Answers
Answer:
\(f^{-1}\) (59) = 20
Step-by-step explanation:
\(f^{-1}\) (x) is the inverse of f(x)
to find the inverse function, let f(x) = y and rearrange to make x the subject.
y = 3x - 1 ( add 1 to both sides )
y + 1 = 3x ( divide both sides by 3 )
\(\frac{y+1}{3}\) = x
change y back into terms of x with x = \(f^{-1}\) (x) , then
\(f^{-1}\) (x) = \(\frac{x+1}{3}\) , then
\(f^{-1}\) (59) = \(\frac{59+1}{3}\) = \(\frac{60}{3}\) = 20
y = 3x-1
——
x = 3y - 1
y = (x+1)/3
f^-1(x) = (x+1)/3
____
f^-1(59) = (59+1)/3 = 60/3 = 20
Related Questions
Use the bar graph to find the experimental probability of the event.
The experimental probability of spinning a 1 or a 3 is
.
Answers
Answer
17/50, which is 34%.
Step-by-step explanation:
1. Add together all the numbers. They add up to 50.
2. Add together the times 1 and 3 were spun. This adds up to 17.
3. Divide 17 by 50 to get the probability.
4. 17/50 equals .34, or 34%. The probability is 34 percent.
Hope this helps!
The probability helps us to know the chances of an event occurring. The probability of the spinner landing on 1 or 3 is 0.34.
What is Probability?The probability helps us to know the chances of an event occurring.
\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)
The total number of outcomes is 50(8+6+9+11+9+7). And the outcomes that land on 1 or 3 are 17(8+9).
Therefore, the probability of the spinner landing on 1 or 3 can be written as,
\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\\\Probability=\dfrac{\text{Number of outcome that lands on 1 or 3}}{\text{Number of total outcomes}}\\\\\\\Probability = \dfrac{17}{50} = 0.34=34\%\)
Hence, the probability of the spinner landing on 1 or 3 is 0.34.
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which statement about qualitative analysis is true? group of answer choices qualitative analysis is typically undertaken after all the data have been gathered there are no universally adopted rules for analyzing qualitative data qualitative results can be summarized in tables qualitative analysis is less time-consuming than quantitative analysis
Answers
The statement that is true about qualitative analysis is: there are no universally adopted rules for analyzing qualitative data.
Qualitative analysis is a research method that involves analyzing non-numerical data, such as text, images, or audio, to identify patterns and themes. One key characteristic of qualitative analysis is that it is often undertaken concurrently with data collection, rather than after all the data has been gathered. This allows researchers to adjust their approach and ask follow-up questions based on emerging findings. Unlike quantitative analysis, there are no universally adopted rules for analyzing qualitative data, and methods may vary depending on the researcher's perspective and goals.
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answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
Answers
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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Suppose y varies inversely with x, and y = 49 when x = 17
. What is the value of x when y = 7 ?
Answers
Answer:
119 is the value of x when y = 7
Step-by-step explanation:
Since y varies inversely with x, we can use the following equation to model this:
y = k/x, where
k is the constant of proportionality.Step 1: Find k by plugging in values:
Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality. We can find k by plugging in 49 for y and 17 for x:
Plugging in the values in the inverse variation equation gives us:
49 = k/17
Solve for k by multiplying both sides by 17:
(49 = k / 17) * 17
833 = k
Thus, the constant of proportionality (k) is 833.
Step 2: Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:
Plugging in the values in the inverse variation gives us:
7 = 833/x
Multiplying both sides by x gives us:
(7 = 833/x) * x
7x = 833
Dividing both sides by 7 gives us:
(7x = 833) / 7
x = 119
Thus, 119 is the value of x when y = 7.
Please help, I am very confused!!!!!
Answers
Answer:
6 times 7 times 8
Step-by-step explanation:
I need an asnwer Tutor and the answer to this question
Answers
Answer:
\( \dfrac{1}{a^6} \)
Step-by-step explanation:
\( a^{-6}x^0 = \)
\( = \dfrac{1}{a^6} \times 1 \)
\( = \dfrac{1}{a^6} \)
Question 6
Which set of data has the weakest linear association?
10
10
8
8
6
6
2
0
3
5
10
10
8
8
6
6
4
2
2
0
un
N
3
Answers
Answer:
the first set is the weakest
Randois samples of four different models of cars were selected and the gas mileage of each car was meased. The results are shown below Z (F/PALE ma II # 21 226 22 725 21 Test the claim that the four d
Answers
In the given problem, random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below:21 226 22 725 21
Given that,The null hypothesis H0: All the population means are equal. The alternative hypothesis H1: At least one population mean is different from the others .
To find the hypothesis test, we will use the one-way ANOVA test. We calculate the grand mean (X-bar) and the sum of squares between and within to obtain the F-test statistic. Let's find out the sample size (n), the total number of samples (N), the degree of freedom within (dfw), and the degree of freedom between (dfb).
Sample size (n) = 4 Number of samples (N) = n × 4 = 16 Degree of freedom between (dfb) = n - 1 = 4 - 1 = 3 Degree of freedom within (dfw) = N - n = 16 - 4 = 12 Total sum of squares (SST) = ∑(X - X-bar)2
From the given data, we have X-bar = (21 + 22 + 26 + 25) / 4 = 23.5
So, SST = (21 - 23.5)2 + (22 - 23.5)2 + (26 - 23.5)2 + (25 - 23.5)2 = 31.5 + 2.5 + 4.5 + 1.5 = 40.0The sum of squares between (SSB) is calculated as:SSB = n ∑(X-bar - X)2
For the given data,SSB = 4[(23.5 - 21)2 + (23.5 - 22)2 + (23.5 - 26)2 + (23.5 - 25)2] = 4[5.25 + 2.25 + 7.25 + 3.25] = 72.0 The sum of squares within (SSW) is calculated as:SSW = SST - SSB = 40.0 - 72.0 = -32.0
The mean square between (MSB) and mean square within (MSW) are calculated as:MSB = SSB / dfb = 72 / 3 = 24.0MSW = SSW / dfw = -32 / 12 = -2.6667
The F-statistic is then calculated as:F = MSB / MSW = 24 / (-2.6667) = -9.0
Since we are testing whether at least one population mean is different, we will use the F-test statistic to test the null hypothesis. If the p-value is less than the significance level, we will reject the null hypothesis. However, the calculated F-statistic is negative, and we only consider the positive F-values. Therefore, we take the absolute value of the F-statistic as:F = |-9.0| = 9.0The p-value corresponding to the F-statistic is less than 0.01. Since it is less than the significance level (α = 0.05), we reject the null hypothesis. Therefore, we can conclude that at least one of the population means is different from the others.
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Write the equation of an ellipse with vertices (-5,1) and (-1,1) and co-vertices (-3,2) and (-3,0)
Please explain.
Answers
Check the picture below.
\(\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-3\\ k=1\\ a=2\\ b=1 \end{cases}\implies \cfrac{(x- (-3))^2}{ 2^2}+\cfrac{(y-1)^2}{ 1^2}=1\implies \cfrac{(x+3)^2}{ 4}+\cfrac{(y-1)^2}{ 1}=1\)
Answer: To find the equation of the ellipse, we need to use the standard form equation of an ellipse:
$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$
where (h,k) is the center of the ellipse, a is the distance from the center to the vertices (the major axis), and b is the distance from the center to the co-vertices (the minor axis).
First, let's find the center of the ellipse. The center of the ellipse is the midpoint of the line segment joining the vertices (-5,1) and (-1,1). Using the midpoint formula, we get:
$(h,k) = \left(\frac{-5+(-1)}{2}, 1\right) = (-3,1)$
Now, we need to find the values of a and b. Since the distance between the vertices is 2a, we have:
$2a = |-5-(-1)| = 4$
So, $a = 2$.
Similarly, the distance between the co-vertices is 2b, we have:
$2b = |2-0| = 2$
So, $b = 1$.
Now, we have all the values we need to write the equation of the ellipse:
$\frac{(x+3)^2}{2^2}+\frac{(y-1)^2}{1^2}=1$
Simplifying this equation, we get:
$\frac{(x+3)^2}{4}+(y-1)^2=1$
So, the equation of the ellipse is:
$(x+3)^2/4 + (y-1)^2/1 = 1$
Step-by-step explanation:
the intrest of 15000for 4 years is 8100. what is the rate percent per annum
Answers
Answer:
Step-by-step explanation:
this is an exemple
For instance, a 5% per annum interest rate on a loan worth $10,000 would cost $500. A per annum interest rate can be applied only to a principal loan amount.
I NEED HELP PLEASE! THANKS :)
Answers
Answer:
\(y = 2 \: cos \: (\frac{1}{3} x)\)
option C is the right option.
Explanation:
General expression of a cosine function is:
y=A cos k X
where A is amplitude and 2 pi/k is its period.
In our case,
\( - y = 2 \: cos \: (\frac{1}{3} x) \:\)
has :
\(amplitude = 2 \\ period = 2\pi \times 3 = 6\pi\)
hence, the right answer is of option C
hope this helps...
Good luck on your assignment..
. An object accelerates 3.2 m/s2 when a force of 6.7 Newtons is applied to it. What is the mass of the object?
Answers
Answer:
2.09 kg
Step-by-step explanation:
f=ma
6.7=m×3.2
m=2.09 kg
f(x) = 10x - 7 what is f (0)
Answers
f(0)=10(0)-7
f(0)=(0)-7
f(0)=-7
"Participants are instructed to walk" an additional 0.5 miles, 1 mile or 1.5 miles every day, whereas others were told to go about their normal daily routine with no additional exercise. In this study, what is the dependent variable?
Answers
The dependent variable in the study where participants were instructed to walk an additional 0.5 miles, 1 mile, or 1.5 miles every day, whereas others were told to go about their normal daily routine with no additional exercise is the change in physical fitness level. However, let's first understand:
what a dependent variable is?
Dependent variable: A dependent variable (DV) is a variable in an experiment or study whose variation or outcome is the effect being studied or measured by the researchers. It is what changes as a result of the variation in the independent variable. The researchers compare the results obtained from the dependent variable across the different groups or conditions to draw conclusions about the effect of the independent variable.
In this study, participants were either instructed to walk an additional 0.5 miles, 1 mile, or 1.5 miles every day or go about their normal daily routine with no additional exercise. The physical fitness level is the dependent variable in the study as it is what changes as a result of the variation in the independent variable, which is the walking instruction given to the participants.
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Blake was a little concerned as he stood in the middle of the overcrowded elevator. The sign clearly stated that the total weight in the elevator must be less than 1,800 pounds.
Write an inequality to show the weight limit for the elevator.
w > 1,800
w < 1,800
w ≤ 1,800
w ≥ 1,800
Answers
Answer:
w<1,800
Explanation: W stands for weight. So the weight must be under 1,800 pounds. And B clearly shows the answer because the smaller side is facing how much weight you have on the elevator and the smaller side of math symbol means how much weight you have on the elevator is less than 1,800 pounds.
Hope that helps! :)
Answer: Probably W > 1,800
( ">" has a line under it)
please help, this is the last day to turn in everything!
Answers
Answer:
B
Step-by-step explanation:
There are many ways to solve this, but the easiest is by noting the first and last points on the plot. These represent the minimum and maximum of the data set, respectively. This means the lowest point is 2, and the highest is 13. So, to find the correct set, just find the corresponding points. In this case, the only set that fits is the second one.
Answer:
:D
Step-by-step explanation:
A little boy mass 10kg is placed at a height of 2cm above the ground,what is the potential energy of the boy with reference to the ground if g=10m stroch 5/2
Answers
mgh
10kg • 10m/s^2 • 0.02 =
2 Joules
For field trips, Stewart Middle School has parents chaperone groups of students. They always keep the same ratio of parents to students. There were 15 parents and 75 students on the aquarium field trip. Only 25 students are going on the museum field trip.
How many parents will go on the museum field trip?
parents
Answers
There'll be 5 parents that'll go to the museum
Let the number of parents that will go to the museum be represented by x.
Based on the information given, the equation to use will be:
15/75 = x/25
Cross multiply
75 × x = 15 × 25
75x = 375
Divide both side by 75
75x/75 = 375/75
x = 5
Therefore, there'll be 5 parents that'll go to the museum.
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After a 5-hour flight from Newark, Harry arrived in
Denver at 2:30 pm. If the time in Newark is 2 hours
later than the time in Denver, what was the time in
Newark when Harry began the flight?
E. 10:30 am
F. 11:30 am
G. 12:30 pm
H. 3:30 pm
Answers
We need to know how to solve different time zone problems to solve this problem. The time in Newark when Harry began the flight is 11:30 am, option (F) is the correct answer.
In this question we have two cities Newark and Denver that have a time difference of 2 hours. Newark is 2hrs later than the time in Denver. The flight from Newark to Denver takes 5 hrs. Harry arrived at 2:30 pm, we need to find out at what time the flight left Newark. If we subtract 5 hrs from 2:30 pm we get 9:30 am, so when the flight left Newark it was 9:30 am in Denver, since the time in Newark is 2 hrs later than Denver, so it was 11:30 am in Newark.
Therefore the time when the flight left Newark is 11:30 am, option (F) is the correct answer.
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Which expression (x^22)(x^7)^3 equivalent to X^p
Answers
Answer:
p = 43
Step-by-step explanation:
22. Which measures could be the side lengths of
a right triangle?
А. 7 cm, 21 cm, 25 cm
B. 30 cm, 72 cm, 78 cm
C. 3 cm, 5 cm, 9 cm
D. 7 cm, 25 cm, 26 cm
Please Help me !!!!!!!
Answers
Answer:
b and d I think are both right but if you can only pick one go with B
The measure that could be the side lengths of a right triangle is 30 cm, 72 cm, 78 cm, the correct option is B.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
The right triangle
Now,
We can use this equation to test each option by plugging in the values and checking if they satisfy the equation.
A. 7 cm, 21 cm, 25 cm
7^2 + 21^2 = 25^2
49 + 441 = 625
490 = 625
False
This option does not satisfy the Pythagorean theorem, so it cannot be the side lengths of a right triangle.
B. 30 cm, 72 cm, 78 cm
30^2 + 72^2 = 78^2
900 + 5184 = 6084
6084 = 6084
True
Therefore, by right angle triangle the answer will be 30 cm, 72 cm, 78 cm.
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Explain, with at least 2 complete sentences, how to determine if a graph is a function or not.
Answers
Describe two ways to solve the equation 3(x - 1) = 9 you get a point for each method you describe correctly and a point for giving the correct solution for x.
Answers
3(x-1)=9
3x-3=9
3x=12
x=4
2. Division Property
3(x-1)=9
x-1=3
x=4
3] Question 5 Consider the vector field F(x, y, z) = y cos (xy) i + x cos (xy)j – sin zk. (i) Calculate the curl of the vector field F. State whether F is conservative. (ii) Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve r(t) = n* i + t}j + tcos atk, 15t52. Calculate the scalar line integral of the vector field. F. dr. F.dr.
Answers
Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)
Now we calculate the partial derivatives as follows,
∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...
and,
∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0
Therefore,
∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j
The curl of F is given by:
(cos(xy) - xy sin(xy)) i - sin(z)j.
To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:
r(t) = n* i + t}j + tcos atk, 15t52.
The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t
= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt
= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt
= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt
= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1
= sin(a) sin(n) - (a/2) cos(2a)
The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).
The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).
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Find the equation of the line that
is perpendicular to y = -4x + 3
and contains the point (8, 1).
Answers
Answer:
x-4y=8
Step-by-step explanation:
y=mx+c comparing with given eq
we get slope(m1)=-4
since both are prependicular
m1×m2=-1
-4×m2=-1
m2=1÷4
eq:-y-y1=m2 (x-x1)
y-1=(1÷4)(x-8)
x-4y=4
perpendicular means the y-intercept stays the same (so 3 stays), but the slope would be the opposite reciprocal of the original.
the opposite of -4 is 4. opposite of negative=positive.
the reciprocal of 4 is 1/4
so the new slope is 1/4
since we have a point, you plus everything on the point slope-form.
y-y1=m(x-x1)
(8,1)—> the 8 is x1 and the 1 is y1
the slope is m
so it’ll be
y-1=1/4(x-8)
solve. first distribute the 1/4
y -1=1/4x - 2
add 1 to both sides
y= 1/4x - 1
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Answers
The slope of the equation is -2/3, and the y-intercept is 490.
To change the equation 2x + 3y = 1,470 to slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to solve for y.
Starting with the given equation:
2x + 3y = 1,470
First, let's isolate y by subtracting 2x from both sides of the equation:
3y = -2x + 1,470
Next, divide both sides of the equation by 3 to solve for y:
y = (-2/3)x + 490
Now we have the equation in slope-intercept form, y = (-2/3)x + 490.
From this form, we can identify the slope and y-intercept:
The slope (m) is the coefficient of x, which is -2/3.
The y-intercept (b) is the constant term, which is 490.
Therefore, the slope of the equation is -2/3, and the y-intercept is 490.
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The aspect ratio of a rectangular shape is its length (L) divided by its width (W). It is expressed as L:W or L/W. If the aspect ratio of a chalkboard is 12:7 and the length is 36 in, what is the width of the chalkboard?
Answers
Answer:21
Step-by-step explanation:12 times three is 36 and 7 times 3 is 21
A small cylinder of hellum gas used for filling balloons has a volume of 2.50 L and a pressure of 1920 atm at 25∘C. Part A How many balloons can you fill if each one has a volume of 1.40 L and a pressure of 1.30 atm at 25 ∘C ?
Answers
3,606 balloons can be filled. A small cylinder of hellum gas used for filling balloons has a volume of 2.50 L and a pressure of 1920 atm at 25∘C. 3,606 balloons can be fill if each one has a volume of 1.40 L and a pressure of 1.30 atm at 25 ∘C.
Given data: Volume of helium gas = 2.50 L Pressure of helium gas = 1920 atm
Temperature of helium gas = 25 degree C Volume of each balloon = 1.40 L Pressure of each balloon = 1.30 atm Temperature of each balloon = 25 degree C
First of all, we will calculate the number of moles of helium gas using the ideal gas law
PV = nRT1920 atm × 2.50 L = n × 0.0821 L atm/(mol K) × (25 + 273) Kn = (1920 atm × 2.50 L)/(0.0821 L atm/(mol K) × 298 K)≈ 204.78 mol
Now, we will calculate the number of balloons that can be filled using the ideal gas lawPV = nRT
For one balloon, the volume and pressure are given. We need to find the number of moles of helium gas present in one balloon using the ideal gas law 1.30 atm × 1.40 L = n × 0.0821 L atm/(mol K) × (25 + 273) Kn = (1.30 atm × 1.40 L)/(0.0821 L atm/(mol K) × 298 K)≈ 0.0568 mol
Number of balloons = Number of moles of helium gas present in the cylinder/Number of moles of helium gas present in each balloon= 204.78 mol/0.0568 mol≈ 3,606 balloons
Therefore, 3,606 balloons can be filled.
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An ice cream store has 12 different flavors of ice cream, 5 toppings, and 3 types of cones. How many different combinations can they make?
Answers
Answer:
180
Step-by-step explanation:
There will be 12 flavors for every 5 toppings for every type of cone. Multiplying the numbers together will get us the quick and easy answer.
12 · 5 · 3
= 180
g how many people chosen at random are needed to make the probability greater than 12 that there are at least two people born on the same day of the week?
Answers
At least 7 people chosen at random are needed to make the probability greater than 1/2 (or 50%) that there are at least two people born on the same day of the week.
To find the number of people needed to make the probability greater than 1/2 (which is 50%) that there are at least two people born on the same day of the week, we can use the concept of the birthday paradox.
The probability of two people having the same birthday is calculated as follows:
P(same birthday) = 1 - P(different birthdays)
The probability of two people having different birthdays can be calculated by considering the first person's birthday (1/7 chance of being born on any particular day of the week) and then multiplying it by the probability that the second person has a different birthday (6/7 chance).
Therefore, P(different birthdays) = (1/7) * (6/7) = 6/49.
To calculate the probability of no two people having the same birthday, we can calculate the complement:
P(no same birthday) = 1 - P(same birthday)
Using the complement rule, we can calculate the probability of no two people having the same birthday for different numbers of people chosen at random. We want to find the minimum number of people needed to make this probability less than 1/2.
For 2 people: P(no same birthday) = (6/49) ≈ 0.122
For 3 people: P(no same birthday) = (6/49) * (5/49) ≈ 0.092
For 4 people: P(no same birthday) = (6/49) * (5/49) * (4/49) ≈ 0.071
As the number of people chosen at random increases, the probability of no two people having the same birthday decreases. To find the minimum number of people needed to make the probability greater than 1/2, we continue this calculation until we find a probability less than 1/2:
For 5 people: P(no same birthday) = (6/49) * (5/49) * (4/49) * (3/49) ≈ 0.052
For 6 people: P(no same birthday) = (6/49) * (5/49) * (4/49) * (3/49) * (2/49) ≈ 0.037
For 7 people: P(no same birthday) = (6/49) * (5/49) * (4/49) * (3/49) * (2/49) * (1/49) ≈ 0.026
Therefore, at least 7 people chosen at random are needed to make the probability greater than 1/2 (or 50%) that there are at least two people born on the same day of the week.
In conclusion, at least 7 people chosen at random are needed to make the probability greater than 1/2 (or 50%) that there are at least two people born on the same day of the week.
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