Answer:
The price of a drink = $4
The price of a bag of popcorn = $5.5
Step-by-step explanation:
Let p represent popcorn and d represent drink
Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79
Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50
Now multiply first equation by -3 and second equation by 10
-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237
10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365
Now add the new equationd
30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)
32d = $128 divide both sides of the equation by 32
32 ÷ 32d = 32 ÷ $128 ➡ d = 4
If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn
3p + 5d = $36.50 (replace d with 4)
3p + 4×5 = $36.50
3p + 20 = $36.50
3p = $36.50 - 20
3p = 16.50 divide both sides by 3
p = $5.5
The question asked to set up a system of equations to determine the price of each bag of popcorn and each drink. Using the variables x and y to represent the price of popcorn and drinks respectively, the system of equations based on the information given is 10x + 6y = $79 and 3x + 5y = $36.50.
Explanation:To solve this problem, we need to setup a series of equations based on the information given. Let's say:
x is the price of each bag of popcorny is the price of each drinkAccording to the first scenario with Harper, we get:
10x + 6y = $79
From Damian's shopping, we have:
3x + 5y = $36.50
This gives us the system of equations which can be used to find individual prices of a bag of popcorn and a drink.
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count backwards by hundreds from 1,000.
Answer:
1,000 900 800 700 600 500 400 300 200 100
Step-by-step explanation:
Perry Angelo is planning to open a restaurant. He has the resources to produce and sell either hamburgers or pizzas. So he does some research
and finds that the new location has a good demand for pizza. He hires cooks, wait staff, and an accounts person for his new pizzeria. He also
arranges for materials such as pizza ingredients and pizza boxes.
Determine three factors affecting Perry's cost of making pizza. Write down the name of the factors and their instances in this scenario in the table.
Answer:
Factors Affecting Cost Factors Affecting Cost
opportunity cost: the opportunity to produce and sell
hamburgers
cost of materials: cost of pizza ingredients and pizza boxes
sunk cost: money spent on researching the best option
fixed cost: money for paying employees
marginal cost:the cost of baking one more pizza
Step-by-step explanation:
Perry Angelo's cost of making pizza is affected by the cost of ingredients, labor costs, and capital costs like the pizza oven and shop rent. These costs, along with a desired profit margin, influence the selling price.
Explanation:The cost of producing pizza or any output involves various factors. In the scenario described for Perry Angelo's pizzeria, three significant factors affecting the cost of making pizza include:
Cost of Ingredients: This includes items like dough, sauce, cheese, and pepperoni, which are essential for making pizzas.Labor Costs: The wages paid to the cooks, wait staff, and the accounts person Perry Angelo hires.Capital Costs: Investments made in the pizza oven and other equipment necessary for the production of pizzas, as well as ongoing expenses like shop rent.These elements contribute to the total production cost, on top of which Perry will need to add his desired profit margin to determine the selling price for the pizzas.
-3 x [75/(9 - 4)^2]^2 simplify
Answer:
[tex]-27x[/tex]
Step-by-step explanation:
Given Equation:
[tex]-3 x [75/(9 - 4)^2]^2[/tex]
On simplifying the equation:
[tex]=-3 x [75/(9 - 4)^2]^2\\=-3 x [75/(5)^2]^2\\=-3 x [75/25]^2\\=-3 x [3]^2\\=-3x*9\\=-27x[/tex]
The value of 'x' can be find by equating the simplified value to some certain value according to the equation.
im really stuck :( can someone please help me ? it would mean a lot
Answer:
Step-by-step explanation:
Populations is who is surveyed or what the questions is targeting. More specifically who. That would be households with a car.
Use what I put as the definition for population to answer the other questions!
The _______ represents the number of standard deviations an observation is from the mean.
Answer:
The z-score represents the number of standard deviations an observation is from the mean.
Step-by-step explanation:
We want to complete the statement:
The _______ represents the number of standard deviations an observation is from the mean.
Whenever we calculate z- scores, we are finding how many standard deviations an observation is from the mean.
A z-score of 3, means an observation is 3 standard deviation above the mean.
Therefore the best complete is:
z-score.
The Z-score represents the number of standard deviations an observation is from the mean. It provides a comparative measure that standardizes data, making it easier to compare data from different sets.
Explanation:The Z-score represents the number of standard deviations an observation is from the mean. In statistics, it is a way to compare the position of any observation relative to the overall distribution.
Here's an example: if a Z-score of a data point is 2, it means that the data point is 2 standard deviations above the mean. Conversely, if a Z-score of a data point is -1, it means that the data point is 1 standard deviation below the mean.
Z-scores provide a standardized way to interpret data, which makes the comparison of different data sets more straightforward and undistorted by differences in units or scales.
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What is the algebraic expression for b divided by 9
Answer:b/9
Step-by-step explanation: the expression b divided by 9 is b/9
Answer: b ÷ 9
Step-by-step explanation:
Well, since the question is to write an expression for b divided by 9, you just write b divided into 9 parts.
NOTE: Remeber, an expression is an equation but WITHOUT an answer.
Hope this helps! Please feel free to correct me if I'm wrong!
[Question Image Attached] If you are given the graph of g (x) = log 2 x, how could you graph f (x) = log 2 x + 5?
Answer:
Translate each point of g(x) 5 units up.
Step-by-step explanation:
The given the graph of the parent function
[tex]g(x) = log_{2}(x) [/tex]
We want to use this graph to draw the graph of
[tex]f(x) = log_{2}(x) + 5[/tex]
We can observe that:
[tex]f(x) = g(x) + 5[/tex]
This means the graph of the parent function, g(x) must be shifted up 5 units.
Therefore the correct answer is A.
A company is expanding its building area from 11,000 square feet to 14,740 square feet. What is the percentage increase of the area
of the building space?
A. 66%
B. 37.4%
C. 3.4%
D. 34%
Option D
The percentage increase of the area of the building space is 34 %
Solution:
A company is expanding its building area from 11,000 square feet to 14,740 square feet
To find: Percentage Increase
The percent increase is given by formula:
[tex]\text{Percent increase } = \frac{\text{Final value - Initial value}}{\text{Initial value}} \times 100[/tex]
From given,
Initial value = 11000
Final value = 14740
Substituting we get,
[tex]Percent\ Increase = \frac{14740-11000}{11000} \times 100\\\\Percent\ Increase = \frac{3740}{110}\\\\Percent\ Increase = 34[/tex]
Thus percentage increase of the area of the building space is 34 %
Write a numerical expression representing the following statement:
"four times the sum of sixty-seven plus forty"
Answer:
47 + 40 x 4
Step-by-step explanation:
sum is adding 2 numbers together and you would then multiply 4 after adding :)
Pam has 24 pencils and 6 erasers. How many times as many pencils as erasers does Pam have?
Answer:
Pam had 4 times as many pencils as erasers
Step-by-step explanation:
24 pencils
6 erasers
24 pencils = x * 6 erasers
Divide by 6 on both sides to isolate x
x = 4
Pam had 4 times as many pencils as erasers
Hope this helps :)
Find the coordinates of the reflected image.
A rectangle with vertices L(1, -1), M(1, -9). N(8.-9), and
(8.-1) is reflected over the y-axis.
1.)L'(-1.-1), M'(-1, -9), N'(-8.-9), and 0%(-8, -1)
2.)L (1.-1), M'(1.-9), N'(8.-9), and Oʻ(8.-1)
3.)L'(-1.–1). M?(-9,-1). N'(-9.–8). and O'(-1, -8)
4.)L'(-1. 1). M'(-1.9), N'(-8. 9), and O'(-8.1)
Answer:
The actual answer is A or 1 as you have it.
Step-by-step explanation:
All you have to do is just map out the coordinates yourself. You're looking for a reflection that goes across the Y axis, but NOT across the X axis.
Hope this helps you and anyone looking for an answer to their headache.
Final answer:
The reflected coordinates of the rectangle over the y-axis are L'(-1, -1), M'(-1, -9), N'(-8, -9), and O'(-8, -1), matching option 1.
Explanation:
The student is asking about finding the coordinates of a rectangle's vertices after it has been reflected over the y-axis. Reflecting a shape over the y-axis changes the sign of the x-coordinate of each vertex, while the y-coordinate remains the same. So, if we have a point (x, y), the reflected point over the y-axis would be (-x, y). Applying this to the rectangle's vertices we have:
For L(1, -1), the reflection L' would be (-1, -1).
For M(1, -9), the reflection M' would be (-1, -9).
For N(8, -9), the reflection N' would be (-8, -9).
For O(8, -1), the reflection O' would be (-8, -1).
Therefore, the correct reflected coordinates are L'(-1, -1), M'(-1, -9), N'(-8, -9), and O'(-8, -1), which corresponds to option 1.
What is the solution to this system of equations?
2x - y = 8
x + y = 4
A. (2, -4)
B. (4, 0)
C. (6, 4)
D. (12, -8)
Answer:
Answer is B. (4,0)
Step-by-step explanation:
2x - y = 8
x + y = 4
solve the equation
2x - y = 8
y = 4 - x
substitute the value of y into the equation
2x - (4 - x) = 8
solve the equation
x = 4
substitute the value of x into an equation
y = 4 - 4
solve the equation
y = 0
answer is (4,0)
Use the drop-down menus to complete the statement about the inequality m ≥ 2.
Answer:
The inequality m ≥ 2 has infinity many solutions because 2 and any number to the right of 2 on the number line can be substituted for m to make this inequality true.
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 69 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 65 miles per hour and 73 miles per hour. (Assume the data set has a bell-shaped distribution)
This is the answer, I hope it will be help
The percent of vehicles whose speeds are between 65 miles/hour and 73 miles/hour will be 68 %.
It is given that mean speed of sample of vehicles (μ) is 69 miles/hour and standard deviation is 4 miles/hour.
We have to find out the percent of vehicles whose speeds are between 65 miles/hour and 73 miles/hour using the empirical rule.
What is the empirical rule if distribution lies within one standard deviation from the mean ?
The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean.
As per the question , we have ;
Mean speed of sample of vehicles (μ) = 69 miles/hour
Standard deviation = 4 miles/hour
To find the % of vehicles , let's check where the distribution lies ;
So ;
μ - 4 ;
= 69 - 4
= 65 miles / hour
μ + 4 ;
= 69 + 4
= 73 miles / hour
Since ; it lies between μ - 4 and μ + 4 , so by using the empirical rule we get that it lies within one standard deviation.
Hence ; by the empirical rule ;
% of vehicles between speed 65 miles/ hour and 73 miles/hour = 68 %
Thus , the percent of vehicles whose speeds are between 65 miles/ hour and 73 miles/hour will be 68 %.
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Simplify the radical 147
Answer and Explanation: The square root of 147 is approximately 12.12436 or 7√3 in radical form. To begin, examine 147's factors. These are: 1, 3, 7, 21, 49, 147.
Hope this helped
Answer:
12.12436 or 7√3
Step-by-step explanation:
Camacho is buying a monster truck. The price of the truck is xxx dollars, and he also has to pay a 13\%13%13, percent monster truck tax.
Which of the following expressions could represent how much Camacho pays in total for the truck?
Answer:
Camacho pays in total for the monster truck = $x + $0.13x = $1.13x
Step-by-step explanation:
i.) The price of truck is $x
ii.) Monstor truck tax = 13% of price of truck = [tex]\frac{13}{100}\times $x[/tex] = $0.13x
iii) Camacho pays in total for the monster truck = $x + $0.13x = $1.13x
Options A and D correctly represent how much Camacho pays in total for the truck:
A. (1 + 0.13)x
D. 1.13x
The total amount Camacho pays for the monster truck includes the price of the truck plus the tax, which is 13% of the price of the truck. Therefore, the total amount can be represented by the expression:
[tex]\[ \text{Total amount} = \text{Price of the truck} + \text{Tax amount} \][/tex]
Given that the price of the truck is x dollars and the tax is 13\% of the price, we can represent the tax amount as 0.13x .
So, the total amount Camacho pays is:
[tex]\[ \text{Total amount} = x + 0.13x \][/tex]
[tex]\[ \text{Total amount} = 1.13x \][/tex]
Therefore, options A and D correctly represent how much Camacho pays in total for the truck:
A. (1 + 0.13)x
D. 1.13x
The complete Question is given below:
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck? Choose 2 answers:
A. (1+0.13)x
B. 13x/100
C. 13x
D. 1.13x
E .13x+x
cotA/tanA simplify each question
[tex]\bf \cfrac{cot(A)}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{\frac{tan(A)}{1}}\implies \cfrac{1}{tan(A)}\cdot \cfrac{1}{tan(A)} \\\\\\ \cfrac{1}{[tan(A)]^2}\implies \cfrac{1}{tan^2(A)}\implies \cfrac{1^2}{tan^2(A)}\implies \left( \cfrac{1}{tan(A)} \right)^2\implies cot^2(A)[/tex]
Final answer:
To simplify cotA/tanA, we recognize that cotA is the reciprocal of tanA. The expression simplifies to cosA^2/sinA^2, which can also be written as cotA^2.
Explanation:
To simplify the expression cotA/tanA, we can use the fundamental trigonometric identities that relate the cotangent and tangent functions. The cotangent function, cotA, is the reciprocal of the tangent function, tanA, which means cotA = 1/tanA. Therefore, when we simplify cotA/tanA, we are effectively dividing the reciprocal of the tangent function by the tangent function itself.
The simplification would thus be:
cotA/tanA = (1/tanA)/tanA = 1/(tanA^2)Since tanA = sinA/cosA, the expression can be rewritten as[tex]1/((sinA/cosA)^2)[/tex]Therefore, cotA/tanA simplifies to [tex]cosA^2/sinA^2, or cotA^2.[/tex]A town has a population of 20000 and grows at 6% every year. What will be the population after 6 years to the nearest whole number
Answer:
27200 rounded will be 30000
Step-by-step explanation:
firstly you find 1% which is 200
then you multiply by 6 to get 6%
then you multiply by 6 again to get the total
Solve the equation: x/2-18=(-28)
Answer:
x = -20
Step-by-step explanation:
First we can rearrange the equation:
[tex]\frac{x}{2}[/tex] -18 = -28
2 * [tex]\frac{x}{2}[/tex] - 18 = -28 * 2
The 2s canel out
x - 36 = - 56
x = -20
A study indicated that the citizens of Newport wasted 38,080 gallons of water last year. This year they wasted 20% less. How many gallons did the citizens wasted this year
Charlotte uses a 50% off coupon when she buys a dress the original price of the dress is $45 how much money does Charlotte save by using the coupon
Answer: $22.50
Step-by-step explanation:
Since the price is 50% off, you need to find half of 45. 45/2 is 22.5, so she saves $22.50
1) In the diagram, l || m. If the measure of angle 3 is 120 find the measure of the following angles
a) angle 4
b) angle 6
c) angle 8
Answer:
a) 60° , b) 120° and c) 60°
Step-by-step explanation:
See the diagram attached to this question.
a) Here, ∠ 4 and ∠ 3 are supplementary angles.
So, ∠ 4 + ∠ 3 = 180° {Here, ∠ 3 is given to be 120°}
⇒ ∠ 4 = 180° - ∠ 3 = 180° - 120° = 60° (Answer)
b) Now, ∠ 3 and ∠ 6 are alternate angles and hence, ∠ 3 = ∠ 6 = 120° (Answer)
c) Here, ∠ 6 and ∠ 8 are supplementary angles.
So, ∠ 6 + ∠ 8 = 180°
⇒ ∠ 8 = 180° - ∠ 6 = 180° - 120° = 60° (Answer)
Help with two Math problems.
1: A bag of dog food weighs 20lb. 15% of the weight is oats.
a) Set up an equation OR proportion to find the weight of the oats in the dog food.
b) What is the weight of the oats in the dog food? Show your work.
2: Some students were asked what kind of animals they have at home. The results are in the image:
(a) List the animals in order of popularity from most popular to least popular.
(b) I estimated that 250 students were interviewed. Based on my estimate, how many students have an "other" pet? Show your work.
Answer:
1. a. o = 3b
b. o = 3 pounds
2. a. Most popular animals:
A. Dogs - 67%
B. Cats - 20%
C. Other - 8%
D. None - 4%
E. Horses - 1%
b. 20 students
Step-by-step explanation:
1. a. The equation is:
o = 0.15 *20b
o = 3b
where, o = weight of oats in pounds and b = number of dog food bags
b. Let's find out the weight of the oats in one dog food bag, using our equation:
o = 0.15 *20b
o = 0.15 *20 * 1
o = 3 pounds
2. a. Most popular animals:
A. Dogs - 67%
B. Cats - 20%
C. Other - 8%
D. None - 4%
E. Horses - 1%
b. If 250 students were interviewed, the 8% who answered "other" are:
8% of 250 = 0.08 * 250 = 20 students
How to write a point slope form of the equation of a line with a slope of -4 and passes through the point (1,6)?
Answer:
y-6=-4(x-1)
Step-by-step explanation:
y-y1=m(x-x1)
y-6=-4(x-1)
what are the two values of x that are roots of this equation x^2+3x-6=0
Answer:
x = - 3 - √33 / 2
x = + 3 + √33 /2
or
x=1.37228132...
x=−4.37228132...
Step-by-step explanation:
The two values of x that are roots of the equation x^2+3x-6=0 are approximately x ≈ -4.16 and x ≈ 1.16.
Explanation:To find the two values of x that are roots of the equation x^2+3x-6=0, we can use the quadratic formula. The formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 3, and c = -6. Plugging in these values, we get:
x = (-3 ± √(3^2 - 4(1)(-6))) / 2(1)
Simplifying further:
x = (-3 ± √(9 + 24)) / 2
x = (-3 ± √33) / 2
So the two values of x that are roots of the equation are approximately x ≈ -4.16 and x ≈ 1.16.
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What is the simplified answer for 8w = 5
Answer:
w = 5/8
Step-by-step explanation:
divide by 8 to both sides to get 8/8w = 5/8
8/8 = 1, w = 5/8.
Answer:
W= 5/8
Step-by-step explanation:
divide both sides by 8
Solve this system of equations using the substitution method. If the system of equations
does not have one solution, indicate whether the system has no solution or infinitely
many solutions.
3x+y=5
4x + 2y = 20
Answer:
well i dont really get ehat yours saying but the qustions are
3x+y=5
3^1+1=5
and then
4z+2y=20
i think
4^6+2^6=20
Step-by-step explanation:
The loan that Nate and Isaac got from their parents was at 2% interest for one year. How much will the boys pay in interest on their loan of \$2,500 ? Show your work .
Answer: they will have to pay 50 dollars
Step-by-step explanation: you have to multiply 2,500 by 0.02 as it is the same as a percent then you should get 50
the answer for this question someone answer fast pleaseeee
Answer:
???
Step-by-step explanation:
you don't have a question to answer
Beginning from a depth of 35 feet below the surface, a whale swims
upward and jumps to a height of nearly 17 feet above the surface.
a. Model with Math Use an inequality to model the possible change in the number of feet, r, of the whale's elevation.
b. Solve the inequality. Explain the meaning in terms of the situation.
a. The inequality that models the possible change in the number of feet, r, of the whale's elevation is: 35 - r ≤ 17.
This inequality represents the starting depth of 35 feet below the surface (35), minus the possible change in elevation (r), which should be less than or equal to the maximum height the whale jumps, which is nearly 17 feet above the surface (17).
b. By solving the inequality 35 - r ≤ 17, we can find the range of possible values for r.
First, subtract 35 from both sides of the inequality: -r ≤ 17 - 35. Simplifying further, we have -r ≤ -18. Then, multiply both sides by -1, remembering to reverse the inequality direction: r ≥ 18.
The solution to the inequality is r ≥ 18, meaning that the possible change in the number of feet of the whale's elevation must be equal to or greater than 18. This implies that the whale's jump cannot be less than 18 feet above the surface.
Therefore, the whale's elevation can change by any value equal to or greater than 18 feet, allowing it to jump to a height of nearly 17 feet above the surface.
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a) The inequality can be written as 35 - r ≤ 17. b) The solution to the inequality is r ≥ 18, which means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.
a.
Since the whale swims upward and jumps to a height of nearly 17 feet above the surface, we can represent the change in elevation as r.
The inequality can be written as:
35 - r ≤ 17
Here, 35 represents the starting depth below the surface, and 17 represents the height above the surface that the whale reaches.
By subtracting r from the starting depth, we account for the possible decrease in elevation as the whale swims upward.
b. To solve the inequality, we can isolate r on one side of the equation:
35 - r ≤ 17
Adding r to both sides of the inequality:
35 - r + r ≤ 17 + r
35 ≤ 17 + r
Subtracting 17 from both sides:
35 - 17 ≤ 17 + r - 17
Simplifying further:
18 ≤ r
Therefore, the solution to the inequality is r ≥ 18.
In terms of the situation, the inequality r ≥ 18 means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.
This indicates that as the whale swims upward and jumps to a height of nearly 17 feet above the surface, the whale's elevation can increase by at least 18 feet from its starting depth of 35 feet below the surface.
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