Answer:
volume=4/3πr³
=4/3×22/7×2.7³
=82.4
82cm³
Hope this will help you.
Subtract: 3.8 - 2.923. Explain in your own words how you would solve this, in detail, from start to finish.
Answer:
Step-by-step explanation:
3.8-2.923
Change to 3.800 to match the number of digits in the second number. Work from right to left. 3 minus 0 is 7. work our way over until the end. You should get 0.877 for an answer.
at a cafeteria, mary orders two pieces of toast and a bagel, which comes out to $\$3.15$. marie orders a bagel and a muffin, which comes out to $\$3.30$. maria orders a piece of toast, two bagels, and three muffins, which comes out to $\$9.15$. how many cents does one bagel cost?
One bagel costs 155 cents.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.
Let x = cost of one bagel
y = cost of one toast
z = cost of one muffin
If two pieces of toast and a bagel costs $3.15, then 2y + x = 3.15.
2y + x = 3.15 ⇒ x = 3.15 - 2y (equation 1)
If a bagel and a muffin costs $3.30, then x + z = 3.30.
x + z = 3.30 (equation 2)
Substitute equation 1 to equation 2.
x + z = 3.30 (equation 2)
3.15 - 2y + z = 3.30 ⇒ z = 0.15 + 2y (equation 3)
If a piece of toast, two bagels, and three muffins costs $9.15, then
y + 2x + 3z = 9.15 (equation 4)
Substitute equations 1 and 3 to equation 4.
y + 2x + 3z = 9.15 (equation 4)
y + 2(3.15 - 2y) + 3(0.15 + 2y) = 9.15
y + 6.30 - 4y + 0.45 + 6y = 9.15
3y = 2.4
y = 0.8
Substitute the value of y to equation 1.
x = 3.15 - 2y (equation 1)
x = 3.15 - 2(0.8)
x = 1.55
Hence, the cost of one bagel is $1.55 or 155 cents.
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a website password must include at least 5 letters and 5 numbers. how many ways can you arrange 5 letters from 26 for your password, if the letters must all be distinct?
You arrange 5 letters in 7893600 ways
How many ways can you arrange 5 lettersFrom the question, we have the following parameters that can be used in our computation:
Letters to use = 5
Total available letters = 26
The letters are distinct
This means that the letters cannot be repeated
So, we have
First = 26, Second = 25 ....... Fifth = 22
Using the above as a guide, we have the following:
Ways = 26 * 25 * 24 * 23 * 22
Evaluate
Ways = 7893600
Hence, the arrangement is 7893600
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Syria has the largest population growth
rate. If Syria has a population of 19.398,448
and a growth rate of 4.3%, what will their
expected population be in a year?
Answer:
834133.264
Step-by-step explanation:
Given that,
The population of Syria is 19.398,448
The growth rate of the population is 4.3%
It means that the population is increasing at the rate of 4.3%. Expected population will be :
\(P=19398448\times \dfrac{4.3}{100}\\\\P=834133.264\)
So, the expected population is 834133.264 .
A+company+packed+8+dark+chocolates+in+a+box+of+32+assorted+chocolates.+which+of+these+does+not+represent+inferential+statistics?+a.)+25%+of+the+chocol
Answer:
it is 3
Step-by-step explanation:
beacuse i did it
. A rectangular tank is 32 cm wide and 45 cm long. It
contains three identical plastic water plants and is
filled with water to a height of 10 cm. When Amy
pulls all three plastic water plants out of the tank,
the height of the water drops to 8 cm. Find the
volume of one plastic water plant.
PLEASE HELP!! WILL GIVE BRAINLIEST
Answer: 960^3 cm or 960 cubic centimeters
Step-by-step explanation:
Cubic because measuring 3 dimensions.
32x45 = area of given face
32x45= 1440
height of water = 10 cm
so,
area of given face x 10 =
32x45x10 or lxwxh (Volume)
so
1440x10= 14,400
1440x8= 11,520
so 14,400 - 11,520 = 2880
V of three plants = 2880
so, 2880/3 = volume of one plant
2880/3=960
V of singe plant = 960 units ^ 3
The difference in volumes represents the total volume of three plants, so answer should be divided by 3.
Hope This Helped!
Answer: one plastic water plant volume = 960 cm³
Step-by-step explanation:
Total volume = Water Volume + 3 plants volume
Total Volume = 32 cm x 45 cm x 10 cm = 14 400 cm³
Water volume = 32 cm x 45 cm x 8 cm = 11 520 cm³
3 Plants volume = 14,400 cm³ - 11,520 cm³ = 2880 cm³
1 Plant volume = 2,880 cm³ : 3 = 960 cm³
If principal=p,rate of interest=R and time=T,then write the formula to find the compound amount
It is given that P = principal, R = rate of interest and T = time
Formula to find compound interest is:
A = P(1 + R/100)^T
where A = amount received after n years
P = principal amount invested
R = rate of interest
T = time for which the amount is invested
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
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The continuous random variable X has a probability density function (pdf) given by f(x) Şi- & for 0 < x < 2 lo otherwise Part(a) Find the median of X, correct to 2 decimal places. 0.59 Part(b) Find P(X >>). Give your answer as a decimal, correct to 2 decimal places. 0.56 Part(c) Two independent observations of X are taken. Find the probability correct to 2 decimal places that one is less than and the other is greater than 2. The order in which we take observations matters. 0.25 Part(d) Find Var(X), correct to 2 decimal places. 0.22 Part(e) Find E(X), correct to 2 decimal places. 0.75 Part(f) Find the value of q such that P(X
The median of X is 1; P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and the value of q such that P(X < q) = 0.95 is 1.9.
(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.
Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.
For 0 < x < 2, the CDF is:
F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x
Setting (1/2) * x = 0.5 and solving for x:
(1/2) * x = 0.5; x = 1
Therefore, the median of X is 1.
(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.
For x > 2, the PDF is 0, so P(X > x) = 0.
Therefore, P(X > 2) = 0.
(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.
P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)
Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.
Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.
(d) The variance of X can be calculated using the formula:
Var(X) = E(X²) - [E(X)]²
To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:
E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3
To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:
E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Now we can calculate the variance:
Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33
Therefore, Var(X) is approximately 0.33.
(e) The expected value of X, E(X), is given by:
E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Therefore, E(X) is 1.
(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:
∫(0 to q) f(x) dx = 0.95
Since the PDF is constant at 1/2 for 0 < x < 2, we have:
(1/2) * (x) | (0 to q) = 0.95
(1/2) * q = 0.95
q = 0.95 * 2 = 1.9
Therefore, the value of q such that P(X < q) = 0.95 is 1.9.
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write the quotient 5/3-i in the form a+bi
The equivalent of the quotient expression 5/3-i is 1.5 + 0.5i
How to rewrite the quotient?From the question, the expression is given as
5/3-i
Rewrite the above expression properly
So, we have
5/(3 - i)
Rationalize the above expression
So, we have the following equation represented as
5/(3 - i) = 5/(3 - i) * (3 + i)/(3 + i)
Evaluate the products in the above equation
So, we have
5/(3 - i) = (15 + 5i)/(9 + 1)
Evaluate the difference and the sum
5/(3 - i) = (15 + 5i)/10
Divide
5/(3 - i) = 15/10 + 5i/10
So, we have
5/(3 - i) = 1.5 + 0.5i
Hence, the equivalent expression is 1.5 + 0.5i
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For a one-tailed dependent samples t-Test, what specific critical value do we need to overcome at the p < .05 level for a study with 30 participants?
1.701
1.699
1.698
1.69
None of the above
The specific critical value for a one-tailed dependent samples t-test at the p < .05 level for a study with 30 participants is :
1.699
To find the specific critical value for a one-tailed dependent samples t-test at the p < .05 level for a study with 30 participants, you will need to refer to the t-distribution table.
1. First, determine the degrees of freedom, which is the number of participants minus 1: df = 30 - 1 = 29.
2. Next, locate the appropriate row for 29 degrees of freedom in the t-distribution table.
3. Look for the value in the one-tailed (0.05) column.
After checking the t-distribution table for 29 degrees of freedom and a one-tailed test with a significance level of p < .05, the critical value is 1.699. Therefore, the answer to your question is 1.699.
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4x - 7y + z - 4 how many terms does the following expression have?
Answer:
4
Step-by-step explanation:
there are three co efficient and three variables
The average age of cars owned by residents of a small city is 6 years with a standard deviation of 2.2 years. A simple random sample of 400 cars is to be selected, and the sample mean age of these cars is to be computed. We know the random variable has approximately a normal distribution because of
Answer:
The random variable \(\bar x\) has approximately a normal distribution because of the central limit theorem.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
\(\mu_{\bar x}=\mu\)
And the standard deviation of the sample means is given by,
\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}\)
Let the random variable X be defined as the age of cars owned by residents of a small city.
It is provided that:
μ = 6 years
σ = 2.2 years
n = 400
As the sample selected is too large, i.e. n = 400 > 30, according to the central limit theorem the sampling distribution of the sample mean (\(\bar x\)) will be approximately normally distributed.
which of the following is described below: there is only one of these in an experiment. they are the cause of some change in the experiment. they are the only thing different between two trials or groups in an experiment.
The description you provided corresponds to an independent variable in an experiment.
How are independent variables used in an experiment?In scientific experiments, researchers manipulate certain factors or conditions to observe their effect on the outcome, which is known as the dependent variable.
The independent variable is the specific factor that is deliberately changed or controlled by the experimenter. It is called "independent" because its value is not influenced by other variables in the experiment.
Thus, the description you provided corresponds to an independent variable in an experiment.
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The Complete Question
which of the following is described below:
independent variable
dependent variable
controlled experiment
uncontrolled experiment
there is only one of these in an experiment. they are the cause of some change in the experiment. they are the only thing different between two trials or groups in an experiment.
What is the answer to
–5(x + 7) = 3x + 29
Answer:
x = -8
Step-by-step explanation:
|-13\ = -(-13)
True False?
Answer:
This statement is true.
Step-by-step explanation:
The absolute value is how far the number is from zero, so how many steps will it take on a number line to get from that particular number to zero?
Since you can't have negative steps, The -13 in absolute value would be 13.
The -(-13) is the same thing as saying -1 ( -13 ). Since negative times a negative is a positive, 13=13 is a true statement.
solve the system using substitution: 4x+3y=23 and x-5y=0
Answer:
4x+3y-23=0
Step-by-step explanation:
4x+3y-23=23-23
4x+3y-23=0
can someone help pls
The radius of the ball, to the nearest hundredth, is approximately 10.63 cm.
To find the radius of the spherical ball, we'll use the formula for the surface area of a sphere, which is given by:
Surface Area = 4πr²
Given that the surface area of the ball is 452 cm², we can set up the equation:
452 = 4πr²
Dividing both sides of the equation by 4π, we get:
113 = r²
Taking the square root of both sides, we find:
r ≈ √113
Evaluating √113 to the nearest hundredth, we have:
r ≈ 10.63 cm
Therefore, the radius of the ball, to the nearest hundredth, is approximately 10.63 cm.
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Find And Sketch The Domain Of The Function. X-Y X + Y G(X, Y) = *7Y У У X X O У У X X
The domain of the function G(x, y) = 7y / (x + y) is all real values of (x, y) except the points where y = -x.
Find and sketch the domain of the function G(x, y) = 7y / (x + y)?The given function is G(x, y) = 7y / (x + y).
To find and sketch the domain of the function, we need to determine the values of x and y for which the function is defined.
Denominator restriction: The denominator (x + y) should not be equal to zero because division by zero is undefined. Thus, we exclude the values of x and y that make the denominator zero. Therefore, x + y ≠ 0.
Range restriction: The numerator (7y) can take any real value, so there are no restrictions on y.
Now, let's examine the denominator restriction further.
If x + y = 0, then y = -x.
This means that any values of x and y that satisfy y = -x will make the denominator zero, resulting in an undefined function.
To summarize, the domain of the function G(x, y) = 7y / (x + y) is all real values of (x, y) except the points where y = -x.
The sketch of the domain can be visualized as a plane excluding the line y = -x, as shown below:
```
|\
| \
| \
| \
----|----\----
| /
| /
| /
| /
|/
```
The shaded region represents the domain of the function, excluding the line y = -x.
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Use the picture below to
# 1) Your realized income is $3,543.22/month.
determine your fixed expenses each month. How much could you save per
month if you take 25% of your discretionary monies and put it in a savings
account?
The amount you could save per month would be 25% of your discretionary money.
How much could you save per month if you take 25% of your discretionary money?Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.
The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses
Amount to be saved = 25% of discretionary money
Amount to be saved = 0.25 * (Realized income - Fixed expenses)
Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.
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The graph shows information about the costs of taxi journeys in France.
For each journey, there is a fixed charge plus a charge for the distance travelled.
a) How much is the fixed charge?
Jean makes two journeys by taxi.
One journey is 6km more than the other journey.
b) Work out the difference between the costs of these two journeys.
The fixed charge is about 5 pound. For extra 6 km, extra cost is about 9 pound
What is a linear equation?A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value of y.
From the graph:
The fixed charge is about 5 pound.
Using the point (0, 5) and (20, 35)
Charge per mile = (35 - 5) / (20 - 0) = 1.5 pound per mile
For extra 6 km, extra cost = 1.5 * 6 km = 9 pound
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In a particular hospital, 6 newborn babies were delivered yesterday. Here are their weights (in ounces).
94, 113, 93, 123, 93, 102
Send data to calculator
Assuming that these weights constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
The standard deviation of the population is approximately 11.8 ounces.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The formula to find the standard deviation is given
σ = √( Σ(x - μ)² / N )
where μ is the mean.
μ = (94 + 113 + 93 + 123 + 93 + 102) / 6 = 100
Next, we can calculate the deviations of each value from the mean:
94 - 100 = -6
113 - 100 = 13
93 - 100 = -7
123 - 100 = 23
93 - 100 = -7
102 - 100 = 2
σ = √( -6)²+( 13)²+( -7)²+( 23)² +( -7)²+( 2)²/ 6 )
=√36+169+49+529+49+4/6
=√836/6=11.8
Hence, the standard deviation of the population is approximately 11.8 ounces.
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Which of the following is a
representation of 11!
if an average adult male has 4 drinks of beverage alcohol in one hour, the alcohol from how many drinks is left in the body after 2 hours?
There would be the alcohol content from 2 drinks remaining in the body after 2 hours.
It is commonly estimated that the body can metabolize about one standard drink per hour.
Multiply the rate of metabolism (1 drink per hour) by the number of hours (2 hours).
1 drink/hour × 2 hours = 2 drinks
Subtract the number of drinks metabolized (2 drinks) from the initial number of drinks consumed (4 drinks).
The alcohol content remaining in the body:
4 drinks - 2 drinks = 2 drinks
Therefore, after 2 hours, there would be the alcohol content from 2 drinks remaining in the body.
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3. (3 pts) Find the general solution of the following homogeneous differential equations. 2xyy' + (x² - y²) = 0
The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)
The given differential equation is: 2xyy' + (x² - y²) = 0
We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.
Put y = vx and y' = v + xv'
Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x
Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x
Substituting these values in the given differential equation:
2x(v)(v + xv') + (x² - v²x²) = 0
2v + 2x²v' + x - v² = 0
2x²v' + 2v/x - v³/x = -1/x
We can write the above differential equation as:
2x²dv/dx + 2v/x = v³/x - 1/x
Separating the variables and integrating both sides:
∫dx/x = ∫[v/(v² - 2)]dv/x
⇒ ln |x| + ln |v² - 2| + C
⇒ ln |x(v² - 2)| = ln |Cx|
⇒ v² - 2 = Cx² (where C is a constant)
⇒ v = ±√(Cx² + 2)
Putting the value of v in y = vx, we get:
y = x√(Cx² + 2) and y = -x√(Cx² + 2)
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The sum of two consecutive multiples of a certain number is 120.Find the number?
If the sum of two consecutive multiples of a given number is 120 then the given number is 20.
Let x be the number we are looking for, then the consecutive multiples of x can be expressed as x and 2x. We are given that the sum of these consecutive multiples is 120, which can be expressed mathematically as:
x + 2x = 120
Simplifying this equation, we get:
3x = 120
Dividing both sides of the equation by 3, we get:
x = 40
Therefore, the number we are looking for is 40. However, we are asked for the consecutive multiples of x, which are x and 2x.
Substituting x = 40 into these expressions, we get:
Consecutive multiples of 40: 40 and 80
However, we are not done yet. The problem asks for two consecutive multiples of the number x that add up to 120. The multiples we found above do not satisfy this condition, as their sum is 120 but they are not consecutive.
Therefore, we need to find the consecutive multiples of 20 that add up to 120. These can be expressed as 20 and 40, which are consecutive multiples of the number 20. We can check that their sum is indeed 120:
20 + 40 = 60
Therefore, the correct answer is that the number we are looking for is 20.
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The graph represents the distribution of the lengths of play times, in minutes, for songs played by a radio station over one hour.
A graph shows the horizontal axis numbered 2.6 to x. The vertical axis is unnumbered. The graph shows an upward trend from 2.8 to 3.4 then a downward trend from 3.4 to 4.
Which statement is true about the songs played during the one-hour interval?
Most of the songs were between 3 minutes and 3.8 minutes long.
Most of the songs were 3.4 minutes long.
Most of the songs were less than 3.2 minutes long.
Most of the songs were more than 3.6 minutes long.
The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.
Based on the given information from the graph, we can determine the following:
The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.
Then, there is a downward trend from 3.4 to 4 on the horizontal axis.
From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.
Therefore, the correct statement is:
Most of the songs were between 3 minutes and 3.8 minutes long.
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Answer:
A
Step-by-step explanation:
suppose f ( x ) = 5 x 2 − 1091 x − 70 . what monomial expression best estimates f ( x ) for very large values of x ?
The highest degree term in the polynomial 5x^2 - 1091x - 70 is 5x^2. As x becomes very large, the other two terms become negligible compared to 5x^2.
To determine the monomial expression that best estimates f(x) for very large values of x, we need to consider the dominant term in the function f(x) = 5x^2 - 1091x - 70.
As x approaches infinity, the highest power term in the function, in this case, 5x^2, becomes the dominant term.
This is because the exponential growth of x^2 will surpass the linear growth of the other terms (1091x and 70) as x becomes increasingly large.
Hence, for very large values of x, we can approximate f(x) by considering only the dominant term, 5x^2. Neglecting the other terms provides a good estimation of the overall behavior of the function.
Therefore, the monomial expression that best estimates f(x) for very large values of x is simply 5x^2. This term captures the exponential growth that dominates the function as x increases without bound.
It is important to note that this estimation becomes more accurate as x gets larger, and other terms become relatively insignificant compared to the dominant term.
Therefore, the monomial expression that best estimates f(x) for very large values of x is 5x^2.
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A set of eight cards were labeled with A, D, D, I, T, I, O, N. What is the sample space for choosing one card?
S = {A, D, D, I, I, N, O, T}
S = {A, D, I, T, O, N}
S = {A, I, O}
S = {D, I}
The correct answer is S = {A, D, D, I, T, I, O, N}.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The sample space is the set of all possible outcomes of an experiment or event.
In this case, the experiment is choosing one card from a set of eight labeled cards.
The sample space for this experiment is the set of all possible cards that can be chosen.
In the given problem, there are eight cards labeled A, D, D, I, T, I, O, N.
The sample space is the set of all possible cards that can be chosen, which is {A, D, D, I, T, I, O, N}.
This is because each card is distinct and can be chosen independently of the others.
Therefore, the correct answer is S = {A, D, D, I, T, I, O, N}.
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Answer: A( A,D, D,I, I,N,O,T)
Step-by-step explanation:
Order does not matter!!
Carrie has 0.74 liters of juice in her pitcher. Sanji's pitcher has 2 times as much juice as Carrie's pitcher. Lee's pitcher has 4 times as much juice as Carrie's pitcher. Sanji and Lee pour all their juice into a large bowl.
How much juice is in the bowl?
Answer:
4.38 liter
Step-by-step explanation:
Find the total area of the solid figure.
3"
3"
3"
6"
(54+\frac(9\sqrt{3}}{2}\)
(46+\frac(9\sqrt{2}]}{2}\)
64+\frac(9\sqrt(3]](21)
(72+\frac{2\sqrt{3}}9}\)
The total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.
To find the total area of the solid figure, we need to determine the areas of each face and then add them together.
The solid figure consists of a rectangular prism with dimensions 3" x 3" x 6" and a pyramid on top with an equilateral triangle base.
First, let's find the area of the rectangular prism. The rectangular prism has two identical square faces with side length 3" and four rectangular faces with dimensions 3" x 6". The total area of the rectangular prism can be calculated as:
Area of the square faces: 2 * (3" * 3") = 2 * 9 square inches
Area of the rectangular faces: 4 * (3" * 6") = 4 * 18 square inches
Total area of the rectangular prism: 2 * 9 + 4 * 18 = 18 + 72 = 90 square inches.
Next, let's find the area of the triangular pyramid. The base of the pyramid is an equilateral triangle with side length 3". The height of the pyramid is 3". The formula to find the area of an equilateral triangle is (sqrt(3) / 4) * (side length)^2. Plugging in the values, we have:
Area of the triangular pyramid: (sqrt(3) / 4) * (3" * 3") * 3" = (sqrt(3) / 4) * 9 * 3 = (sqrt(3) / 4) * 27 = 27sqrt(3) / 4 square inches.
Now, we can find the total area of the solid figure by adding the area of the rectangular prism and the area of the triangular pyramid:
Total area = Area of rectangular prism + Area of triangular pyramid
Total area = 90 square inches + 27sqrt(3) / 4 square inches.
Thus, the total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.
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