The price of each bag of popcorn and the price of each drink is $7.5 and $4 respectively.
How to calculate the equation?Let the drinks be represented as d.
Let the popcorn be represented as p.
From the information, Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Thus will be:
6p + 4d = 65
Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. This will be:
9p + 8d = 107.50
Equating the equation
6p + 4d = 65 ..... i
9p + 8d = 107.50 ..... ii
Multiply equation i by 8
Multiply equation ii by 4
48p + 32d = 520
36p + 32d = 430
12p = 90
Divide
p = 90/12
= 7.5
6p + 4d = 65 .
6(7.5) + 4d = 65
4d = 65 - 45
4d = 20
d = 20/4
drink = 5
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What expression could be used to add 3/4+1/6
The expression that could be used to add 3/4+1/6 is [tex]\frac{9 + 2}{12}[/tex]
How to determine the expression?The sum expression is given as:
3/4 + 1/6
Rewrite properly as:
[tex]\frac 34 + \frac 16[/tex]
Take the LCM.
The LCM of 4 and 6 is 12.
So, we have:
[tex]\frac{9 + 2}{12}[/tex]
Hence, the expression that could be used to add 3/4+1/6 is [tex]\frac{9 + 2}{12}[/tex]
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4/10x - 2x + 8/5 = 4/5
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]
Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$}[/tex]Subtract 8/5 from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}[/tex]Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}[/tex]Subtract 8 from 4 to get -4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$}[/tex]Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$}[/tex]Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}[/tex]Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x=\frac{1}{2} \end{gathered}$}}[/tex]Good luck in your studiesWILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
The correct order of reasons that complete the proof about the rectangle and square is that D. definition of congruence, distance formula if two consecutive sides of a rectangle are congruent, then it's a square.
What is congruence?It should be noted that congruence simply means an agreement or a correspondence between shapes.
In geoemtry, it should be noted that figures are said to be congruent if it is possible to superpose one of them on another.
It should be noted that the opposite sides of a rectangle are parallel while in a square, all the sides that are given are equal.
Therefore, the correct order of reasons that complete the proof about the rectangle and square is the definition of congruence, and that if two consecutive sides of a rectangle are congruent, then it's a square.
In conclusion, the correct option is D.
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.....................
Answer: 5020
Step-by-step explanation:
10^3= 1000
1000*5.02=5020
2. Which of the following graphs show a function with domain 1 ≤ x ≤ 6? Select two that
apply.
Answer:
Graphs A and B
Step-by-step explanation:
Graphs A & B are using x-values 1-6 and stop there, which is what the domain is trying to find. Though, for the other graphs, these graphs are rather starting at 1 via the domain, while not going up to 6 on the domain.
while sshopping ,you see a jacket mark down 20%.if the original price of the jacket $175.what is the sale price of the jacket?
The sales price of the jacket is $140.
What is a markdown price?A price markdown is a planned decrease in the retail item's selling price. It is used to accelerate an item's sales rate, usually for clearing at the closing of a season or to get rid of outdated goods when their useful lives have passed.
Markdown prices are reductions in a product's selling price from its initial selling price expressed as a rate called markdown percentage. Markdown prices are more commonly referred to as discounts.
From the given information:
The markdown price of the jacket = 20% of the original price.If the original price of the jacket is $175.Then the sales price of the jacket is:
= $175 - (20% of $175)
=$175 - $35
= $140
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Simplify the following
= 4×8 +2×3 -1+9
___________
20
= 8+6-9
_______
20
= 14 - 9
_______
20
= 5
____
20
ramon is a parking lot attendant. he estimates that 30% of the cars in the lot are sedans, 10% are minivans, and 20% are suvs. he designs a simulation. let 0,1, and 2 represent sedans. let 3 represent minivans. let 4 and 5 represent suvs. let 6,7,8 and 9 represent other cars. the table show the simulation results. what is the probability that at least one of the next four cars the enter the lot is a sedan?
The probability that the nest set of cars that would enter the lot is a sedan is given as 80 percent
How to solve for the probabilityThe total number of trials can be seen to be 20 in number. The numbers that represents the sedan are 0, 1, 2
Now we would have to count the number of trials in these 20 that have 0, 1, 2
In the table we have 16 of these 0, 1 or 2 numbers
Hence we would have
16 /20
= 0.8
= 80 percent
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Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 35.5 inches and a standard deviation of 2.5 inches. About 2.4% of the years, the annual rainfall will exceed how many inches? (Round your answer to one decimal place.)
The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.
What is the average annual rainfall?Generally, the equation for the probability is mathematically given as
[tex]P( X < x) = p( Z < x - \mu / \sigma)[/tex]
Therefore
[tex]P( X > x) = 0.021[/tex]
[tex]P( X < x ) = 1 - 0.021\\\\\p( X < x) = 0.979[/tex]
[tex]P( Z < x - \mu / \sigma) = 0.979[/tex]
The z score for the probability of 0.979 is 2.034, according to the table of z values.
[tex]x - \mu / \sigma \\\\x= 2.034[/tex]
In the given equation, replace the values of mu and sigma with their respective values, and then solve for x.
[tex]x - 35.5 / 2.5 \\x= 2.034[/tex]
In conclusion, The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.
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You buy almond milk in 1 gallon containers. One portion of waffles requires 2.5 ounces of almond milk. How many portions can be made with one container
Answer:
61 portions
Step-by-step explanation:
First, the conversion between gallon and ounces is:
1 Gallon = 153.722 ounces (oz)
GIven 1 portion of waffles requires 2.5 ounces of milk
Number of portions of waffles = Total amount of milk / milk required per portion of waffles
= 153.722 / 2.5
= 61.489 portions
Of course, we are unable to make part portions in this case, so we will take the highest possible whole number, which is 61 portions.
Solve equation -1/9 / (-1/3)
Answer: 1/3
Step-by-step explanation:
-1/9 / -1/3 = ?
Keep: -1/9
Change: *
Flip: -3/1
Solve: -1/9 * -3/1 = 3/9
Simplify: 1/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textsf{Convert:}[/tex]
[tex]\mathsf{= -\dfrac{1}{9} \times -\dfrac{3}{1}}[/tex]
[tex]\huge\textsf{Multiply:}[/tex]
[tex]\mathsf{= \dfrac{-1\times3}{9\times -1}}[/tex]
[tex]\mathsf{= \dfrac{-3}{-9}}[/tex]
[tex]\mathsf{= \dfrac{-3 \div -3}{-9\div-3}}[/tex]
[tex]\mathsf{= \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can someone please explain the steps to get too the second answer also please answer too thank you
The wheel of the average bicycle is 28 inches in diameter. How many feet will be covered in 9
turns of the wheel?
Answer:
Approximately 66 feet
Step-by-step explanation:
Given d = 28 inFind the circumference:
C = πd = 3.14*28 = 87.92 inFind the distance covered by 9 turns:
9C = 9*87.92 = 791.28 inConvert inches to feet:
1 foot = 12 in791.28 in = 791.28/12 ft = 65.94 ft ≈ 66 ft39. Solve for x. SHOW ALL WORK FOR FULL CREDIT m n 6x-4 112°
Answer:
x = 12
Step-by-step explanation:
6x - 4 and 112 are same- side interior angles and sum to 180° , that is
6x - 4 + 112 = 180
6x + 108 = 180 ( subtract 108 from both sides )
6x = 72 ( divide both sides by 6 )
x = 12
Answer:
x = 12
Step-by-step explanation:
Consecutive Interior Angles Theorem
When a straight line intersects two parallel straight lines, the consecutive interior angles formed are are supplementary (sum to 180°).
Therefore:
⇒ 6x - 4 + 112 = 180
⇒ 6x + 108 = 180
⇒ 6x + 108 - 108 = 180 - 108
⇒ 6x = 72
⇒ 6x ÷ 6 = 72 ÷ 6
⇒ x = 12
10 points please answer correctly (due soon)
Let’ pretend that in an American city there were 2000 new cases on Monday which is a 12% decrease from two weeks ago.
1. Write a linear/exponential equation that
models this situation (consistent with the data
provided). Time is the explanatory variable, and
New Cases is the response variable.
B) Explain what the slope/multiplier (consistent
with your choice above) means in this context
of the problem. Be sure to use units.
The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week
The function that models the dataThe given parameters are:
New, A(t) = 2000
Rate, r = 12%
The function is represented as:
A(t) = A * (1 - r)^t
So, we have:
2000 = A * (1 - 12%)^t
This gives
2000 = A * (0.88)^t
2 weeks ago implies that;
t = 2
So, we have:
2000 = A * 0.88^2
Evaluate
2000 = A * 0.7744
Divide by 0.7744
A = 2583
Substitute A = 2583 in A(t) = A * 0.88^t
A(t) = 2583 * 0.88^t
Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t
The interpretation of the multiplierIn this case, the multiplier is 88% or 0.88
This means that the number of new cases in a week is 88% of the previous week
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A machine can pack 5000 articles in 24 hours.How long will 3 such machine take to pack the same number of articles
The time taken for 3 machines to pack 5000 articles is 8 hours.
What are word problems?Word problems are mathematical problems expressed completely in words.The given problem is the rate of work done kind of word problem.To solve a word problem, first, observe the data given in words and apply the basic algebraic operations.The basic algebraic operations are addition, subtraction, multiplication, and division.How long will 3 such machines take to pack 5000 articles?It is given that,
A machine can pack 5000 articles in 24 hours. I.e,
1 machine → 5000 articles → 24 hours
3 machines → 5000 articles → 24/3 hours
Thus, 3 of such machines can pack the same number of articles in
24 ÷ 3 = 8 hours.
Therefore, 3 of such machines take 8 hours to pack 5000 articles.
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Explain how to draw a line segments that measures 2 7/16 inches.
Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart.
Step-by-step explanation: On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches long.
I need some help with this question for a self-taught course
The support pole must be approximately 7.8 meters long.
What is the length of the support pole?
Based on all the information given in the statement, we prepare a geometric diagram that describes the system formed by the high-security fence and the support pole. The representation is attached below. Lastly, the length of the pole is found by using the law of sines:
l/sin 84° = 6 m /sin 50°
l = 6 m × (sin 84°/sin 50°)
l ≈ 7.790 m
The support pole must be approximately 7.8 meters long.
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Special Right Triangles
Find x.
Answer:
8
Step-by-step explanation:
The cos of 30 is [tex]\sqrt{x}[/tex] / 2. Since the adjacent angle is 4 times that. We would multiply 2 x 4 and get 8
Koos spent 3/7 of his monthly pocket money during the first week. The following week he spends two- thirds of what he had spent the previous week. The fraction of the pocket money that is still left is.
Answer: 2/7
Step-by-step explanation:
The total amount of pocket money he has is 7/7.
He spent 3/7 of his pocket money during the first week.
He then spends 2/3 of what he spent the previous week, 2/3 * 3/7 which is 2/7.
What he has left is 7/7 - 3/7 - 2/7 = 2/7.
IQ scores are approximately normally distributed with a mean of 100 and a standard
deviation of 15. What IQ score is about 1.5 standard deviations above the mean?
A. 77.5
B. 120
OC. 115
D. 122.5
The IQ score of 122.5 is about 1.5 standard deviations above the mean.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The z score is given by:
z = (raw score - mean) / standard deviation.
Given a mean of 100 and standard deviation of 15. The IQ score that is 1.5 standard deviations above the mean corresponds to a z score of 1.5, hence:
1.5 = (x - 100)/15
x = 122.5
The IQ score of 122.5 is about 1.5 standard deviations above the mean.
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The segment below is dilated by a scale factor of 22 to form I ′J ′ What is the measure of I ′J ′ ?
Answer:
18
Step-by-step explanation:
When dilating a segment by a scale factor, we multiply the original length by the scale factor to find the length.
2*9 = 18
Using traditional methods, it takes 103 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 60 students and observed that they had a mean of 102 hours. Assume the variance is known to be 9. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.
The test statistic based on the probability illustrated is -2.57.
How to calculate the probability?The basic training is given as 103 hours. The variance is also given as 9.
The test statistic will be:
= (102 - 104/3/✓60)
= -1/(3/7.7)
= -2.57.
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look at the pictures
Factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)
Inequality functionsFor us to determine if a set of inequality function has a solution, we will equate the functions and determine the point of intersection if there are any,
Given the inequalities
y ≤ x^2 - 3
y > -x^2 + 2
Equate
x^2 - x = -x^2 + 2
Collect like terms
2x^2 - x - 2 = 0
In order to determine the value of x, we will factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)
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The diagram shows a field, ABCD, on horizontal ground. (a) There is a vertical post at C. From B, the angle of elevation of the top of the post is 19º. Find the height of the post.
10) Find the mean of the data set.
O a.) 5
Ob.) 9
O c.) 10
O d.) 13
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
Answer:
b
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{5+8+12+6+7+10+14+6+13}{9}[/tex]
= [tex]\frac{81}{9}[/tex]
= 9
Answer:
9
Step-by-step explanation:
The mean is also known as the average. To find it, we add up all of the data and divide it by how many numbers were added.
5 + 8 + 12 + 6 + 7 + 10 + 14 + 6 + 13 = 81
81/9 = 9
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The value of Kayla's investment can be modeled by the equation y=2650(1.05)x where x is the number of years invested and y is the value in dollars. What will be the value of the investment after 25 years? Round your answer to the nearest dollar.
Answer:
8,974 dollars
Step-by-step explanation:
y=2650.(1.05)^x
x=25
2650(1.05)^25 = 8974 dollars
Need help with this one
Answer:
The answer is a.2x/9Step-by-step explanation:
[tex] \frac{x {}^{2} }{3y} \div \frac{3x}{2y} \\ \frac{x {}^{2} }{3y} \times \frac{2y}{3x} \\ \frac{x {}^{2} }{3} \times \frac{2}{3x} \\ \frac{x}{3} \times \frac{2}{3} = \frac{2x}{9} [/tex]
Find the sum of the arithmetic series 8 +13 +...+ 58.
a) 726
Ob) 1914
Oc) 330
d) 363
Answer:
363 (d)
Step-by-step explanation:
Sum = (a1+an)(n)/2
n = (an-a1)/d +1 = 11
Plug into the sum formula.
Sum = 363
A function and its inverse are shown on the same graph. A function and its inverse are shown on the same graph.
Which statement describes the relationship between the function and its inverse?
The slope of f–1(x) is the same as the slope of f(x).
The slope of f–1(x) is the opposite as the slope of f(x).
The x-intercept of f–1(x) is the same as the y-intercept of f(x).
The x-intercept of f–1(x) is the opposite as the y-intercept of f(x).
Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
Which statement is the correct one?
On the image, we can see two linear equations, such that the orange one is f(x) and the blue one is the inverse.
If you follow the orange line, you can see that the y-intercept of f(x) is y = 1.If you follow the blue line, you can see that the x-intercept of the inverse is x =1.Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
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