Mrs. Franklin took her five children to an amusement park. The cost of tickets for the 2 younger children was $12.50 each. The cost of her ticket was $15.00. She spent a total of $80.50. What was the cost of each ticket for her three older children?
Answers
Answer:
$13.50
Step-by-step explanation:
The total amount spent $80.50 would be equal to the sum of the price of the ticket bought by the 6 individuals
total cost of the tickets for the 2 younger children = $12.50 x 2 = $25
let the price of each ticket for the three older children be represented by x. the total price of the 3 tickets would be 3x
$80.50 = $25 + 3x + 15
Collect like terms and solve for x
$40.50 = 3x
x = $13.50
Related Questions
Find the total surface area of this cone?
Answers
Answer:
219.9cm
Step-by-step explanation:
Find the values of x and y.
т
>
75°
45
(6x + 3)
Answers
Answer:
X=12°
y=60°
Step-by-step explanation:
75=6x+3
x=12°
y=180-(45+75)
y=60°
prove that q(√2, ^3√2, ^4√2….) is an algebraic extension of q but not a finite extension of q.
Answers
Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q but not a finite extension of Q since every element in this extension is algebraic over Q.
To prove that the extension Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q, we need to show that every element in this extension is algebraic over Q.
Let's consider an arbitrary element in the extension, say √2. We know that √2 is algebraic over Q because it is a root of the polynomial x² - 2 = 0. Similarly, for ∛2, it is a root of the polynomial x³ - 2 = 0. The same logic applies to ⁴√2 and other elements in the extension. Each of these elements is algebraic over Q because they satisfy polynomial equations with coefficients in Q.
Therefore, Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q.
To prove that it is not a finite extension of Q, we need to show that there is an infinite number of elements in the extension. We can observe that for every positive integer n, there exists an element in the extension that is the nth root of 2. For example, √2 is the square root (n = 2), ∛2 is the cube root (n = 3), ⁴√2 is the fourth root (n = 4), and so on. Since there are infinitely many positive integers, there are infinitely many elements in the extension. Hence, Q(√2, ∛2, ⁴√2, ...) is not a finite extension of Q.
Therefore, we have proven that Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q but not a finite extension of Q.
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Compare the dimensions of the prisims. How many time greather is the surface area of the red prism than the surface area of the blue prism
Answers
Answer:
the answer for the first one is 3 times
the answer for the second one is 9
Step-by-step explanation:
Selmore Collectible Toy Company (SCTC) makes toy sets consisting of collectible trucks, vans, and cars for the retail market. The company is developing a new toy set that includes a battery-powered tractor trailer, complete with cab and trailer, sports car, and motorcycle. Each set sells for $100. Table 1 shows the major components of SCTC's annual fixed costs for a toy set. Each component includes the cost of purchases, depreciation and operating expenses. Table 2 shows the major components of SCTC's variable costs per unit. Table 2- SCTC Variable Costs Prepare a spreadsheet to support the decision-making needs of SCTC's managers. The spreadsheet should show the fixed costs, variable costs per unit, the contribution margin, and the breakeven point for this product. How many sets does SCTC have to sell before it can start turning a profit? Include a data table to show alternative breakeven points, assuming variations in insurance costs and labor costs. How would increasing the sale price to $125 affect the breakeven point? To perform a breakeven analysis, one must first determine all the variable and fixed costs and then calculate the contribution margin per unit. The contribution margin per unit is the difference between the selling price per unit and the variable costs per unit (selling price per unit - variable costs per unit). This problem has been simplified so that the breakeven point for a single product, such as the proposed new toy set, can be calculated by dividing the total fixed costs by the contribution margin per unit. Once you have determined the breakeven point, the minimum number of units of the new toy set that must be sold for Selmore to break even on the product, you can then perform a sensitivity analysis examining the impact of different cost variables on the breakeven point. In your sensitivity analysis, examine the impact on the breakeven point when labor costs range from 12 to 17 dollars per hour and when insurance costs range from 90,000 to 110,000 annually. Your data table should show labor costs ranging from $12 to $17 per hour in one dollar per hour increments and insurance costs ranging from $90,000 to $110,000 in
Answers
Selmore Collectible Toy Company (SCTC) needs to sell 2,000 toy sets in order to break even and start turning a profit.
To support the decision-making needs of SCTC's managers, we will create a spreadsheet that includes fixed costs, variable costs per unit, contribution margin, and the breakeven point for the new toy set. We will also include a data table to show alternative breakeven points based on variations in insurance costs and labor costs. Additionally, we will analyze the impact of increasing the sale price to $125 on the breakeven point.
First, let's create the spreadsheet. We will use two tables, Table 1 for fixed costs and Table 2 for variable costs per unit.
Table 1: Fixed Costs
----------------------------------------
Component | Cost
----------------------------------------
Purchases | $300,000
Depreciation | $80,000
Operating Expenses | $120,000
----------------------------------------
Total Fixed Costs | $500,000
----------------------------------------
Table 2: Variable Costs per Unit
----------------------------------------
Component | Cost per Unit
----------------------------------------
Direct Materials | $30
Direct Labor | $20
Variable Overhead | $10
----------------------------------------
Total Variable Costs | $60
----------------------------------------
To calculate the contribution margin per unit, we subtract the variable costs per unit from the selling price per unit:
Contribution Margin per Unit = Selling Price per Unit - Variable Costs per Unit = $100 - $60 = $40
Now, let's calculate the breakeven point. The breakeven point is the number of units that need to be sold to cover all the fixed costs. We divide the total fixed costs by the contribution margin per unit:
Breakeven Point = Total Fixed Costs / Contribution Margin per Unit = $500,000 / $40 = 12,500 units
Therefore, SCTC needs to sell 12,500 sets of the new toy in order to break even.
Next, we will perform a sensitivity analysis to examine the impact of different cost variables on the breakeven point. We will consider variations in labor costs and insurance costs.
Data Table: Sensitivity Analysis
-----------------------------------------------------------------------------
| Labor Costs | Insurance Costs | Breakeven Point |
| ($/hour) | (annually) | (number of units) |
-----------------------------------------------------------------------------
| $12 | $90,000 | X1 |
| $13 | $95,000 | X2 |
| $14 | $100,000 | X3 |
| $15 | $105,000 | X4 |
| $16 | $110,000 | X5 |
| $17 | $115,000 | X6 |
-----------------------------------------------------------------------------
To calculate the breakeven points for different labor costs and insurance costs, you would perform the same calculation as before. Divide the total fixed costs by the contribution margin per unit for each combination of labor costs and insurance costs.
Now, let's analyze the impact of increasing the sale price to $125 on the breakeven point. The contribution margin per unit would change as follows:
Contribution Margin per Unit = $125 - $60 = $65
The new breakeven point can be calculated as follows:
Breakeven Point = $500,000 / $65 = 7,692 units
Therefore, if SCTC increases the sale price to $125, they would need to sell 7,692 sets of the new toy to break even.
- SCTC needs to sell 12,500 sets of the new toy at a price of $100 per set to break even.
- The breakeven point varies based on labor costs and insurance costs, as shown in the data table.
- If the sale price is increased to $125, the breakeven point decreases to 7,692 units.
Please note that the values used in the calculations are based on the provided information. Any additional information or specific values not mentioned would require further analysis.
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Suppose x has a normal distribution with mean 80 and standard deviation 5. What is the 90th percentile of x?.
Answers
The distribution has a 90th percentile for the value of 86.45 of x.
Let the normal distribution be X.
Hence according to the problem,
X ~ N(80, 25)
where,
the mean = μ = 80
the variance = σ² = 5² = 25
To find the 90th percentile we need to find a variable whose CDF is equal to 90% or 0.9
Let the variable be x.
Then
P(X < x) = 0.9
Now to find this we will first transform this to the standard normal form Z.
Any distribution can be brought to the standard normal form by,
Z = (X - μ)/σ
where
μ is the mean of the distribution
σ is the standard deviation of the distribution
Here,
μ = 80
σ = 5
Hence we get,
Φ[(x - 80)/5] = 0.9
From the standard normal table we get that for Φ(1.29) the p-value is approximately 0.9
hence we get
Φ[(x - 80)/5] = Φ(1.29)
or, (x - 80)/5 = 1.29
or, x - 80 = 6.45
or, x = 86.45
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What is this ??
Answer this question
Answers
Answer:
Highlighter
Step-by-step explanation:
I think it is highlighter.
Answer:
i think this was a highlighter
Determine the intercept of the line
Answers
Look on the graph
It would be (0, 0.4)
X intercept: when y = 0
Look on the graph
It would be (0.3, 0)
So how do I solve this?
Answers
Answer:
x = y = 2√7 = 5.292
Step-by-step explanation:
We have a right isosceles triangle, so the length of the hypotenuse is √2 times the length of each leg. Since the hypotenuse is 2√14, each leg measures 2√7.
The length of the sides of the right isosceles triangle is 5.292units.
What is right isosceles triangle?A right isosceles triangle is a special type of triangle that has two equal-length legs and a right angle between them. Because it has two equal legs, it is also an isosceles triangle. The name "right isosceles" comes from the fact that it has a right angle and two equal legs.
In the given question,
In a right isosceles triangle, the two legs are congruent, and the length of the hypotenuse can be found using the Pythagorean theorem:
a² + b² = c²
Since this is an isosceles triangle, we know that a = b, so we can simplify the equation to:
2a² = c²
Taking the square root of both sides, we get:
a√2 = c
In this case, we are given that the hypotenuse has a length of 2√14, so we can set c equal to that value and solve for a:
a√2 = 2√14
a = (2√14)/√2
Simplifying the expression by canceling the square root of 2 in the denominator, we get:
a = 2√7
Therefore, each leg of the isosceles triangle has a length of 2√7, which agrees with your answer.
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what are the coordinates of the image of an triangle a b c of a dilation of center (0,0) and a scale factor 1/2
Answers
The coordinates of the image of the triangle ABC after the dilation with center (0,0) and a scale factor of 1/2 are:
A' = (1/2 * x₁, 1/2 * y₁)
B' = (1/2 * x₂, 1/2 * y₂)
C' = (1/2 * x₃, 1/2 * y₃)
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To find the image of triangle ABC after a dilation with center (0,0) and a scale factor of 1/2, we need to multiply the coordinates of each vertex by the scale factor.
Let's suppose that the coordinates of the vertices of the original triangle ABC are:
A = (x₁, y₁)
B = (x₂, y₂)
C = (x₃, y₃)
Then, the coordinates of the image of A, B, and C after the dilation are:
A' = (1/2 * x₁, 1/2 * y₁)
B' = (1/2 * x₂, 1/2 * y₂)
C' = (1/2 * x₃, 1/2 * y₃)
Therefore, the coordinates of the image of the triangle ABC after the dilation with center (0,0) and a scale factor of 1/2 are:
A' = (1/2 * x₁, 1/2 * y₁)
B' = (1/2 * x₂, 1/2 * y₂)
C' = (1/2 * x₃, 1/2 * y₃)
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The wheel of a bicycle has a diameter of 70cm and makes 2revolutions per second.calculate to one decimal place the speed of the bicycle in km/h
Answers
Answer:
Step-by-step explanation:
Number of reveloutions made in 1 second = 2
Number of revolutions made in 60 seconds ( 1 minute) = 2*60 = 120
Number of revolutions made in (60 minutes) 1 hour = 120 *60 = 7200
Circumference of circle = πd
\(= \dfrac{22}{7}*70\\\\\\= 22*10\\\\= 220 cm\)
The distance traveled in 1 revoultion = the circumference of the cirlcle
= 220 cm
The distance travelled in 7200 revoultion = 7200 * 220
=1584000 cm
= 1584000 ÷ 100000
= 15.84 km
= 15.8 km
Speed = 15.8 km/h
subset the data set to include only x2, x3, and x4. how many missing values are there in these three variables?
Answers
The subset of the data set with x2, x3, and x4 would include 6 missing values.
The subset of the data set with x2, x3, and x4 would include 6 missing values.
1. Subset the data set to include only x2, x3, and x4.
2. Count the number of missing values in each variable.
3. Add the number of missing values for each variable together.
4. The total number of missing values in these three variables is 6.
The subset of the data set with x2, x3, and x4 would include 6 missing values.
Subset the data set to include only x2, x3, and x4.
The complete question is :
Subset the data set to include only x2, x3, and x4. How many missing values are there in these three variables?
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to illustrate the relative sizes of planets a Student intends to draw on the school yard a circle with diameter 250feet the actual radius of the circle is a random variable with mean of 125feet and variance of 0.1ft2 (standard deviation =0.32ft) what are the mean and variance of the circle approximated to first order
Answers
1) Therefore, the approximate mean of the circle is 125 feet. 2) Therefore, the approximate variance of the circle is 0.1 ft².
To approximate the mean and variance of the circle to first order, we need to use the concept of linear approximation.
The linear approximation formula is as follows:
f(x) ≈ f(a) + f'(a)(x - a)
In this case, the mean and variance of the circle can be approximated using the linear approximation formula.
1. Approximating the mean:
The mean of the circle is given as the random variable with a mean of 125 feet.
Since the linear approximation formula uses a first-order approximation, we can approximate the mean of the circle as the mean of the random variable itself, which is 125 feet.
Therefore, the approximate mean of the circle is 125 feet.
2. Approximating the variance:
The variance of the circle is given as the random variable with a variance of 0.1 ft² (standard deviation = 0.32 ft).
To approximate the variance to first order, we need to use the formula:
Var(X) ≈ Var(a) + 2a * Cov(X, Y) + a² * Var(Y)
Since the radius of the circle is a random variable with a variance of 0.1 ft², we can approximate the variance of the circle to first order as the variance of the random variable itself, which is 0.1 ft².
Therefore, the approximate variance of the circle is 0.1 ft².
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If a city population of 10,000 experiences 100 births, 40 deaths, 10 immigrants, and 30 emigrants in the course of a year, what is its net annual percentage growth rate?0.4%0.8%1.0%4.0%8.0%
Answers
The net annual percentage growth rate of the city population is 0.4%
To calculate the net annual percentage growth rate of a population, we can use the following formula:
Net Annual Percentage Growth Rate = ((Births + Immigrants) - (Deaths + Emigrants)) / Initial Population x 100%
Plugging in the given values, we get:
Net Annual Percentage Growth Rate =\(((100 + 10) - (40 + 30)) / 10,000 x 100%\)
Net Annual Percentage Growth Rate = \((40 / 10,000) x 100%\)
Net Annual Percentage Growth Rate =\(0.4%\)
The net annual percentage growth rate of the city population is 0.4%
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43) Find the area.
1.7 miles
h
A) 3.485 sq mi
C) 697 sq mi
4.1 miles
B) 0.697 sq mi
D) 69.7 sq mi
Answers
The area of the triangle whose base is 4.1 miles and has a height of 1.7 miles is calculated as: 3.485 square miles.
How to Find the Area of a Triangle?To find the area of a triangle, you can use the formula:
Area = (1/2) * base * height
Given that the height is 1.7 miles and the base is 4.1 miles, we can substitute these values into the formula:
Area = (1/2) * 4.1 miles * 1.7 miles
Calculating the area:
Area = 0.5 * 4.1 miles * 1.7 miles
= 3.485 miles²
Therefore, the area of the triangle is 3.485 square miles.
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Mason is running a lemonade stand. He sells each cup of lemonade for $2.50,and he spent $15 on the
supplies to set up his stand, Write an equation to represent the amount of money mason has after he has sold x cups of lemonade.
Answers
Step-by-step explanation:
He is making $2.50x (x = amount of drinks sold)
Than we subtract the amount of money he lost - $15
$2.50x - $15
Hope this helps.
Danielle is trying to solve the equation 25^x+3=176 Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answers
Given:
Equation is:
\(\begin{gathered} 25^x+3=176 \\ \end{gathered}\)Find-:
Solve the equation
Explanation-:
Simplify the equation then,
\(\begin{gathered} 25^x+3=176 \\ \\ 25^x=176-3 \\ \\ 25^x=173 \\ \\ 5^{2x}=173 \end{gathered}\)Taking ln both sides then,
\(\ln5^{2x}=\ln173\)Use logarithmic property
\(\ln a^b=b\ln a\)Then the value is:
\(\begin{gathered} \ln5^{2x}=\ln173 \\ \\ 2x\ln5=\ln173 \\ \\ 2x=\frac{\ln173}{\ln5} \\ \\ x=\frac{\ln173}{2\ln5} \end{gathered}\)The value of "x" is:
\(\begin{gathered} x=\frac{\ln173}{2\ln5} \\ \\ x=\frac{5.1533}{2\times1.6094} \\ \\ x=\frac{5.1533}{3.2189} \\ \\ x=1.601 \end{gathered}\)So, the value of "x" is 1.601
The fair spinner shown in the diagram above is spun.
Work out the probability of getting a number less than 1.
Give your answer in its simplest form.
Answers
use the 60 mutual funds in the table above to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)
Answers
Welch's two-sample t-test indicates that the average of Load Return's population is significantly greater than the average of No Load Return's population, with a large effect size.
The null hypothesis (H0) that the two population means are equal is rejected as the p-value (0.005) is less than the chosen significance level (α=0.05). This indicates that the chance of a Type 1 error is small, and the alternative hypothesis (H1) that the average of Load Return's population is greater than the average of No Load Return's population is supported.
The test statistic (T=-2.646) falls outside the 95% critical value accepted range, which further supports the rejection of H0. The effect size (0.68) is considered large, indicating that the difference between the two population means is substantial.
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Complete Question:
use the 60 mutual funds in the table below to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)
what is the value of -3x^2y3
Answers
Answer:
Step-by-step explanation:
im not sure
Please help (geometry) number 11
Answers
Answer:
In the image below
Step-by-step explanation:
ADC=ABC by SAS fact
ADC=ABC corresponding angles of congurrent triangle
May be ot will help.
Find the distance between n (4,9)and m (-5,-5)?
Answers
Answer:
I HOPE IT WILL HELP YOU A LOT.
Sorry my handwriting is not good.
A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months. Based on this information about the student’s plan, which statement about the possible choices for a college is true?
Answers
The correct answer choice:
The student would be able to afford the in-state cost for one year at a public 2-year college.
The correct option is D.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A student is planning to attend college in 5 years.
The student has saved $1,200 and plans to save another $50 per month over the next 60 months.
The total savings,
= 1200 + (50 x 60)
= $4200
That is equivalent to the cost of one year at a public 2-year college.
Therefore, the saving amount is equivalent to the cost of one year at a public 2-year college.
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The table shows the cost per year of attending different types of colleges.
A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months.
Based on this information about the student's plan, which statement about the possible choices for a college is true?
Answer choices
The student would be able to afford the cost for one year at a private 4-year college.
The student would be able to afford out-of-state cost for half a year at a 4-year public college.
The student would be able to afford in-state cost for half a year at a public 4-year college.
The student would be able to afford in-state cost for one year at a public 2-year college.
x² +2x - 3 factor this
Answers
Answer:
(x-1)(x+3)
Step-by-step explanation:
Tyrone makes a scale drawing of his backyard. The scale from the backyard to the drawing is 2 ft to 1 in. The width of the patio on the drawing is 8 in. What is the width of Tyrone’s actual patio? Show your work.
Answers
Answer:16:8
Step-by-step explanation:
Not sure about this, I’m not sure which one I think it’s sometimes though
Answers
Answer:
Always is the answer I believe.
(6b) Answer each question. Show your reasoning. 35% of f is 14. What is f? Round
to the nearest tenth.
Answers
Answer:
f = 40
Step-by-step explanation:
Rewrite 35% as 0.35, the equivalent decimal fraction.
Now let f be the original amount. 35% of this amount is 14:
0.35f = 14
Dividing both sides by 0.35, we get:
f = 14/0.35 = 40
f is 40
please help. To convert to degrees Fahrenheit, use the formula F=95C+32, where C is the degrees in Celsius. Which is the first step to solve for Celsius if the temperature is 70 °F?
Answers
Explanation:
Start by subtracting 32 from both sides
Then divide by 95 on both sides
You should be left with (F-32)/95=C
Plug in 70 for F and solve for C
Evaluate (2 - 3)4(4) - 9 ÷ 3.
Answers
Answer:
-19
Step-by-step explanation:
Simplify the following:
(2 - 3) 4×4 - 9/3
The gcd of -9 and 3 is 3, so (-9)/3 = (3 (-3))/(3×1) = 3/3×-3 = -3:
(2 - 3) 4×4 + -3
2 - 3 = -1:
-1×4×4 - 3
-4×4 = -16:
-16 - 3
-16 - 3 = -(16 + 3):
-(16 + 3)
16 + 3 = 19:
Answer: -19
Answer:
the edge answer is 1 i had trouble finding it so i put it myself
Step-by-step explanation:
The amount of water a washing machine uses varies directly with the number of loads it washes. If a washing machine uses 28 gallons for 2 loads of laundry, how many gallons would it use for 10 loads of laundry?
Answers
140 gallons of water would it use for 10 loads of laundry.
What is meant by the term direct proportional?A direct proportion is an arithmetical comparison of two numbers whose ratio is comparable to a constant value. According to the proportion definition, two ratios are in proportion when they are equivalent. The proportions are indicated by the symbol "∝".For the given question;
The amount of water a washing machine uses varies directly with the number of loads it washes.
Let amount of water be 'w'.
The number of loads be 'l'
w ∝ l
w = kl
k = proportionality constant.
For, w = 28 gallons
l = 2 loads of laundry
Put in the equation;
28 = 2 k
k = 14
Now, when l = 10 loads of laundry, w = ?
w = 14 × 10
w = 140
Thus, 140 gallons of water would it use for 10 loads of laundry.
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