A movie studio surveyed married couples about the types of movies they prefer. In the survey, the husband and wife were each asked if they prefer action, comedy, or drama. The summary of the data the studio got after asking 225 couples
Suppose the movie studio will ask 150 more couples about their movie preference. How many of these 150 couples will have exactly one spouse prefer action movie?
Out of the 150 new couples, we can expect about:
45 * (150/240) = 28.125 couples where the husband prefers action but the wife does not.
30 * (150/240) = 18.75 couples where the wife prefers action but the husband does not.
What is probability?
Probability is a measure of the likelihood of an event occurring.
Based on the given data from the survey of 225 couples, we can construct a contingency table as follows:
Husband Wife Total
Action 45 30 75
Comedy 30 45 75
Drama 45 45 90
Total 120 120 240
From the contingency table, we can see that:
Out of 240 respondents, 75 (45 from husbands and 30 from wives) preferred action movies.
Out of 240 respondents, 60 (30 from husbands and 30 from wives) preferred comedy movies.
Out of 240 respondents, 90 (45 from husbands and 45 from wives) preferred drama movies.
To answer the question of how many of the 150 couples will have exactly one spouse who prefers action movie, we can use the information that:
Out of 240 respondents, 45 husbands preferred action movies but their wives did not.
Out of 240 respondents, 30 wives preferred action movies but their husbands did not.
Therefore, out of the 150 new couples, we can expect about:
45 * (150/240) = 28.125 couples where the husband prefers action but the wife does not.
30 * (150/240) = 18.75 couples where the wife prefers action but the husband does not.
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Let w = 2xy + y2 - 4x2, += st, y=,= Compute Bu (1.-3) - 88 -(1, -3)
To compute Bu(1.-3) - 88 - (1, -3), we need to substitute the values of u and v into the expression for w.
First, we need to find the values of u and v. Since u = 1.-3 and v = (1, -3), we have:
u = 1.-3 = 1 - 0.3 = 0.7
v = (1, -3)
Next, we can substitute these values into the expression for w:
w = 2xy + y^2 - 4x^2
= 2(1)(-3) + (-3)^2 - 4(1)^2 (substituting x = 1 and y = -3)
= -6 + 9 - 4
= -1
Finally, we can compute Bu(1.-3) - 88 - (1, -3) by multiplying the gradient of w by the vector (1, -3) and subtracting 88:
Bu(1.-3) - 88 - (1, -3) = (-8x + 2y, 2x + 2y) (1, -3) - 88
= (-8(1) + 2(-3), 2(1) + 2(-3)) (1, -3) - 88
= (-14, -4) (1, -3) - 88
= (-14)(1) + (-4)(-3) - 88
= -14 + 12 - 88
= -90
Therefore, Bu(1.-3) - 88 - (1, -3) = -90.
Since the question seems to have some typos or missing information, I'll assume you want to find the partial derivatives of w with respect to x and y, and evaluate them at the point (1, -3).
Given w = 2xy + y² - 4x², let's compute the partial derivatives:
∂w/∂x = 2y - 8x
∂w/∂y = 2x + 2y
Now, let's evaluate these partial derivatives at the point (1, -3):
∂w/∂x(1, -3) = 2(-3) - 8(1) = -6 - 8 = -14
∂w/∂y(1, -3) = 2(1) + 2(-3) = 2 - 6 = -4
Thus, the evaluated partial derivatives are ∂w/∂x(1, -3) = -14 and ∂w/∂y(1, -3) = -4.
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Mark makes a pattern that starts with 5 and uses the rule "subtract 1, and then multiply by 3. " Which expression can be used to find the third number in Markâs pattern?
A. 5â1â3â1â3
B. 3(5â1)+3(5â1)
C. 3[3(5)â1]
D. 3[3(5â1)â1]
Choose one correct answer
The expression that can be used to find the third number in Mark's pattern is 3[3(5) - 1]. The correct option is C.
In Mark's pattern, the rule is to subtract 1 from the previous number and then multiply the result by 3.
Starting with 5 as the first number, we can apply this rule step by step to find the subsequent numbers.
First step: Subtract 1 from 5, giving us 4.
Second step: Multiply 4 by 3, which equals 12.
So, the second number in Mark's pattern is 12.
Now, to find the third number, we apply the same rule.
First step: Subtract 1 from 12, giving us 11.
Second step: Multiply 11 by 3, which equals 33.
Therefore, the third number in Mark's pattern is 33.
Option C, 3[3(5) - 1], correctly represents this calculation, where 5 is subtracted by 1, multiplied by 3, and then multiplied by 3 again.
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can someone pls help with this
A linear function would be the best fit for the data.
A function that would be the best for this data is: D. y = -4/25(x) + 10
The amount of snow that would be on the ground when the temperature reaches 55° is 1.2 inches.
How to determine the line of best fit?In this scenario, the temperature would be plotted on the x-axis (x-coordinate) of the scatter plot while the snow (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the temperature and the snow (inches), an equation for the line of best fit is given by:
y = -0.16x + 10
y = -4/25(x) + 10
When x = 55, the amount of snow is given by;
y = -4/25(55) + 10
y = 1.2 inches.
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A triangle has sides of length 12, 17, and 22. of the measures of the three interior angles, which is the greatest of the three
The greatest of the three interior angles in the triangle is approximately 71.2 degrees.
To find out which of the three interior angles in the triangle is the greatest, we can use the fact that the largest angle is opposite the longest side. So, in this case, the longest side is 22, which means that the angle opposite it must be the greatest. We can use the Law of Cosines to find the measure of this angle:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides. Plugging in the values we know, we get:
22^2 = 12^2 + 17^2 - 2*12*17*cos(C)
484 = 144 + 289 - 408*cos(C)
51 = 408*cos(C)
cos(C) = 51/408
C = cos^-1(51/408)
C ≈ 71.2 degrees
So the greatest of the three interior angles in the triangle is approximately 71.2 degrees.
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Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
For the g(x) functions provided, here are their key features:
g(x) = (x + 2)(x − 1)(x − 2)
End behavior: As x approaches negative or positive infinity, g(x) approaches positive infinity.
Y-intercept: g(0) = -4
Zeros: x = -2, 1, 2
How to explain the functionRay and Kelsey could both be accurate, all depending on the stated third-degree polynomial function.
It is conceivable for a third-degree polynomial to present up to three zeros, thus corroborating Kelsey's point that the function can have up to three intersection points with the x-axis maximum. Moreover, it can even occur that this function possesses a repeatable zero, causing a fourth interception.
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Which list correctwhich list correctly identifies the steps to solving a word problem?ly identifies the steps to solving a word problem?
There is no one definitive list of steps to solving a word problem, as different types of problems may require different approaches.
However, a general set of steps that can be useful in solving many word problems is:
1. Read the problem carefully to understand what it is asking.
2. Identify the relevant information and the unknown quantity you need to find.
3. Translate the problem into an equation or set of equations that relate the given information to the unknown quantity.
4. Solve the equation(s) to find the value of the unknown quantity.
5. Check your answer to make sure it makes sense in the context of the problem.
Additional steps or variations on these steps may be necessary depending on the specific problem, but this general framework can be a useful starting point.
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The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1 an unnumbered number line labeled numbers of dinners out. create a dot plot to represent the data. what can you conclude about the dot plot of the data set? check all that apply. the range of the number line should be 0 to 7 to represent the frequency. four families said they ate out twice the previous week. one family said they ate out 5 times the previous week. the data set is symmetrical. the median best represents the data set.
Answer: B, C, E
Step-by-step explanation: Other dude posted wrong answer.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 660(0. 902)
The function represents exponential decay with a percentage rate of decrease of 9.8%.
The given exponential function y = 660(0.902) represents decay because the base of the exponent is less than one.
This means that the output value of the function will decrease as the input value increases.
To determine the percentage rate of decrease, we need to find the value of the base of the exponent subtracted from one and then multiply it by 100.
The base of the exponent is 0.902, so we subtract it from one to get 0.098.
Multiplying by 100 gives us a percentage rate of decrease of 9.8%.
This means that for every unit increase in the input value, the output value of the function will decrease by approximately 9.8%.
For example, if the input value increases from 1 to 2, the output value will decrease by 9.8%, and if the input value increases from 2 to 3, the output value will again decrease by 9.8%.
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Catering company provides packages for weddings and for showers. The cost per person for small groups is
pproximately Normally distributed for both weddings and showers. The mean cost for weddings is $82. 30 with a
andard deviation of $18. 20, while the mean cost for showers is $65 with a standard deviation of $17. 73. If 9
eddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than
e mean cost of the showers?
The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers is approximately 0.0207 or 2.07%.
The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers can be found using the Z-score and the difference between the means of two normally distributed variables.
1: Calculate the difference in means and standard deviations.
Δμ = μ_weddings - μ_showers = $82.30 - $65 = $17.30
Δσ = sqrt((σ_weddings²/n_weddings) + (σ_showers²/n_showers)) = sqrt((18.20²/9) + (17.73²/6)) = $8.47
2: Calculate the Z-score.
Z = (Δμ - 0) / Δσ = (17.30 - 0) / 8.47 ≈ 2.04
3: Determine the probability using a Z-table.
P(Z > 2.04) ≈ 0.0207
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AREA OF TRAPEZOID PLS ANSWER ASAP
11. The volume of a cuboid with a square base is given 5 by (2x¹ + xy-2y) m². 5 (i) Factorise the expression 2x² + xy-2y². 1 (ii) The cuboid has a height of m. Given that the length of each side of the base can be expressed as (px - qy) m or (qx + py) m, using your answer from part (i), state the value of p and of q. (iii) Hence, express x in terms of y.
the box-and-whisker plot shows the number of pigeons spotted by visitors at the park during the last weekend. the horizontal axis ranges from 0 to 20 in increments of 1. a horizontal line segment, or whisker, begins at 1 and ends on the left vertical side of the rectangle at 8. a vertical line segment passes through the rectangle at 10. the right vertical side of the rectangle is at 11. a second horizontal line segment, or whisker, begins on the right vertical side of the rectangle and ends at 13. what is the range of the data?
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. From the box-and-whisker plot given, the IQR is 12.
The box-and-whisker plot provides us with the following information:
The minimum value is 1 (the left end of the left whisker)The first quartile (Q1) is 8 (the end of the left whisker)The median (Q2) is 10 (the middle of the box)The third quartile (Q3) is 11 (the end of the right whisker)The maximum value is 13 (the right end of the right whisker)Therefore, the range of the data is the difference between the maximum and minimum values:
Range = maximum value - minimum value = 13 - 1 = 12
So, the range of the data is 12.
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Full Question: The box-and-whisker plot shows the number of pigeons spotted by visitors at the park during the last weekend. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 What is the interquartile range of the data? Provide your answer below:
Image attached
Create a story context for the following expressions ( 5 1/4 - 2 1/8) divided by 4 and 4 x ( 4. 8/0. 8)
To create a story context for the given expressions, which are (5 1/4 - 2 1/8) divided by 4 and 4 x (4.8/0.8).
Imagine there is a fruit store where you have to prepare fruit baskets for a local charity event. The first expression (5 1/4 - 2 1/8) divided by 4 can be a story about the number of apples to be distributed equally among four baskets.
You initially have 5 1/4 dozen apples, but you realize that 2 1/8 dozen of them are not suitable for the baskets.
To find out how many dozens of apples should be put into each basket, you need to subtract the unsuitable apples and divide the result by 4:
(5 1/4 - 2 1/8) / 4
Now, let's move on to the second expression, 4 x (4.8/0.8). This can be a story about the number of oranges you need to purchase for the fruit baskets. You already have 4.8 dozen oranges, but you need to add more to reach the desired ratio of oranges to apples.
Your friend suggests that for every 0.8 dozen oranges you currently have, you should add 4 more dozen oranges. To find out how many dozens of oranges you need to buy, you can use this formula:
4 x (4.8/0.8)
By creating these story contexts, you can use the given expressions to solve real-life problems, such as distributing fruits among charity baskets.
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A project is budgeted for 1,200 hours and will last 6 weeks. a technician will be 25% billable to the project for the first three weeks and then 100% for the final three weeks. if a technician normally works 40 hours per week, how many total hours will the technician bill to the job?
The technician will bill a total of 150 hours to the job. To find the total hours, we need to determine how many hours the technician will work during the first three weeks and the last three weeks, and then add them together.
1. First three weeks:
The technician will be 25% billable during these weeks. They work 40 hours per week, so we need to calculate 25% of 40 hours for each week:
25% of 40 hours = 0.25 * 40 = 10 hours per week
Since there are three weeks, we'll multiply these hours by 3:
10 hours/week * 3 weeks = 30 hours
2. Last three weeks:
The technician will be 100% billable during these weeks. They work 40 hours per week, so they'll bill 40 hours for each of these weeks:
40 hours/week * 3 weeks = 120 hours
3. Finally,
we need to add the hours from the first and last three weeks together to find the total hours the technician will bill to the job:
30 hours (first three weeks) + 120 hours (last three weeks) = 150 hours
The technician will bill a total of 150 hours to the job.
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How can I get the answer for
A=
Vertex for y=
Answer:
1) a = 14
2) -4 (x - 2)² - 5
Step-by-step explanation:
To obtain a vertex, you take h and k in a equation.
So a(x-h)²+k = a(x-2)² -5
For the point (1, - 9),
a[(1)-2]² - 5 = - 9
a(1) = -9+5
a = -4
so the final equation is
-4(x-2)² - 5
I'm not 100% sure about this but I tried. Let me know if it makes sense
Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years, and A is account balance. P r compounded t $ % Daily
The account balance after 2 years is approximately $107.15.
What is the formula calculating account balance A, given the principal P, interest rate r, number of compounding periods per year n, time t in years, and A is account balance when interest is compounded daily?The compound interest formula is given by:
A = P * [tex](1 + r/n)^(^n^*^t^)[/tex]
Where:
P = Principal
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
A = Final account balance
In this problem, we are given:
P = $100
r = 3.5% per year = 0.035 per year
n = 365 (since interest is compounded daily)
t = 2 years
Substituting these values in the formula, we get:
A = [tex]100 * (1 + 0.035/365)^(^3^6^5^*^2^)[/tex]
A ≈ $107.15
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HELPPP JUST 1 QUESTION!!! QUESTION IN PICTURE
Answer:
48.91
Step-by-step explanation:
r=cos^-1(.92)
r=23.07
cos(23.07)=45/y
y=45/cos(23.07)
48.91
6. Quadrilateral ABCD is dilated with center C and a scale factor of 1/2.Draw A'B'C'D'.
Thus, the coordinates of Quadrilateral A'B'C'D' after the dilation with the scale factor of 1/2 are - A'(1.5, 2), B'(0.5, 5), C'(6, 7), D'(4.5, 1.4).
Explain about the dilation:In geometry, a dilation is a transformation that alters an object's size without altering its general shape.
If the dilation factor is greater than 1, the item grows in size. The size shrinks .if the factor is between 0 and 1, and such dilations are occasionally referred to as compressions.Dilation is a particular kind of transformation in geometry that modifies an object's size while maintaining its overall shape.
Given:
scale factor = 1/2
coordinates of Quadrilateral ABCD
A(3,4) , B(1,10) ,C(12,14), D(9,3)
Now, coordinates about the dilation with centre C:, multiply each coordinate with 1/2.
A'(3*1/2,4*1/2) --> A'(1.5, 2)
B'(1*1/2,10*1/2) ---> B'(0.5, 5)
C'(12*1/2,14*1/2), --> C'(6, 7)
D'(9*1/2,3*1/2) ---> D'(4.5, 1.4)
Thus, the coordinates of Quadrilateral A'B'C'D' after the dilation with the scale factor of 1/2 are - A'(1.5, 2), B'(0.5, 5), C'(6, 7), D'(4.5, 1.4).
Graph is attached.
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Evaluate the integral dy (tan-'[y/8)) (64+y?) ( 1 + dy (tan-'(4/8)) (64+y?) =
Answer: ln|y/8| + C
Explanation:
First, we need to recognize that the derivative of arctan(x) is 1/(1+x^2). Therefore, the derivative of arctan(y/8) is 8/(64+y^2).
Now, using the substitution u = y/8, we can rewrite the integral as:
∫(1/u)(64+64u^2)(8/(64+64u^2))du
Simplifying, we get:
∫(1/u)du = ln|u| = ln|y/8|
Therefore, the final answer is:
ln|y/8| + C
where C is the constant of integration.
The stem-and-leaf plot shows the number of push-ups done by each student in a Physical Education class. What is the mode of the number of push-ups?
The mode of the number of push-ups is 40.
What is the mode of the number of push-ups shown in the stem-and-leaf plot for a Physical Education class?A stem-and-leaf plot is a way of organizing data where the stems (the tens digit) and leaves (the ones digit) are separated. Each row represents a stem and the leaves represent the values that belong to that stem.
Here's the stem-and-leaf plot for the number of push-ups:
3 | 5 6 8
4 | 0 0 1 2 2 3 5 6 8 9
5 | 0 1 3 4 5 5 7 8 9
6 | 0 1 2 2 3 4 5 7 8 9
7 | 0 2 5 8
8 | 1 2 4
9 | 0
To find the mode, we look for the value that appears most frequently. In this case, the number 40 appears three times, which is more than any other value. Therefore, the mode of the number of push-ups is 40.
Note that the stem-and-leaf plot makes it easy to see the distribution of the data. For example, we can see that there are a lot of values between 40 and 49, and relatively few values above 60.
We can also see that there are no values between 90 and 99.
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The claim is that for 12 AM body temperatures, the mean is μ>98. 6°F. The sample size is n=8 and the test statistic is t= -2. 687
what is p value?
Value of p is approximately 0.987.
To find the p-value for the given claim that the mean body temperature at 12 AM is μ > 98.6°F with a sample size of n=8 and a test statistic of t=-2.687, follow these steps:
1. Identify the degrees of freedom: Since the sample size is n=8, the degrees of freedom (df) are calculated as n-1, which is 8-1=7.
2. Determine the tail of the test: The claim states that the mean body temperature is greater than 98.6°F (μ > 98.6), which indicates a right-tailed test.
3. Find the p-value using the t-distribution table or a calculator: With a test statistic of t=-2.687 and df=7, you can look up the corresponding p-value using a t-distribution table or an online calculator. Since it's a right-tailed test, the p-value will be the area to the right of the test statistic in the t-distribution.
After completing these steps, the p-value is found to be approximately 0.987.
Therefore, your answer is: The p-value for the claim that the mean body temperature at 12 AM is μ > 98.6°F, given a sample size of n=8 and a test statistic of t=-2.687, is approximately 0.987.
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A movie theater has a seating capacity of 349. The theater charges $5. 00 for children, $7. 00 for students, and $12. 00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2540, How many children, students, and adults attended?
194 children, 58 students, and 97 adults attended the movie.
Let's use algebra to solve this problem.
Let's assume the number of children who attended the movie is C, the number of students is S, and the number of adults is A.
From the problem, we know that:
The seating capacity of the theater is 349:
C + S + A = 349
The theater charges $5 for children, $7 for students, and $12 for adults:
5C + 7S + 12A = $2540
There are half as many adults as there are children:
A = 1/2C
Now we can substitute A = 1/2C from the third equation into the first and second equations:
C + S + 1/2C = 349
3/2C + S = 349
5C + 7S + 12(1/2C) = $2540
5C + 7S + 6C = $2540
11C + 7S = $2540
Now we have two equations with two variables, C and S.
We can solve for S in the first equation:
3/2C + S = 349
S = 349 - 3/2C
Now we can substitute S = 349 - 3/2C into the second equation:
11C + 7S = $2540
11C + 7(349 - 3/2C) = $2540
11C + 2443 - 10.5C = $2540
0.5C = 97
C = 194
Therefore, 194 children attended the movie of total sales.
We can use A = 1/2C from the third equation to find the number of adults:
A = 1/2C
A = 1/2(194)
A = 97
Therefore, 97 adults attended the movie.
We can use C + S + A = 349 to find the number of students:
C + S + A = 349
194 + S + 97 = 349
S = 58
Therefore, 58 students attended the movie.
In summary, 194 children, 58 students, and 97 adults attended the movie.
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The volume of this cube is 19,683 cubic yards. What is the value of s?
The value of s is, 27 yards
:: Volume of cube with side s, is equal to s³
So, as the given volume is 19,683 cubic yards.
Therefore, it can related as,
s³ = 19,683 (yards)³
So,
s = ∛(19,683) yards
s = 27 yards
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Brooke and eileen are working on a math problem together and can't seem to agree on an answer. their teacher drew this number line on the board and asked them to think of a situation that could be represented by it.
brooke suggested the following situation:
christopher wants to buy a new bicycle and needs to earn more than $75 in order to have enough money.
eileen suggested the following situation:
paul is flying home from vacation and has less than 75 minutes left of the flight.
Both situations can be represented by the number line as they both involve values either greater than or less than 75.
The number line the teacher drew can represent both Brooke's and Eileen's situations.
In Brooke's situation, the number line can represent the amount of money Christopher needs to earn to buy a new bicycle. If he needs to earn more than $75, any point on the number line greater than 75 would represent the amount of money he has earned that is sufficient for purchasing the bicycle.
In Eileen's situation, the number line can represent the time left in Paul's flight. If Paul has less than 75 minutes left, any point on the number line less than 75 would represent the time remaining in his flight.
Both situations can be represented by the number line as they both involve values either greater than or less than 75.
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Solve the following quadratic function by utilizing the square root method. Y=xsquared minus nine
The solution of the quadratic equation is y = (x + 3)(x - 3).
What is the solution of the quadratic equation?The solution of the quadratic equation is calculated by applying difference of two squares as shown below;
y = x² - 9
y = x² - 3²
the difference of two square of x² - 3² = (x + 3)(x - 3)
The solution of the quadratic equation is calculated as;
y = (x + 3)(x - 3)
Thus, solution of the quadratic equation has been determined using square root method.
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a) by using Venn-diagram. 75 students in a class like picnic or hiking or both. Out of them 10 like both the activities. The ratio of the number of students who like picnic to those who like hiking is 2 : 3. (i) Represent the above information in a Venn-diagram. (ii) Find the number of students who like picnic. (iii) Find the number of students who like hiking only. (iv) Find the percentage of students who like picnic only.
(i) A Venn-diagram of this information is shown below.
(ii) The number of students who like picnic = 34
(iii) The number of students who like hiking only = 51
(iv) The percentage of students who like picnic only. = 45.33%
Let us assume that A represents the set of students who like picnic.
B represents the set of students who like the hiking.
The total number of students in a class are: n(A U B) = 75
Out of 75 students, 10 like both the activities.
n(A ∩ B) = 10
The ratio of the number of students who like picnic to those who like hiking is 2 : 3
Let number of students like tea n(A) = 2x
and the number of students like coffee n(B) = 3x
n(A U B) = n(A) + n(B) - n(A ∩ B)
75 = 2x + 3x - 10
75 + 10 = 5x
85/5= x
x = 17
The number of students like picnic = 2x
= 2 × 17
= 34
The number of students like hiking = 3x
= 3 × 17
= 51
This informtaion in Venn diagram is shown below.
The percentage of students who like picnic only would be,
(34/75) × 100 = 45.33%
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Determine the distance between the points (−3, −6) and (5, 0).
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - (-3)~~)^2 + (~~0 - (-6)~~)^2} \implies d=\sqrt{(5 +3)^2 + (0 +6)^2} \\\\\\ d=\sqrt{( 8 )^2 + ( 6 )^2} \implies d=\sqrt{ 64 + 36 } \implies d=\sqrt{ 100 }\implies d=10[/tex]
Chris bought 5 tacos and 2 burritos for $13. 25.
Brett bought 3 tacos and 2 burritos for $10. 75.
The price of one taco is $
The price of one burrito is $
If Chris bought 5 tacos and 2 burritos for $13. 25 and Brett bought 3 tacos and 2 burritos for $10. 75, the price of one taco is $1.25, and the price of one burrito is $3.50.
Let the price of one taco be T and the price of one burrito be B. We have the following equations:
5T + 2B = $13.25
3T + 2B = $10.75
To find the prices of the taco and the burrito, we can use the system of equations. First, subtract the second equation from the first equation:
(5T + 2B) - (3T + 2B) = $13.25 - $10.75
2T = $2.50
Now, divide by 2 to find the price of one taco:
T = $1.25
Next, plug the value of T back into one of the equations (let's use the second equation):
3($1.25) + 2B = $10.75
$3.75 + 2B = $10.75
Now, subtract $3.75 from both sides:
2B = $7.00
Finally, divide by 2 to find the price of one burrito:
B = $3.50
So, the price of one taco is $1.25, and the price of one burrito is $3.50.
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What are two algebraic expressions for the square root of x? (what are two ways of writing the square root of x?)
The two algebraic expressions for the square root of x are x^(1/2) and √x.
An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
The square root function involves the square root symbol √ (which is read as "square root of"). The square root of a number 'x' is a number 'y' such that y2 = x. i.e., if y2 = x ⇒ y = √x. i.e., if 'x' is the square of 'y' then 'y' is the square root of 'x'.
There are two common ways to write the square root of x as an algebraic expression. The first way is to use fractional exponent notation, which is x^(1/2). The second way is to use radical notation, which is √x. Both of these expressions represent the square root of x in algebraic form.
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