The cost of each drink purchased at the AMC theaters is $6.09
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cost of one drink. After using the coupon, their total cost before tax was $29.18. Hence:
2(11) + 2(x) - 5 = 29.18
x = 6.09
The cost of each drink purchased at the AMC theaters is $6.09
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Writs the equation in exponential form. Assume that alt constants are positiver and not equal to 1. log(π)=4
The exponential form of the equation log(π) = 4 is π = 10⁴. The equation is written in exponential form by raising the base 10 to the power of the logarithmic expression, which in this case is 4.
We are given the equation in logarithmic form as log(π) = 4. To write this equation in exponential form, we need to convert the logarithmic expression to an exponential expression. In general, the exponential form of the logarithmic expression logb(x) = y is given as x = by.
Applying this formula, we can write the given equation in exponential form as:
π = 10⁴
This means that the value of π is equal to 10 raised to the power of 4, which is 10,000. To verify that this is indeed the correct answer, we can take the logarithm of both sides of the equation using the base 10 and see if it matches the given value of 4:
log(π) = log(10⁴)log(π) = 4
Thus, we can conclude that the exponential form of the equation log(π) = 4 is π = 10⁴.
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HELP!!! 10 POINTS OFFERED
Answer:
option 2
Step-by-step explanation:
5( x + 9)
What is the answer to that
Answer:
5x + 45
Step-by-step explanation:
distribute 5 to both x and 9 so multiply them both
Why do you suppose we watched this film (wargames) while we are studying the cold war? what is the significance of what happens in the plot of this film and how does it help us study the events of this time period?
We watched the film "WarGames" because it provides a unique perspective on the Cold War era, highlighting the fear and tensions surrounding nuclear war.
The plot revolves around a teenage hacker who accidentally accesses a military supercomputer and nearly triggers a global thermonuclear war. The film reflects the heightened paranoia and constant threat of a nuclear attack during this time. By analyzing the events in the film, we can better understand the political and social climate of the Cold War era. The film also highlights the dangers of technological advancement and the need for caution in the face of nuclear proliferation. The film's plot, which involves a computer system mistaking a simulation for an actual nuclear attack, highlights the risk of misunderstandings and technological errors escalating into full-scale war. By watching "WarGames," you gain a deeper understanding of the Cold War's atmosphere and the importance of diplomacy and communication in avoiding a devastating conflict.
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Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5
1.9
Step-by-step explanation:
The above is direct and inverse variation.A = kB/C -----------(1)
A=12
B = 3
C= 2
substitute A, B and C into equation (1).
12 = K × 3/2
12 = 3k/2
12×2 = 3k
3K = 24
dividing bothsides by 3
3K/3 = 24/3
K = 8
substitute K = 8 into equation (1)
A = 8B /C --------------(2)
Equation (2) is the equation connecting
A,B and C.
Finding B when A = 10 and C = 1.5
10 = 8B / 1.5
10× 1.5 = 8B
15 = 8B
Dividing bothsides by 8 :
B = 15/8
B = 1.875
B = 1. 9 ( approximately)
Find the value of x
please help
Please show work
- 7.4x = - 22.2
Answer:
divide both sides by -7.4
x=3
Answer:
divide -7.4 on both sides. the answer will be +3
Step-by-step explanation:
A craftsman wants to build this fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the area?
The Area of Trapezium is 50, 267 mm².
We have,
base 1 = 224 mm
base 2 = 77 mm
Height = 334 mm
Now, Area of Trapezium
= 1/2 (Sum of parallel side) x height
= 1/2 (224 + 77) x 334
= 1/2 x 301 x 334
= 50, 267 mm²
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the mean age of 8 people is 16 years. when mrs. hernandez's age is included, the mean age increases to 20. how old is mrs. hernandez?
Answer:
52
Step-by-step explanation:
8*16 = 128
8*20 = 180
180-128 =52
Rosa bought d drawings to and art show. After selling 14 of them she had 34 left. Identify the equation that represents this situation and the correct solution
Answer:
14+34=d hope this helps
add the equations
3x- y= -1
+ -3x + 3y =27
Answer:
2y=26, y=13
3x-(13)= -1, 3x=12, x=4
The area of a blackboard is 1 1 third square yards. A poster's area is 8 over 9 square yards. What is the unit rate of the blackboard's area to the poster's area?
Step-by-step explanation:
Given that,
The area of a blackboard is \(1\dfrac{1}{3}=\dfrac{4}{3}\ \text{yards}^2\)
The area of poster is \(\dfrac{8}{9}\ \text{yards}^2\)
We need to find the unit rate of the blackboard's area to the poster's area. So, it can be calcualted by dividing blackboard's area to the poster's area.
So,
\(\dfrac{\dfrac{4}{3}}{\dfrac{8}{9}}=\dfrac{4}{3}\times \dfrac{9}{8}\\\\=1.5\)
So, the rate of \(1.5\ \text{yard}^2\).
A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles. event a = drawing a brown marble on the first draw event b = drawing an orange marble on the second draw if two marbles are drawn from the jar, one after the other and not replaced, what is p(b|a) expressed in simplest form?
The probability of event A and event B IS 15/91.
What is the probability?
Probability determines the odds that a random event would occur. The odds lie between 0 and 1.
The probability of event A = number of brown marbles / total number of marbles
= 6/14
The probability of event B = number of orange marbles / total number of marbles -1
= 5/13
P(A and B) =6/14 x 5/13
= 30/182
= 15/91
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Answer:
B.) 5/13
Step-by-step explanation:
15/3=5
91/7=13
5/13
BRAINEST IS VERYYYY APPRECATED
A motel clerk counts his $1 and $10 bills at the end of a day. He finds that he has a total of 60 bills having a combined monetary value of $186. What is the system of equations that can be used to find the number of $1 bills, x, and the number of $10 bills, y, that he has? (1 point)
A. x+y=60
x+10y=186
B. x+y=186
10x+y=60
C.x+y=186
x+10y=60
D.x+y=60
10x+y=186
Answer:The motel clerk has 33 $1 bills and 18 $10 bills.
Step-by-step explanation:
Let the number of $1 bills = x, so then number of $10 bills is 51-x.From the problem description, you can write:x($1)+(51-x)($10) = $213 Simplify and solve for x.x+510-10x = 213-9x+510 = 213 Add 510 to both sides.-9x = -297 Divide both sides by -9x = 33 and 51-x = 51-33 = 18.
3. The system of equations for two liquid surge tanks in series is
A₁ dh'₁/dt = q'ᵢ - 1/R₁ h'₁, q'₁ = 1/R₁ h'₁
A₂ dh'₂/dt = 1/R₁ h'₁ - 1/R₂ h'₂ q'₂ = 1/R₂ h'₂
Using state-space notation, determine the matrices A,B,C, and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ , and the output variable is the flow rate deviation, q'₂.
The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.
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1. valerie paid $170 for an item that was originally priced at $550. what percent of
the original price did valerie pay? round your answer to the nearest tenth of a
percent.
Valerie paid 30.91% of the original price of an item.
For given question,
an item that was originally priced at $550.
Valerie paid $170 for an item.
Let she paid 'x' percent of the original price Valerie paid.
⇒ x percent of 550 = 170
⇒ (x/100) × 550 = 170
⇒ (x) × 5.5 = 170
⇒ x = 30.91 %
Therefore, Valerie paid 30.91% of the original price of an item.
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A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 6.5 inches and standard deviation of 0.5 inches. If a sample of 46 items are chosen at random, what is the probability the sample's mean length is greater than 6.3 inches? Round answer to four decimal places.
The probablity that the sample's mean length is greate than 6.3 inches is0.8446.
Given mean of 6.5 inches,standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event. It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
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A rope 24m long is divided into three pieces in a ratio 1:2:5. The length of the shortest piece in
metre is
Answer:
3 m
Step-by-step explanation:
sum the parts of the ratio, 1 + 2 + 5 = 8 parts
Divide the length by 8 to find the value of one part of the rope
24 m ÷ 8 = 3 m ← value of 1 part of the ratio
Thus the shortest piece is 3 m
The required length of the shortest piece is 3 meters.
Given that,
A rope 24m long is divided into three pieces in a ratio of 1:2:5. The length of the shortest piece in meters is to be determined.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Here,
let the required proportion is equal to x,
then,
x + 2x + 5x = 24
8x = 24
x = 3
Now the lengths
x = 3 meter
2x = 6 meter
5x = 15 meter
Thus, the required length of the shortest piece is 3 meters.
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what are the steps to evaluate an exponential expression
The steps to evaluate an exponential expression include:
Identify the base and the exponent in the expressionReplace the base with the value that you want to use.Use the exponent to determine how many times the base should be multiplied by itself.Perform the multiplication and simplify the expression.How to evaluate an exponential expression ?First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.
Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.
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FIRST TO GET RIGHT GETS BRAINLIEST.
Answer:
770
Step-by-step explanation:
So start by adding 140 + 70 and then you get 210 and then so you muliply 70*11 and you get 770. :D
Answer your answer and show all the steps that you used to solve this problem in the space provided use the 30° - 60° - 90° triangle theorem to find the answer
The value of x is 8 inches.
To find the value of x, we can use the property of similar triangles that states that the corresponding sides of similar triangles are in proportion. Specifically, we can set up the proportion:
4/10 = x/20
We can then cross-multiply to get:
4 * 20 = 10 * x
Simplifying this equation gives us:
80 = 10x
Dividing both sides by 10, we get:
x = 8
Therefore, the value of x is 8 inches.
In summary, we used the property of similar triangles and set up a proportion involving the corresponding sides of the two triangles. By cross-multiplying and simplifying, we were able to find the value of x.
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Complete Question:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.
The two triangles above are similar. Find the value of x. Be sure to explain your steps.
a researcher uses an anonymous survey to investigate the study habits of american college students by sending surveys to a randomly selected set of students. based on the data she obtains, the researcher finds that these students spend an average of 4.1 hours each week working on course material outside of class. for this study, the set of 56 students who returned surveys is an example of a . group of answer choices
In the given case the set of 56 students who returned surveys is an example of a sample
A sample would be the 56 students who responded to the surveys. A sample is a portion of the population that is chosen for a study in research. American college students would be the population in this scenario. The 56 students who returned the surveys were chosen at random for the sample by the researcher.
The researcher is attempting to guarantee that the sample is representative of the greater population of American college students by utilising a random selection process. The researcher discovered that these students spend an average of 4.1 hours per week working on course material outside of class based on the data collected from the sample. This is an example of a descriptive statistic that provides a summary of the information gleaned from the sample.
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A rectangular building ha a bae that i 255ft long, 255 feet wide, and the building i 42 ft tall. Find the unit for the volume of the building
The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.
The volume of the building will be calculated by the formula -
Volume = length × breadth × height
Thus, keeping the value of each component of building in the formula to find the volume of the building.
Volume of building = 255 × 255 × 42
Performing multiplication on Right Hand Side of the equation to find the value of volume
Volume of building = 2,731,050 feet³
Therefore, the volume of the building is 2,731,050 feet³.
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What’s the value of x
Answer:
x = 50/7, or x = 7 1/7
Step-by-step explanation:
Create and solve an equation of ratios, as follows:
5 x
--- = ----
7 10
Cross-multiplying, we get: 7x = 50, or x = 50/7, or x = 7 1/7
uppose that P(E) = 0.6. What can you say about P(E|F) when
(a) E and F are mutually exclusive?
(b) E ⊂ F?
(c) F ⊂ E?
Given that P(E) = 0.6, we can determine the conditional probability P(E|F) based on the relationship between events E and F.
a) If they are mutually exclusive, P(E|F) = 0
b) If E is a subset of F, P(E|F) = P(E)
c) If F is a subset of E, P(E|F) = P(E) / P(F).
(a) If E and F are mutually exclusive, then they cannot occur at the same time. In other words, if event F occurs, event E cannot occur, and vice versa. Thus, P(E|F) = 0, since the occurrence of F makes E impossible.
(b) If E is a subset of F, then every outcome in E is also an outcome in F. Thus, if F occurs, then E must also occur. In this case, P(E|F) is equal to P(E), which is 0.6.
(c) If F is a subset of E, then every outcome in F is also an outcome in E. In this case, P(E|F) can be determined using Bayes' theorem:
P(E|F) = P(F|E) * P(E) / P(F)
where P(F|E) is the probability of F given that E has occurred, and P(F) is the probability of F occurring. Since F is a subset of E, we can assume that P(F|E) = 1.
Thus, we have:
P(E|F) = P(E) / P(F)
Since we do not have information about the probability of F, we cannot determine the exact value of P(E|F) in this case. In summary, the value of P(E|F) depends on the relationship between events E and F.
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Breyelle is planning on purchasing a new sports-utility vehicle. The list price of the one she is most interested in buying is $32,000. This vehicle is expected to depreciate in value by 8.5% per year.
Which model could be used to calculate the daily depreciation for this vehicle?
V(t)=32,000(0.0233)^t
V(t)=32,000(0.9150)^t
V(t)=32,000(0.9767)t^t
V(t)=32,000(0.9998)^t
Answer:
V(t)=32,000(0.9767)t^t
Step-by-step explanation:
The correct model which could be used to calculate the daily depreciation for this vehicle is,
⇒ V (n) = 32,000 (0.915)ⁿ
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
Breyelle is planning on purchasing a new sports-utility vehicle.
Here, The list price of the one she is most interested in buying is $32,000.
And, This vehicle is expected to depreciate in value by 8.5% per year.
Hence, the daily depreciation for this vehicle is,
V (n) = 32,000 (1 - 8.5%)ⁿ
V (n) = 32,000 (1 - 0.085)ⁿ
V (n) = 32,000 (0.915)ⁿ
Thus, The correct model which could be used to calculate the daily depreciation for this vehicle is,
⇒ V (n) = 32,000 (0.915)ⁿ
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What relationship do the ratios of sin x° and cos yº share?
a. The ratios are both identical (12/13 and 12/13)
b. The ratios are opposites (-12/13 and 12/13)
c. The ratios are reciprocals. (12/13 and 13/12)
d. The ratios are both negative. (-12/13 and -13/12)
The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.
In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.
It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.
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find all abelian groups (up to isomorphism) of order 360
The abelian groups (up to isomorphism) of order 360 are:
1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.
How can we determine the abelian groups of order 360?To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.
First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.
In this case, we can form the following abelian groups of order 360:
C360: This is the cyclic group of order 360 itself.
C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.
These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.
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Which equation represents a line which is parallel to the line 7x-5y=-30?
Answer:
Y=7/5x+8
Is the answer to question don't ask me how I know I cheated
The equation y = 7x/5 + b represents a line which is parallel to the line 7x-5y=-30.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
We have an equation,
7x-5y=-30
Simplifying,
y = 7x/5 + 30/5
y = 7x/5 + 6.
The general formula of line parallel to a given line is,
y = 7x/5 + b, where b is the y-intercept of the line.
Therefore, y = 7x/5 + b is the required line.
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consider the probability experiment: a fair, six-sided, die is rolled three times. a. how many outcomes are in the sample space? b. what is the probability that all three flips are 2?
Given that each roll is independent and that the odds of rolling a 2 are 1/6, the probability of receiving three 2s in a row is 1/216.
a. We can apply the multiplication principle to determine how many outcomes there are overall in the sample space.
There are 666 = 216 possible outcomes in the sample space because there are six outcomes for each die roll and we are rolling the die three times.
b. As each die roll is independent of the others, there is a 1/6 chance that any particular roll will result in a 2.
Therefore, the probability of getting three 2's in a row is (1/6)(1/6)(1/6) = 1/216.
So the probability of all three rolls being 2 is 1/216.
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Rational Numbers are closed under Subtraction
a) True
b) False
Answer:
False not subtraction I thought it is division
Step-by-step explanation:
false lolollllllllllll