There are 6 cute numbers in total which are 14, 19, 49, 55, 79, 85.To find the cute numbers, we need to check all numbers greater than 9 and see if they satisfy the cute condition.
Let's start by analyzing the digits of a number. Suppose the number has two digits, x and y. The cute condition requires:
x + y + xy = 10x + y
Rearranging this equation, we get:
xy - 9x = y - x
xy - x - y = -9x
(x - 1)(y - 1) = 9x - 1
For a number to be cute, the right-hand side of the equation must be divisible by the left-hand side. Since 9x - 1 is odd, the left-hand side must also be odd, which means one of the factors (x - 1) or (y - 1) must be odd and the other even.
We can now check all possible pairs of (x,y) that satisfy this condition. We find that the cute numbers are:
14, 19, 49, 55, 79, 85. Therfore, there are total 6 cute numbers.
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Suppose that an insurance company has 190 policy holders, and pays out $38000 in claims in a given year. The company also spends $1750 for marketing, $6000 for labor, and wants to earn a 20% profit. Given we do not have risk groups, what would a fair price be for annual premiums for the policy holders to pay?
The fair price for annual premiums for the policy holders to pay is $288.42
To determine the fair price for annual premiums, we need to take into account the company's expenses and desired profit. The company's total expenses can be calculated as the sum of the claims paid, marketing expenses, and labor expenses:
Total expenses = Claims paid + Marketing expenses + Labor expenses
Total expenses = $38000 + $1750 + $6000
Total expenses = $45750
To calculate the fair price for annual premiums, we need to add the desired profit to the total expenses and divide by the number of policy holders:
Fair price = (Total expenses + Desired profit) / Number of policy holders
Fair price = ($45750 + 20% of $45750) / 190
Fair price = ($45750 + $9150) / 190
Fair price = $54900 / 190
Fair price = $288.42
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Find the divergence of each of the following vector fields at all points where they are defined. div ( (2x2 - sin(xz)) i + 5j - (sin(xz)) k) = _____
The divergence of the vector field div((2[tex]x^2[/tex]L - sin(xz)) i + 5j - (sin(xz)) k) at all points where it is defined is: div(F) = 4x - z*cos(xz) - x*cos(xz).
To find the divergence of the given vector field, we need to apply the divergence operator to the vector field.
The divergence operator is given by the following formula:
div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
Where F = (Fx, Fy, Fz) is the vector field.
Let's apply this formula to the given vector field:
F = (2[tex]x^2[/tex] - sin(xz)) i + 5j - (sin(xz)) k
div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
= (4x - zcos(xz)) + 0 + (-xcos(xz))
Therefore, the divergence of the given vector field is:
div(F) = 4x - zcos(xz) - xcos(xz)
This expression gives the divergence of the vector field at all points where it is defined.
In this case, the vector field is defined for all values of x, y, and z, so the divergence is defined for all points in space.
It is worth noting that the divergence of a vector field represents the rate at which the vector field flows out of a small volume of space surrounding a point.
If the divergence is positive, the vector field is flowing out of the volume; if it is negative, the vector field is flowing into the volume and if it is zero, the vector field is not flowing into or out of the volume.
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The divergence of the given vector field is div(F) = 4x - z × cos(xz) - x × cos(xz).
To find the divergence of the given vector field div( (2[tex]x^2[/tex] - sin(xz)) i + 5j - (sin(xz)) k), follow these steps:
Identify the components of the vector field:
F(x, y, z) = (2[tex]x^2[/tex]- sin(xz), 5, -sin(xz))
Compute the partial derivatives with respect to each variable:
∂F1/∂x = ∂(2[tex]x^2[/tex] - sin(xz))/∂x
∂F2/∂y = ∂(5)/∂y
∂F3/∂z = ∂(-sin(xz))/∂z
Calculate each partial derivative:
∂F1/∂x = 4x - z × cos(xz)
∂F2/∂y = 0
∂F3/∂z = -x × cos(xz)
Add the partial derivatives to find the divergence:
div(F) = ∂F1/∂x + ∂F2/∂y + ∂F3/∂z
div(F) = (4x - z × cos(xz)) + 0 + (-x × cos(xz))
Simplify the expression:
div(F) = 4x - z × cos(xz) - x × cos(xz)
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Let y=tan(5x+3)
.
Find the differential dy when x= 5 and dx= 0.1.
Find the differential dy when x= 5 and dx= 0.2.
When x = 5 and dx = 0.1, the differential dy is approximately 96.375.
When x = 5 and dx = 0.2, the differential dy is approximately 192.75.
We can use the chain rule to find the differential of y with respect to x. Let u = 5x + 3, then y = tan(u).
Using the chain rule, we have:
dy/dx = dy/du * du/dx
Taking the derivative of y with respect to u, we have:
dy/du = sec^2(u)
Substituting u = 5x + 3, we have:
dy/du = sec^2(5x + 3)
Taking the derivative of u with respect to x, we have:
du/dx = 5
Substituting x = 5 and dx = 0.1, we have:
dy = dy/du * du/dx * dx
= sec^2(5(5) + 3) * 5 * 0.1
= 192.75 * 0.5
= 96.375
Therefore, when x = 5 and dx = 0.1, the differential dy is approximately 96.375.
Substituting x = 5 and dx = 0.2, we have:
dy = dy/du * du/dx * dx
= sec^2(5(5) + 3) * 5 * 0.2
= 192.75 * 1
= 192.75
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The mean absolute deviation of Mr. Zimmerman's class is 0. 46. What does this mean?
A smaller MAD indicates less variability in the data set, while a larger MAD indicates greater variability.
The mean absolute deviation (MAD) is a measure of the variability of a set of data. It measures the average distance between each data point and the mean of the data set.
In this case, the MAD of Mr. Zimmerman's class is 0.46. This means that, on average, each data point in the class is about 0.46 units away from the mean of the data set.
The MAD gives an idea of how spread out the data is from the mean, regardless of whether the data is positively or negatively deviated from the mean.
A smaller MAD indicates less variability in the data set, while a larger MAD indicates greater variability.
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Help Please
Show your work so I can understand to get brainly
The maximum value represents (b) the point where most profits are made
What the maximum value representsGiven that the graph is the graph of a company's profit
The maximum value represents (b) the point where most profits are made
What the x-intercept representsGiven that the graph is the graph of a company's profit
The x-intercept is when the profit = 0
So
The x-intercept represents (b) the price per pen where no profit is made
The approximate average rateThis is calculated as
Rate = [f(6) - f(3)]/[6 - 3]
So, we have
Rate = [0 - 120]/[6 - 3]
Rate = -40
The domain in this contextThe domain of this graph given the situation is (0, 6] because the values do not makes sense beyond those points
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PLS HELP ️️ “The area of the circle is 7 square units.”
“Drag the black point to create a sector with an area of 2 square units.”
In order to create a sector with an area of 2 square units, we need to draw a central angle of approximately 24.4 degrees and a radius of approximately 1.49 units.
How to create the sectorIn order to create a sector with an area of 2 square units, we need to find the radius of the circle and then calculate the central angle that corresponds to an area of 2 square units.
Let's start by using the formula for the area of a circle, which is:
A = πr²
We know that the area of the circle is 7 square units, so we can write:
7 = πr²
Solving for r, we get:
r = √(7/π)
r ≈ 1.49
Now, we can use the formula for the area of a sector, which is:
A = (θ/360)πr²
where θ is the central angle in degrees.
To find the central angle that corresponds to an area of 2 square units, we can write:
2 = (θ/360)π(1.49)²
Solving for θ, we get:
θ ≈ 24.4 degrees
So, to create a sector with an area of 2 square units, we need to draw a central angle of approximately 24.4 degrees and a radius of approximately 1.49 units.
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We have a dataset measuring the average weight of apples in Walmart. We randomly weighed 200 apples among all of them, 120 apples have weight larger than 100 grams. Wal- mart want to perform a null hypothesis that the true proportion of apple weights larger than 100 grams is 0. 5. And the alternative hypothesis is that the proportion is larger than 0. 5. Find the p-value of the hypothesis testing
The p-value for the hypothesis test is approximately 0.000006.
To find the p-value, we follow these steps:
1. State the null hypothesis (H0) and alternative hypothesis (H1):
H0: p = 0.5
H1: p > 0.5
2. Calculate the sample proportion (p-hat): p-hat = 120/200 = 0.6
3. Calculate the test statistic (z) using the formula: z = (p-hat - p) / √((p * (1 - p)) / n)
z = (0.6 - 0.5) / √((0.5 * 0.5) / 200) ≈ 2.683
4. Find the corresponding p-value using a z-table or calculator. The area to the right of the test statistic (2.683) is approximately 0.000006.
Since the p-value (0.000006) is less than the significance level (typically 0.05), we reject the null hypothesis, indicating that the true proportion of apple weights larger than 100 grams is larger than 0.5.
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Based on the percentage of daily of total daily calories and the number of calories needed how many biscuits packages of pemmican and packages of butter and cocoa does one person need each day?
To determine how many biscuit packages, pemmican packages, and butter and cocoa packages are needed per day for one person.
What factors are necessary for daily food requirements?
Calculating an individual's daily Caloric food requirements based on calorie intake and percentage of calories from each food group requires several pieces of information. The first is the total daily calorie requirement, which varies based on factors such as age, gender, height, weight, and physical activity level.
The second is the percentage of daily calories that should come from each food group, which is determined by dietary guidelines and varies based on factors such as age and gender. Finally, the calorie content of each food item must be known to determine how much of each food is needed to meet daily calorie and nutrient requirements.
Once these factors are known, it is possible to calculate how many biscuit packages, pemmican packages, and butter and cocoa packages are needed per day for one person. However, without knowing the specific calorie content and nutritional value of each food item, it is impossible to provide a specific answer.
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In the diagram to the right, GKNM ~ VRPT.
Find the value of x. Give the scale factor of the left polygon to the right polygon.
The value of x is 2.8 The scale factor of left polygon to the right polygon, GKNM to RPTV is 1.4.
Since the two polygons GKNM and RPTV are similar, their corresponding sides are proportional. Thus, we can set up the following proportion
(GK + KN + NM)/GK = (RP + PT + TV + VR)/RP
Plugging in the given values and simplifying, we get
(8.4 + 3x - 2 + 4)/8.4 = (x + 5 + 3 + 3 + 6.3)/(x + 5)
15.4/(3x + 2.4) = (x + 17.3)/(x + 5)
Cross-multiplying and solving for x, we get
x = 2.8
To find the scale factor of GKNM to RPTV, we can divide the corresponding side lengths
(GK + KN + NM)/(RP + PT + TV + VR) = (8.4 + 3(2.8) - 2 + 4)/(2.8 + 5 + 3 + 3 + 6.3) = 1.4
Therefore, the scale factor of GKNM to RPTV is 1.4.
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Fred bought 5 liters of liquid laundry detergent, 3,250 milliliters of fabric softener, and 2. 8 liters of bleach. Select true or false for each statement. Fred bought 45 milliliters more fabric softener than bleach. ?
Fred bought 2. 45 liters more laundry detergent than bleach. ?
Fred bought 450 milliliters more fabric softener than bleach. ?
Fred bought 220 milliliters more laundry detergent than bleach. ?
Fred bought 0. 45 liters more fabric softener than bleach. ?
Fred purchased more 2. 45 liters of laundry detergent than bleach is false statement, Fred took 450 milliliters more fabric softener than bleach is false, Fred placed 220 milliliters more laundry detergent than bleach is true, Fred has taken 0. 45 liters more fabric softener than bleach is false.
Fred in total bought 5 liters of liquid laundry detergent which is equal to 5000 milliliters. Then he bought 3,250 milliliters of fabric softener and 2.8 liters of bleach which is equal to 2800 milliliters.
Fred purchased 45 milliliters more fabric softener than bleach. This statement is false because Fred bought 250 milliliters less fabric softener than bleach.
Fred bought 2.45 liters more laundry detergent than bleach. This statement is false because Fred bought 2.2 liters more laundry detergent than bleach.
Fred has taken 450 milliliters more fabric softener than bleach. This statement is false because Fred bought 250 milliliters less fabric softener than bleach.
Fred on the event of taking 220 milliliters more laundry detergent than bleach is considered a true statement because Fred bought 2200 milliliters more laundry detergent than bleach.
Fred on the event of taking 0.45 liters more fabric softener than bleach is considered a false statement due to the fact that Fred bought 0.25 liters less fabric softener than bleach.
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Directions: Continue the patterns by counting backwards. Write the missing terms in the blanks. Find how many terms will it take to get to zero starting with the first term of the given pattern.
1. 32, 30, 28, 26, ___________________________, 0
2. 75, 70, 65, 60, 55, 50, ____________________, 0
3. 30, 27, 24, 21, ___________________________, 0
4. 81, 72, 63, ______________________________, 0
5. 48, 44, 40, 36, __________________________, 0
The missing terms in the blanks and number of terms are determined below.
How many terms will it take to get to zero starting?
The missing terms in the blanks for the pattern and number of terms can be determined as follows:
1. 32, 30, 28, 26, 32__________________________, 0
The difference is 2. Thus, subtract 2 till you reach 0. That is:
32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0
Number of terms: 16
2. 75, 70, 65, 60, 55, 50, ____________________, 0
The difference is 5. Thus, subtract 5 till you reach 0. That is:
75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0
Number of terms: 15
3. 30, 27, 24, 21, ___________________________, 0
The difference is 3. Thus, subtract 3 till you reach 0. That is:
30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0
Number of terms: 10
4. 81, 72, 63, ______________________________, 0
The difference is 9. Thus, subtract 9 till you reach 0. That is:
81, 72, 63, 54, 45, 36, 27, 18, 9, 0
Number of terms: 9
5. 48, 44, 40, 36, __________________________, 0
The difference is 4. Thus, subtract 4 till you reach 0. That is:
48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0
Number of terms: 12
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I Need help with these please answer someone omg
Step-by-step explanation:
suppose 2 more variable y and z
(- 3 / (2/5)), - 1/2 please someone slove this answer
Answer:
The answer is -8
Step-by-step explanation:
Here's a key
()= Do first
/ = Divide
If something is outside the () and there is no symbol then multiply.
Given the exponential model y= 200(.80)^x, tell whether the model represents exponential growth or decay. What is the growth/decay factor? A. Growth: (0.80) B. Decay: (200) C. Growth: (200) D. Growth: (0.80)
The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases.
what is exponent ?
In mathematics, an exponent (also known as a power or index) is a number that indicates how many times a given number (the base) must be multiplied by itself.
In the given question,
The given exponential model is:
y = 200(0.80)ˣ
where:
y is the output (dependent variable)
x is the input (independent variable)
To determine whether the model represents exponential growth or decay, we need to examine the base of the exponent, which is 0.80 in this case.
If the base is greater than 1, then the model represents exponential growth, and if the base is between 0 and 1, then the model represents exponential decay.
In this case, the base of the exponent is 0.80, which is between 0 and 1. Therefore, the model represents exponential decay.
The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases. The factor represents the rate of decay per unit of the independent variable, which in this case is 0.80.
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The entrance of a tunnel can be modeled
by y =-1/18x^2 +2x-2. Where x and y
are measured in feet. What is the height of the tunnel
If the entrance of the tunnel is modeled by y = -1/18x^2 + 2x - 2 then the height of the tunnel is 16 feet.
The entrance of a tunnel can be modeled by the equation y = -1/18x^2 + 2x - 2, where x and y are measured in feet. To find the height of the tunnel, follow these steps:
1. Determine the vertex of the parabola, which represents the highest point (or the height) of the tunnel.
2. The vertex can be found using the formula: x_vertex = -b / (2a), where a and b are the coefficients in the quadratic equation y = ax^2 + bx + c.
In this case, a = -1/18 and b = 2. So:
x_vertex = -2 / (2 * -1/18) = -2 / (-1/9) = 18
3. Now that we have the x-coordinate of the vertex, we can find the y-coordinate (height) by plugging the x_vertex value into the equation:
y = -1/18(18^2) + 2(18) - 2
4. Calculate the value of y:
y = -1/18(324) + 36 - 2 = -18 + 36 - 2 = 16
So, the height of the tunnel is 16 feet.
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The function f(x) = 2x^3 +30x^2 – 54x +5 has one local minimum and one local maximum. This function has a local minimum at x = with value
and a local maximum at x =
with value
The local maximum is at x = -9 with a value of 2575, and the local minimum is at x = 1 with a value of -17.
To find the local minimum and maximum of the given function, we need to find its critical points, where the derivative is zero or undefined.
[tex]f(x) = 2x^3 + 30x^2 - 54x + 5[/tex]
[tex]f'(x) = 6x^2 + 60x - 54[/tex]
Setting f'(x) = 0, we get:
[tex]6x^2 + 60x - 54 = 0[/tex]
[tex]x^2 + 10x - 9 = 0[/tex]
(x + 9)(x - 1) = 0
x = -9 or x = 1
Now, we need to determine if these critical points correspond to local minimum or maximum.
To do so, we can use the second derivative test. We calculate the second derivative of f(x):
f''(x) = 12x + 60
At x = -9:
f''(-9) = 12(-9) + 60 = -48 < 0
This means that f(x) has a local maximum at x = -9.
At x = 1:
f''(1) = 12(1) + 60 = 72 > 0
This means that f(x) has a local minimum at x = 1.
To find the values of the local minimum and maximum, we plug in the corresponding x-values into the original function:
[tex]f(-9) = 2(-9)^3 + 30(-9)^2 - 54(-9) + 5 = 2575[/tex]
[tex]f(1) = 2(1)^3 + 30(1)^2 - 54(1) + 5 = -17[/tex]
Therefore, the local maximum is at x = -9 with a value of 2575, and the local minimum is at x = 1 with a value of -17.
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find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→5 x2 − 25 x2 − 5x
The limit is equal to 10. We didn't need to use L'Hospital's rule or any other advanced method, as the limit was easily evaluate through simplification and direct substitution.
We can simplify the expression as follows:
[tex]lim x→5 (x + 5) x = lim x→5 (10) = 10[/tex]
Now, we can directly evaluate the limit by substituting 5 for x:
[tex]lim x→5 (x + 5) x = lim x→5 (10) = 10[/tex]
Therefore, the limit is equal to 10. We didn't need to use L'Hospital's rule or any other advanced method, as the limit was easily evaluatable through simplification and direct substitution.
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i need help please
20pts
Answer:
the answer is A
Step-by-step explanation:
√3 = Irrational
√12 = Irrational
but if
√3 × √ 12 = √36 = 6 = rational
What is the answer?
What is the gradient of the blue line?
Step-by-step explanation:
the gradient = the slope = the incline = ...
many different names for the same thing.
however you call it, it is the ratio
y coordinate change / x coordinate change
whet going from one point on the line to another.
for questions like this we should look for points with integer coordinates (going through a vertex of the coordinate grid squares).
I see for example right at the left beginning (0, 1).
the next one is then (4, 2).
when going from (0, 1) to (4, 2) :
x changes by +4 (from 0 to 4).
y changes by +1 (from 1 to 2).
so, the slope or gradient is
+1/+4 = 1/4
Solve this for me. In a office,2/3 of the water bill is paid by yaw,1/5 by kwame and remaining by aba. What fraction is paid by aba
Convert the numeral to a numeral in base ten ABC4 base
16
ABC4 base 16 is equal to 43972 in base ten (decimal).
What is numeral?In order to represent any given number, numerals might be numbers, symbols, figures, or sets of figures.
To convert the number ABC4 base 16 to a numeral in base ten (decimal), we can use the positional notation system. Each digit in the number represents a power of 16, starting from the rightmost digit.
The rightmost digit is 4, which represents 4 x 16⁰ = 4 x 1 = 4.
The next digit is C, which represents 12 (since C is equivalent to the decimal number 12), and it is in the second position from the right. So the value of the second digit is 12 x 16¹ = 12 x 16 = 192.
The next digit is B, which represents 11, and it is in the third position from the right. So the value of the third digit is 11 x 16² = 11 x 256 = 2816.
The leftmost digit is A, which represents 10, and it is in the fourth position from the right. So the value of the fourth digit is 10 x 16³ = 10 x 4096 = 40960.
Now we can add up the values of each digit to get the decimal equivalent of the number:
4 + 192 + 2816 + 40960 = 43972
Therefore, ABC4 base 16 is equal to 43972 in base ten (decimal).
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ashley measured a line to be 3.9 inches long. if the actual length of the line is 4.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error in measuring if the actual length is 4.1 cm and the measured length is 3.9 cm is 4.88%
The error refers to the estimated difference between the measured and actual measurement of an object. Error is mainly of three types systematic errors, random errors, and negligent errors.
Measured length = 3.9
Actual length = 4.1
Error = actual value - measured value
= 4.1 - 3.9
= 0.2
Error percent is the ratio of error to the actual value multiplied by 100
Error percent = [tex]\frac{0.2}{4.1}[/tex] * 100
= 4.88%
Thus, the error percent in the given question comes out to be 4.88%
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Students in a class were surveyed about the number of children in their families. The results of the survey are shown in the table. Two surveys are chosen at random from the group of surveys. After the first survey is chosen, it is returned to the stack and can be chosen a second time. What is the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family?.
The probability that the first survey indicates four children in the family and the second survey indicates one child in the family is 1/50.
We have,
To find the probability of the first survey indicating four children in the family and the second survey indicating one child in the family, we need to consider the number of surveys that fit this condition and divide it by the total number of possible surveys.
According to the table, the number of surveys indicating four children in the family is 8, and the total number of surveys is:
= 9 + 18 + 22 + 8 + 3 = 60.
Since the first survey is returned to the stack and can be chosen again, the probability of the first survey indicating four children in the family is 8/60.
For the second survey, there are 9 surveys indicating one child in the family (as the first survey is returned to the stack and can be chosen again), and the total number of surveys remains 60.
Therefore, the probability of the second survey indicating one child in the family is 9/60.
To find the probability of both events occurring, we multiply the individual probabilities:
Probability = (8/60) x (9/60) = 72/3600 = 1/50
Thus,
The probability that the first survey indicates four children in the family and the second survey indicates one child in the family is 1/50.
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The complete question:
Number of children in family Number of surveys
one 9
tqo 18
three 22
four 8
five or more 3
Help me please I don’t know what to do
Answer:
179.3
Step-by-step explanation:
Rectangle:
L x W
10 x 14 = 140
Semicircle:
(π · r²) / 2
D = 10, r = 10 ÷ 2 = 5
(3.14 · 5²) / 2 = 39.25
Area of figure = 140 + 39.25 = 179.25 = 179.3 (rounding to tenth)
MAGIC SHOW A magician currently sells tickets to his shows for $15 and averages 180 spectators per show. He estimates that he can sell 10 more tickets for each $0.75 decrease in price. a. Let x represent the number of $0.75 price decreases. Write a function P(x) to represent the price of a ticket and a function T(x) to represent the number of tickets sold. b. Write a function R(x) that can be used to find the revenue from ticket sales. c. If the magician decides to sell the tickets for $12, find his revenue. m
On the basis of given data & Using combining-functions, We can say that
a).The function P(x) which represents the price of a ticket can we given by where x represents the number of 0.75 price decreases= ($15 - 0.75x)
b). the function T(x) which represents number of tickets sold on a day
=(180 + 10x)
c). the revenue would be if the magician decides to sell the tickets for
$12 = $ 2640
What are combining-functions?The process of composition, in which the result of one function becomes the input of another, allows us to create complex functions from basic ones. A complicated function may occasionally need to be broken down into two or more simpler ones, using the opposite method.
Given that:
Current price of ticket = $15
Average tickets sold per day = 180
Price decrease each time = $0.75
Number of price decreases = x
Total Price decrease = 0.75x
Increase in number of tickets with price decrease each time = 10
Total increase in number of tickets with x times price decrease = 10x
a). Function to represent total price of tickets
P(x) = current price - total price decrease
= ($15 - 0.75x)
Function to represent number of tickets T(x)
= average number of tickets+ total increase in tickets
= (180 + 10x)
b)Function to represent total revenue R(x) = total tickets x total price
= T(x) . P(x)
= (180 + 10x) ($15 - 0.75x)
c)Given that total price of tickets=$12
P(x)=$12
($15 - 0.75x) = $12
- 0.75x = $12 - $15
- 0.75x = - $3
x = 3 ÷ 0.75
x = 4 times
The number of times price decreased=4
Total tickets sold T(x) =(180 + 10x)
=(180 + 10(4))
=180+40
=220 tickets
Total revenue= T(x) . P(x)
= 220 x 12
=$2640
Total revenue earned on 220 tickets at $12 is $ 2640
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what is the aproximate length of the base triangle ?
The approximate length of the base of the triangle is 5 units
What is area of triangle?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of a triangle is expressed as;
A = 1/2 bh
The hexagon is divided into six equal triangles.
The area of the hexagon is 65 units²
Therefore, the area of the triangle = 65/6
= 10.83
Area of a triangle = 1/2 b h
height = 4.3 units
10.83 = 1/2 × 4.3 × b
4.3b = 10.83 × 2
4.3b = 21.66
divide both side by 4.3
b = 21.66/4.3
b = 5.04
therefore the approximated value of the base is 5 units.
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Mr. Cromleigh noticed that tickets were on sale for an upcoming game and wanted to take his mom. Tickets were 25% off for teachers and originally cost $45. He also had to account for a 5% sales tax. What was the total cost of the 2 tickets?
The 2 tickets cost --------------- dollars. He better ask his mom for a higher allowance!
The total cost of the two tickets is $70.88.
What is discount?A discount is a reduction in the original price of an item or service. It is often used as a marketing strategy to increase sales by making the product more affordable or attractive to consumers. The amount of the discount is typically expressed as a percentage of the original price.
In the given question,
The cost of one ticket after a 25% discount is:
45 * 0.75 = $33.75
The cost of two tickets is:
2 * 33.75 = $67.50
Adding the 5% sales tax:
67.50 * 1.05 = $70.88
Therefore, the total cost of the two tickets is $70.88.
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I’m Can you guys give me the answer please or at least help me find the answer
Answer:
Median: 5.2IQR: 0.8Step-by-step explanation:
You want the median of the Blue box plot and the IQR of the Pink box plot shown in the figure.
Box PlotA box plot has 5 vertical lines. From left to right, they are ...
Minimum of the data set values1st QuartileMedian3rd QuartileMaximum of the data set valuesMedianBased on the above, we can see the median is the middle line inside the box of the box plot.
The median of the blue plot is 5.2.
Interquartile rangeThe "Interquartile range" is the difference between the 3rd quartile and the 1st quartile. That is, it is the difference between the two ends of the box, the length of the box.
The IQR of the pink plot is 6.4 -5.6 = 0.8.
__
Additional comment
This is basically an exercise in understanding the terms associated with a box plot, and reading a graph. The only calculation involved is figuring out the missing graph coordinates and finding the difference of the coordinates at the ends of the pink plot.
A business with two locations buys seven large delivery vans and five small del...
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21 of 21
next >
x
a business with two locations buys different sized delivery
vans (small vans - x and large vans - y).
location a receives five small vans and two large vans for
a total cost of $72,500. location b receives two small
vans and six large vans for a total cost of $107,000.
what is the cost of each type of van?
cost of small vans (x)
cost of large vans (y)
After solving the cost function, the cost of each small van is $8,500 and the cost of each large van is $15,000.
Let's use the variables x and y to represent the cost of a small van and a large van, respectively.
From the information given, we can set up a system of two equations:
5x + 2y = 72500
2x + 6y = 107000
We can solve for x and y by using any method of linear equations, such as substitution or elimination. Here, we'll use elimination:
Multiplying the first equation by 3 and the second equation by -1, we get:
15x + 6y = 217500
-2x - 6y = -107000
Adding these two equations, we eliminate the y variable:
13x = 110500
Dividing both sides by 13, we get:
x = 8500
Now we can use this value to find y:
5x + 2y = 72500
5(8500) + 2y = 72500
42500 + 2y = 72500
2y = 30000
y = 15000
Therefore, the cost of each small van is $8,500 and the cost of each large van is $15,000.
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Use the binomial series to find the MacLaurin polynomial of degree 6 of the furnction g(x) = ³√1+x² . Express the coefficients are fractions in lowest terms. 0.4 Use the polynomial from problem #1 to approximate 0∫⁰.⁴ ³√1+x² dx
Using the Maclaurin polynomial of degree 6, the approximation for the integral ∫³√(1+x²)dx from 0 to 0.4 is ≈ 0.41721.
To find the Maclaurin polynomial of degree 6 for the function g(x) = ³√(1+x²), we will use the binomial series expansion:
(1+x)^(n) = 1 + nx + (n(n-1)x²)/2! + (n(n-1)(n-2)x³)/3! + ...
In our case, n = 1/3, and x = x²:
g(x) = (1+x²)^(1/3) = 1 + (1/3)x² - (1/9)(2/3)x⁴/2! + (1/27)(2/3)(-1/3)x⁶/3! + ...
Now, we can write the Maclaurin polynomial of degree 6:
g(x) ≈ 1 + (1/3)x² - (1/27)x⁴ + (2/729)x⁶
To approximate the integral, we can integrate the polynomial from 0 to 0.4:
∫(1 + (1/3)x² - (1/27)x⁴ + (2/729)x⁶)dx from 0 to 0.4 ≈ [x + (1/9)x³ - (1/135)x⁵ + (1/2187)x⁷] evaluated from 0 to 0.4
Now, plug in the limits:
≈ [0.4 + (1/9)(0.4³) - (1/135)(0.4⁵) + (1/2187)(0.4⁷)] - [0 + (1/9)(0³) - (1/135)(0⁵) + (1/2187)(0⁷)]
≈ 0.4 + 0.01778 - 0.00059 + 0.00002
≈ 0.41721
Thus, using the Maclaurin polynomial of degree 6, the approximation for the integral ∫³√(1+x²)dx from 0 to 0.4 is ≈ 0.41721.
This can be evaluated using basic integration techniques to get an approximate value of the integral. This method is useful for approximating integrals that cannot be solved exactly, and the accuracy of the approximation can be improved by using higher degree Maclaurin polynomials.
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