income gap between the richest and poorest in the United States. Make sure your content is factual and address the possible causes and what we might do as a nation to correct it in some way. At least 2 sources - APA format.
An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.5 years of the population mean. Assume the population of ages is normally distributed.
(a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.8 years.
(b) The sample mean is 20 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 10% of the sample mean? within 11% of the sample mean? Explain.
a) The minimum sample size required is 45.
b) The population mean could be within 10% of the sample mean, but less likely that it could be within 11% of the sample mean.
(a) How to determine the minimum sample size?
To determine the minimum sample size required to construct a 90% confidence interval for the population mean with a margin of error of 1.5 years, we use the formula n = (z ×σ / E)²
where n is the sample size, z is the z-score for the desired confidence level (in this case, 1.645 for a 90% confidence level), σ is the population standard deviation (1.8 years), and E is the margin of error (1.5 years).
Substituting the given values,
n = (1.645 × 1.8 / 1.5)² = 6.67² = 44.5
Rounding up to the nearest whole number, the minimum sample size required is 45.
(b) Using the minimum sample size of 45 with a 90% confidence level, the margin of error is 1.5 years. Therefore, the 90% confidence interval for the population mean is:
20 - 1.5 ≤ μ ≤ 20 + 1.5
18.5 ≤ μ ≤ 21.5
To determine whether it is likely that the population mean could be within 10% or 11% of the sample mean, we need to calculate the ranges of values that correspond to these percentages of the sample mean,
10% of 20 = 2
11% of 20 = 2.2
The range of values that are 10% of the sample mean is 20 ± 2 = 18 to 22
The range of values that are 11% of the sample mean is
20 ± 2.2 = 17.8 to 22.2
Comparing these ranges to the 90% confidence interval for the population mean, we see that:
The range of values that are 10% of the sample mean (18 to 22) is completely within the 90% confidence interval (18.5 to 21.5), so it is likely that the population mean could be within 10% of the sample mean.
The range of values that are 11% of the sample mean (17.8 to 22.2) extends slightly beyond the 90% confidence interval, so it is less likely that the population mean could be within 11% of the sample mean.
Therefore, we can conclude that it is likely that the population mean could be within 10% of the sample mean, but less likely that it could be within 11% of the sample mean.
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Suppose that, for a certain exam, a teacher grades on a curve.
It is known that the mean is 60 and the standard deviation is 5. There are 35 students in the class. (Round your answers to the nearest whole number.)
(a) How many students should receive a C?
student(s)
(b) How many students should receive an A?
student(s
2 students to get a grade C and 0 students to get a grade A.
What is the mean?In mathematics , in addition to the mode and median, the mean is one of the measures of central tendency. the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
What is the z-score?The relation between a value and a set of values of mean is described by the statistical measurement is known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point of score is the same as the mean score.
We require the distribution of scores in order to estimate the number of students who should earn a given grade. We may determine the z-score for each grade using the mean and standard deviation, presuming that the scores have a normal distribution.
(a) We must locate the z-score equivalent to a C grade in order to establish the number of pupils who should receive a C. Assuming that a C equals a score between 70 and 79, the following formula can be used to determine the z-scores for these values:
(70 - 60) / 5 = 2 is the z-score for 70.
79's z-score is (79 - 60) / 5 = 3.8
We can calculate the percentage of the distribution that falls between these two z-scores using a z-table or a calculator:
P(2 ≤ z ≤ 3.8)
This implies that roughly 4.55% of the students to get a C grade. We can multiply this percentage by the total number of students Than we get
0.0455 x 35 ≈ 2
therefore,approximately 2 students to get a grade C.
b) the z-score to calculate the number of pupils who should receive an grade A. Considering that a grade A of 90 or above 90,Now we can calculate the z-score for 90
than we get .
the z-score for 90 = (90 - 60) / 5 = 6 .
We calculate the percentage of the distribution that lies to the right of this z-score using a z-table or a calculator:
P(z ≥ 6) ≈ 0
therefore,0 students to get a grade A.
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find the range of h(x)=-4x^2-6x-4
The range of h(x)=-4x^2-6x-4 is (∞, -13).
How to find the range of range of h(x)=-4x^2-6x-4Using the vertex notion, find the range of the function h(x)=-4x2-6x-4.
The function's vertex is at x = -b/2a,
where a and b are the coefficients of x2 and x, respectively.
Because a = -4 and b = -6 in this situation, the vertex is at x = -(-6)/(2*(-4)) = 3/4.
To find the vertex's y-coordinate, enter x = 3/4 into the function:
h(3/4) = -4(3/4)^2 - 6(3/4) - 4 = -13
As a result, the function's vertex is at (3/4, -13).
Hence, the function's range is (∞, -13).
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Change 14,277 s to h, min, and s.
Answer:
1 min = 60s
1 h = 60 mins
14277s/60s = 237 mins and 57s = 237.95 mins
237.95mins/60mins = 3 hours 57 mins 57s
= 3.97 h （cor.ti 3 sig fig.）
Answer: 237.95 minutes and 3.97 hours
Step-by-step explanation:
If you have 14,277 seconds and need to convert them into minutes, you can set up the equation 1(minute)/60(seconds) x 14,277(seconds), which equals 237. 95 minutes. To convert into hours, you just take the minutes and set up the equation 1(hour)/60(minutes) x 237.95, which equals approximately 3.966 hours. I assume your asking to convert to seconds was an accident because you started with seconds to begin with.
Determine the volume.
6 units
10 units
8 units
5
Answer:
Step-by-step explanation:
11.7
The Battery Park Stable feeds and houses horses used to pull tourist-filled carriages through the streets of Charleston’s historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to keep the overall daily cost of feed to a minimum. The feed mixes available for the horses’ diet are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a certain amount of five ingredients (labeled as A, B, C, D, and E) needed daily to keep the average horse healthy. The table below shows these minimum requirements, units of each ingredient per pound of feed mix, and costs for the three mixes. In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that 6 pounds of feed per day are the most that any horse needs to function properly.
a) (4 pts) Is this a maximization or a minimization problem? What is the objective?
b) (8 pts) Formulate this problem mathematically. Use X1, X2, and X3 to represent the amount of
oat product, enriched grain, and mineral product, respectively. Write down or type the objective
function and all constraints clearly. (Don’t forget the nonnegativity constraints when applicable.)
c) (8 pts) Set up this problem in Excel and use Solver to find the optimal daily mix of the three
feeds, i.e., the optimal value for X1, X2, and X3.
Answer:
Step-by-step explanation:
a) This is a minimization problem. The objective is to minimize the daily cost of feed for the horses while meeting their minimum nutritional requirements.
b) Let X1, X2, and X3 represent the number of pounds of oat product, enriched grain, and mineral product, respectively, that the stable owner should feed to the horses daily.
The objective function is:
Minimize 0.8X1 + 0.9X2 + 1.1X3
The constraints are:
Ingredient A: 0.15X1 + 0.20X2 + 0.25X3 >= 2.5
Ingredient B: 0.10X1 + 0.15X2 + 0.05X3 >= 2.0
Ingredient C: 0.05X1 + 0.05X2 + 0.10X3 >= 1.0
Ingredient D: 0.02X1 + 0.04X2 + 0.03X3 >= 0.3
Ingredient E: 0.08X1 + 0.07X2 + 0.06X3 >= 1.4
Non-negativity: X1 >= 0, X2 >= 0, X3 >= 0
c) To set up this problem in Excel, we can create a spreadsheet with the following columns: "Feed Mix," "Ingredient A," "Ingredient B," "Ingredient C," "Ingredient D," "Ingredient E," "Cost per Pound," and "Amount to Feed."
We can then enter the data from the table provided in the problem, and add formulas to calculate the total amount of each ingredient in each feed mix and the total cost of each feed mix based on the amount fed.
Next, we can use Solver to find the optimal mix of feed for the horses. We will set the objective to minimize the total cost of feed, subject to the constraints listed above. Solver should be able to find the optimal values of X1, X2, and X3 that meet the nutritional requirements and minimize the cost of feed.
Identify the horizontal shift (h) and the vertical shift (k). Then find the amplitude (|a|), if applicable, the frequency (b), and the period (P). y=tan x, y=cot x
Answer:
For y = tan(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.
For y = cot(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.
you pick a card at random; 456. What is P (greater than 4 or less than 5) write your answer as a percentage
The probability that a card greater than 4 or less than 5 is 1 or 100%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability of picking a card greater than 4 i.e 5 or 6 = 2/3
The probability of picking a card less than 5 i.e
4 = 1/3
Therefore the probability of picking of a card greater than 4 or less than 5 = 2/3 + 1/3 = 3/3
= 1
the total probably is given by 1.
therefore in percentage , it will be 1/1 × 100 = 100%
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11. Arrange the following number in order of magnitude starting from the smallest: ⅔, ¾, ⁵/⁷, ⅖ [A] ⅔, ¾, ⅖, ⁵/7 [B]⅖, ¾, ⅔, ⁵/7 [C]⁵/7, ⅖, ¾, ⅔ [D]⅖, ⅔, ⁵/7, ¾
The numbers arranged in the ascending order is A = 2/5 , 2/3 , 5/7 , 3/4
Given data ,
Let the numbers be represented as A
Now , the value of A is
A = { 2/3 , 3/4 , 5/7 , 2/5 }
On simplifying , we get
The value of 2/3 = 0.67
The value of 3/4 = 0.75
The value of 5/7 = 0.71
The value of 2/5 = 0.4
And , 0.4 < 0.67 < 0.71 < 0.75
Hence , the ascending order is 2/5 , 2/3 , 5/7 , 3/4
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Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
- The cost of the gummy worms is proportional to the amount, in pounds, of gummy -worms purchased.
- This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
What is the constant of proportionality?
A. $8.30
B. $8.40
C. $14.70
D. $4.73
Answer:
B
Step-by-step explanation:
If you take any set of the values and divide the cost (y) by the gummy worms (x) you get 8.4
Trevor bought an antique desk. The net value of the desk is equal to the resale value of the desk minus what Trevor paid to buy it. Exponential function f, shown in the table, represents the net value of the antique desk, rounded to the nearest whole dollar, x years after Trevor purchased it.
x 0 1 2 3 4 5
f(x) -37 -26 -13 0 15 32
The exponential function that represents the net value of the antique desk is: f(x) = -37 × [tex]0.7027^{x}[/tex]
Define Exponential function?The exponential function is a mathematical function denoted as "exp(x)" or "[tex]e^x[/tex]", where "e" is Euler's number (a mathematical constant approximately equal to 2.71828) and "x" is the input variable. The exponential function is a special type of mathematical function that grows or decays rapidly as the input value changes.
What is known by the term net value?"Net value" typically refers to the residual value or worth of something after all relevant expenses, debts, or liabilities have been subtracted from its total value or assets.
The table provides values of f(x) for x = 0, 1, 2, 3, 4, and 5. The corresponding values of f(x) are -37, -26, -13, 0, 15, and 32, respectively.
Using the given data, we can create the following exponential function in the form f(x) = a × [tex]b^{x}[/tex], where a and b are constants to be determined:
f(0) = a ×[tex]b^{0}[/tex] = -37
f(1) = a × b¹= -26
f(2) = a × b² = -13
f(3) = a × b³ = 0
f(4) = a × b⁴ = 15
f(5) = a × b⁵ = 32
To find the values of a and b, we can use a system of equations. We can divide the equations f(1) = a × b¹ = -26 by f(0) = a ×b⁰ = -37 to eliminate a:
(-26) / (-37) = b¹ / b⁰
0.7027 ≈ b
Substituting the value of b back into any of the equations, we can solve for a. Using f(0) = a ×b⁰ = -37:
-37 = a × 1
a = -37
So, the exponential function that represents the net value of the antique desk is:
f(x) = -37 × [tex]0.7027^{x}[/tex]
The values are rounded to the nearest whole dollar.
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Answer:
During the first three years Trevor owned the desk, the resale value was less than the cost. Then it exceeded the cost after year 3.
Step-by-step explanation:
See attachment
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 110 engines and the mean pressure was 4.6 pounds/square inch. Assume the standard deviation is known to be 0.8. A level of significance of 0.01 will be used. Determine the decision rule. Enter the decision rule.
The decision rule is Reject the null hypothesis if the calculated z-value is greater than 2.33.
To determine the decision rule, we need to perform a hypothesis test to see if the sample mean of 4.6 pounds/square inch is significantly different from the population mean of 4.4 pounds/square inch.
Null hypothesis: The population mean pressure is equal to 4.4 pounds/square inch.
Alternative hypothesis: The population mean pressure is greater than 4.4 pounds/square inch.
We will use a one-tailed z-test with a level of significance of 0.01. Since the standard deviation is known, we can use the z-test formula:
z = (x - μ) / (σ / √n)
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (4.6 - 4.4) / (0.8 / √110) = 2.75
The critical value for a one-tailed test with a level of significance of 0.01 is 2.33 (obtained from a standard normal distribution table). Since our calculated z-value of 2.75 is greater than the critical value of 2.33, we reject the null hypothesis.
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ASAPP RIGHT TOO PLS Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
C
Step-by-step explanation:
The correct equation that represents the relationship between d (the number of dollars Rajindri earns) and t (the amount of time Rajindri works in hours) is: C
The speeds of vehicles traveling on a highway are normally distributed with an unknown population mean and standard deviation. A random sample of 13 vehicles is taken and results in a sample mean of 55 miles per hour and a sample standard deviation of 7 miles per hour. find the margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution
The margin of error is given as 4.22 mph
How to solve for margin of errorMargin of Error = t * (sample standard deviation / √(sample size))
degrees of freedom (df), which is calculated as:
df = n - 1 = 13 - 1 = 12
95% confidence level with 12 degrees of freedom = 2.179.
Margin of Error = t * (s / √n)
Margin of Error = 2.179 * (7 / √13)
Margin of Error ≈ 2.179 * (7 / 3.606)
Margin of Error ≈ 2.179 * 1.939
Margin of Error ≈ 4.22 mph
The margin of error is given as 4.22 mph
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tion K Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be 99% confident that your estimate is in error by no more than three percentage points? Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of adults who gamble online. n= (Round up to the nearest integer.)
a) n = 4148
b) n = 2449
How to solveThe sample size for proportion:
Given that,
E = 2% = 0.02
c = 99% = 0.99
Using the z table,
= 2.576 for 99% confidene level.
Using the z-table, search for 0.9950 probability and see where is 0.9950 cumulative probability nearly and then see the corresponding z value.
Step 2/2
a)
Here p is unknown.
In this case, take p = 0.5
n = 4147.36
= 4148
b Here, p = 18% = 0.18
Now,
n = 2448.601344
= 2449
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Which measure do you think is more typical of the data?
The measure that is more typical of the data is the Median.
When to use median ?In comparison to the mean, utilizing the median is oftentimes a more suitable option when analyzing data sets with significant outliers or extreme values.
As these likely cause an aberrant affect on the mean, it can provide an unreliable measure of central tendency; without being subject to anomalies, the median serves as a more reliable gauge of the typical salary. Here, the Median proves significantly less than the Mean, reaffirming its superiority in cases involving considerable disparities.
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What is the volume of the rectangular prism?
A rectangular prism where the area of the base is 12 square centimeters and the height is 7 centimeters.
84 cm3
84 cm2
19 cm3
19 cm2
84cm³
V= 12 x 7 = 84
volume is always cubed btw
Evaluate lim (x ^ 2 - 1)/(x ^ 3 - 1)
the limit of (x² - 1)/(x³ - 1) as x approaches 1 is equal to 2/3. got answer by try substituting x = 1 directly into the expression
what is limit of equation ?
In calculus, the limit of a function is the value that the function approaches as the input (usually denoted by x) approaches a certain value (usually denoted by a). In other words, it describes the behavior of a function as the input value gets closer and closer to a certain point.
In the given question,
To evaluate the limit of (x² - 1)/(x³ - 1) as x approaches 1, we can try substituting x = 1 directly into the expression:
(1² - 1)/(1³ - 1) = 0/0
We cannot determine the limit using direct substitution because we get an indeterminate form of 0/0.
One way to evaluate this limit is to factor the numerator and denominator and cancel out any common factors. We can factor the numerator using the difference of squares formula:
x² - 1 = (x + 1)(x - 1)
We can factor the denominator using the difference of cubes formula:
x³ - 1 = (x - 1)(x² + x + 1)
Canceling out the common factor of (x - 1) in the numerator and denominator, we get:
(x + 1)/(x² + x + 1)
Now we can substitute x = 1 directly into this expression:
(1 + 1)/(1² + 1 + 1) = 2/3
Therefore, the limit of (x² - 1)/(x³ - 1) as x approaches 1 is equal to 2/3.
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Every attendant at a town's Chili Cook-off received a raffle ticket. There were 9 raffle prizes,
including 7 that were gift certificates to restaurants.
If 6 prizes were randomly raffled away in the first hour of the cook-off, what is the probability
that all of them are gift certificates to restaurants?
the probability that all 6 prizes are gift certificates to restaurants is: 0.083.
What is the probability that all of them are gift certificates to restaurants?There are a total of 9 prizes, out of which 7 are gift certificates to restaurants. If 6 prizes are randomly raffled away in the first hour, there are a total of 9 choose 6 possible outcomes, or 84 possible sets of 6 prizes.
The number of outcomes in which all 6 prizes are gift certificates to restaurants is 7 choose 6, or 7 possible sets of 6 gift certificates.
Therefore, the probability that all 6 prizes are gift certificates to restaurants is:
7/84 = 0.0833 or approximately 8.33%
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Find the surface area of
a right cylinder with a
radius of 2.5 feet and a
height of 7.5 feet.
Round your answer to
the nearest hundredth.
The surface area is about
feet.
長
square
The surface area is about 157.08 square feet. use formula for the surface area of a right cylinder to get answer .
what is surface area ?
Surface area is the measure of the total area that the surface of a three-dimensional object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units
In the given question,
The formula for the surface area of a right cylinder is:
S = 2πr² + 2πrh
where r is the radius of the cylinder, h is its height, and π is a mathematical constant approximately equal to 3.14159.
Substituting the given values, we get:
S = 2π(2.5)² + 2π(2.5)(7.5)
S ≈ 2π(6.25) + 2π(18.75)
S ≈ 39.27 + 117.81
S ≈ 157.08
Rounding this to the nearest hundredth, we get:
The surface area is about 157.08 square feet.
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Find the exact values of x and y.
The exact values of x and y in the triangles are calculated and listed below
Finding the exact values of x and yFigure 7
Here, we have
y = √(6² + 1²) --- pythagorean theorem
This gives
y = √37
And, we have
x = √(10² - 6²) --- pythagorean theorem
x = 8
Figure 8
Here, we have
x = 1/2 * 10 --- midsegment of equilateral triangle
This gives
x = 5
And, we have
y = √(10² - 5²) --- pythagorean theorem
y = 5√5
Figure 10
Here, we have
2x = √(6² + 8²) --- pythagorean theorem
2x = 10
x = 5
So, we have
x = y = 5
Figure 11
Here, we have
y = 5
And we have
x = √(13² - 5²) --- pythagorean theorem
x = 12
Figure 13
By similar triangles, we have
x/5 = (x + y)/10
This gives
x = y
So, we have
x = y = 3
Figure 14
By similar triangles, we have
x = 6/3 * 4
x = 8
And then, we have
y = √(6² + 8²) --- pythagorean theorem
y = 10
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