The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.
What is an expression that represents the total amount that Zoe paid?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.
The expression will be:
= x + (5% × x) + (15% × 1.05x)
= x + 0.05x + 0.1575x
= 1.2075x
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two half-cylinders of diameter 2 meet at a right angle in the accompanying figure. find the volume of the solid region common to both half-cylinders. (hint: consider slices parallel to the base of the solid.)
The volume of the solid region common to both cylinder is 8/3 when two half-cylinders of diameter 2 come together at a right angle.
Given that,
In the following figure, two half-cylinders of diameter 2 come together at a right angle.
We have to determine the solid region's common volume for the two half-cylinders. (Hint: Take into account slices that are parallel to the solid's base.)
We know that,
Using the Pythagoras theorem,
S²+x²=r²
Diameter=2
2r=2
r=1
S²+x²=1
S²=1-x²
S=√(1-x²)
[tex]\int\limits^1_0 {Area(x)} \, dx[/tex]
4[tex]\int\limits^1_0 {1-x^{2} } \, dx[/tex]
4(x-x³/3)₀¹
4(1-1/3)
4(2/3)
8/3
Therefore, The volume of the solid region common to both cylinder is 8/3 when two half-cylinders of diameter 2 come together at a right angle.
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Suppose a school has three periods (called 1, 2, and 3) during which a class can be scheduled. For each class, there are three variables. For example, for class A, there are variables XA1, XA2, and XA3. Setting XA2 = 1 represent scheduling class A during period 2. a. give a boolean expression that evaluates to 1 if and only if a is scheduled in at least one of the three periods.
The boolean expression that evaluates to 1 if and only if A is schedule in at least one of the three periods is [tex]x_{ A1}+x_{ A2} +x_{ A3}[/tex].
A logical assertion that can only be TRUE or FALSE is called a Boolean expression. As long as both sides of the expression have the same fundamental data type, boolean expressions can compare data of any kind. Data can be tested to check if it is more than, less than, or equal to other data.
An expression that may only be evaluated as true or false is called a boolean expression (after mathematician George Boole). Let's examine some examples in everyday language: Pink is one of my favorite colors. I'm apprehensive about programming computers. • It's entertaining to read this book.
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Solve -6 = a/-4 the a/-4 is in fraction form by the way
Answer:
a = 24
Step-by-step explanation:
1. Multiply all terms by the same value to eliminate fraction denominators
-6 = [tex]\frac{a}{-4}[/tex]
-4(-6) = -4 · [tex]\frac{a}{-4}[/tex]
2. Cancel multiplied terms that are in the denominator
-4(-6) = -4 · [tex]\frac{a}{-4}[/tex]
-4(-6) = a
3. Multiply the numbers
-4(-6) = a
24 = a
4. Move the variable to the left
24 = a
a = 24
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One column of numbers consists of 33, 58, and 17. When the digits of the numbers are added together, the result is 3 + 3 + 5 + 8 + 1 + 7 = 27, and when the digits of 27 are then added together, the end result is 2 + 7 = 9. If the same process is performed on the numbers in a second column, what can be concluded?.
If the final result of the second column is not 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
One column of numbers consists of 33, 58, and 17. When the digits of the numbers are added together, the result is 3 + 3 + 5 + 8 + 1 + 7 = 27, and when the digits of 27 are then added together, the end result is 2 + 7 = 9.
If the final result of the second column was not nine, the numbers in the first column would not be the same as those in the second column, because the second column comes from the sum of the digits of the first column.
Therefore, If the final result of the second column is not 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
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At a candy store, erika bought kilograms of cinnamon red hots and kilogram of gummy bears for. Meanwhile, irene bought kilograms of cinnamon red hots and kilograms of gummy bears for. What is the cost of one kilogram of each type of candy?.
The cost of one kilogram of each type of candy is 9 dollars per kilogram and 4 dollars per kilogram.
Given that,
Erika spent $21.00 at a candy store to purchase 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears. Irene spent $39.00 on 3 kilograms of gummy bears and 3 kilograms of cinnamon red hots.
We have to find how much would one kilogram of each kind of candy cost.
We know that,
Let's change the price of cinnamon red hots per kg to c and the price of gummy bears per kg to b.
3c+1b=21
3c+3b=39
By substitution method
-3c-b=-21 (Multiply one of the equation's terms by -1 to eliminate c.)
3c+3b=39
We get
2b=18
b=9 dollars per kilogram
To find c you can plug the value of b back into one of the equation above and 3c+9=21 which lead to 3c =12 so c=4 dollars per kilogram.
Therefore, the cost of one kilogram of each type of candy is 9 dollars per kilogram and 4 dollars per kilogram.
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What is the value of this expression when a = 4, b = -5, and c = -7?
(a + 26c)/(За)
HELPPPP PLEASE
the answer is C 6 1/6
a probability distribution has a mean of 22 and a standard deviation of 2. use chebychev's inequality to estimate the probability that an outcome of the experiment lies between 13 and 31. a) 0.9506 b) 0.9917 c) 0.0494 d) 0.0083 e) 0.2222 f) none of the above
Using Chebychev's inequality the probability shows an outcome of the experiment between 13 and 31 is equal to 0.9506.
As given in the question,
Mean 'μ' = 22
Standard deviation 'σ' = 2
Apply Chebychev's inequality we have,
P ( | X - μ | ≤ kσ ) ≥ 1 - (1/k²)
Where 'k' is the constant value.
Estimation of probability with outcome lies between 13 and 31 using Chebychev's inequality is :
P ( 13 < X < 31 )
= P ( 13 -22 < X - μ < 31 - 22 )
= P ( -9 < X - μ < 9 )
= P ( | X - μ |≤ 9)
= P [ |X - μ | ≤ (9/2) ×2 ]
= P( |X - μ | ≤ Kσ)
≥ 1 - ( 1/k²)
here k = 9/2
= 1 - (1 / (9/2)²)
= 1 - 4/81
= (81 -4) / 81
= 77/ 81
= 0.9506
Therefore, the probability for which outcome lies between 13 and 31 using Chebychev's inequality is equal to 0.9506.
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The mass of a white-tailed deer is about 1.4 times the mass of a cougar. The average mass of a white-tailed deer is 98 kg. Calculate the mass of a cougar. Start with an equation that includes a variable. show all work
Butterfly is 3 times Blossom's age. In 5 years, Butterfly will be 2 times Blossom's age. How old is Blossom now?
bag contains 9 real diamonds and 5 fake diamonds. if 9 diamonds are picked from the bag at random, what is the probability that all of them are real?
The probability that all of them are real is 0.01875 or 1.875%
If the diamonds are replaced after each draw:
The probability of drawing a real diamond is 9/14, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 5+9 = 14.
To find the probability of all 9 diamonds drawn being real, multiply 9/14 by itself 9 times. = 387420489/ 20661046784. This creates a probability of 387420489/ 20661046784. This cannot be reduced because there is no common factor. To express as a decimal, divide. 387420489/ 20661046784 = 0.01875. To turn this into a percent, multiply by 100. 0.01875*100 = 1.875
Hence, the probability that all of them are real is 0.01875 or 1.875%
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The top and bottom margin of a poter are 6 cm and the ide margin are each 4 cm. If the area of printed material on the poter i fixed at 380 quare centimeter, find the dimenion of the poter with the mallet area
The dimensions of the poster found having the smallest area is H = 35. 87 cm and W = 25.63 cm.
Explain the term rate change of area?We understand that we are attempting to find the minimum of both the area function because we are instructed to locate the smallest area.Let "W" represent the poster's overall width and "H" represent its overall height.Area A = H.W
Its printed material is either W - 4(2) or W - 8.
Its printed material is H - 6(2)
height = H - 12
The printed area is therefore (W - 8)(H - 12) = 380.
(W - 8)(H - 12) = 380
WH - 12W - 8H + 96 = 380
W(H - 12) - 8H = 284
W = (284 + 8H)/(H - 12)
Put the values in the area;
A(H) = H(284 + 8H)/(H - 12)
A(H) = (284H + 8H²)/(H - 12)
Differentiate with respect to H to find the rate change of area.
A'(H) = [(284 + 16H)(H - 12) - (284H + 8H²)(1)]/(H - 12)²
A'(H) = (284H - 3408 + 16H² - 192H - 284H - 8H²)/(H - 12)²
A'(H) = (8H² - 192H - 3408)/(H - 12)²
A'(H) = 8(H² - 24H - 426)/(H - 12)²
Put A'(H) = 0
8(H² - 24H - 426)/(H - 12)² = 0
Solving;
H = 35. 87 cm
Thus, W = 25.63 cm
Thus, the dimensions of the poster found having the smallest area is H = 35. 87 cm and W = 25.63 cm.
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Find the absolute extrema for the given function on the interval [15.6, 19.2). Write your answer in the form (x.f(x)). Round your answers to two decimal places. f(x) = In (12x^2 - 11x + 2)
Absolute Minimum: Absolute Maximum
the absolute extrema of the linear equation f(x) = 12x^2 -11x +2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).
What are the absolute extrema of a linear equation within a closed interval?
According to the functions theory, linear equations have no absolute extrema for all real numbers, but things are different for any closed interval as absolute extrema are the ends of linear function. Now we proceed to evaluate the function at each point:
Absolute maximum
f(- 8) = 12x^2 -11x +2
f(- 8) = 27
Absolute minimum
f(4) = - 3 · 4 + 3
f(4) = - 9
By means of functions theory and the characteristics of linear equations, the absolute extrema of the linear equation f(x) = 12x^2 -11x+2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).
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A health researcher conducted a survey and recorded the percentage of body fat of 20 randomly selected men from two different towns. Ten of the men surveyed were from Pythagoria and 10 of the men were from Bernoullia. The following statistical information was calculated from the researcher's findings.
Pythagoria Bernoullia
First Quartile 12 15
Second Quartile (Median) 16 19.5
Third Quartile 19 25
Based on these samples, what generalization can be made?
A.
Not enough information is provided to draw any of these conclusions.
B.
Pythagoria has men with higher body fat percentages than Bernoullia.
C.
The interquartile range of body fat percentages for Pythagoria is less than Bernoullia.
D.
At least half of the men from both towns have between 10 and 20 percent body fat.
Answer:
Step-by-step explanation:
C.
The effectiveness of a blood-pressure drug is being investigated.
An experimenter finds that, on average, the reduction in systolic blood pressure is 55.8 for a sample of size 29 and a standard deviation 7.9.
Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level).
Assume the data is from a normally distributed population.
Answer as a tri-linear inequality accurate to 3 decimal places.
A tri-linear inequality for the estimate of the drug that would lower a typical patient's systolic blood pressure (using a 90% confidence level) is; 53.3 ≤ x-bar ≤ 58.3.
Explain the term tri-linear inequality?Equal does not imply inequality. Tri signifies three. The range is defined in terms of inequalities by the tri-linear inequality.For the stated question-
Average of reduction in systolic blood pressure μ = 55.8.
Standard deviation s = 7.9.
Sample of size n = 29
The confidence interval is estimated as-
μ - t₀.₀₅(s/√n) ≤ x-bar ≤ μ + t₀.₀₅(s/√n)
Put the values-
55.8 - t₀.₀₅(7.9/√29) ≤ x-bar ≤ 55.8 + t₀.₀₅(7.9/√29)
On simplifying,
53.3 ≤ x-bar ≤ 58.3
Thus, a tri-linear inequality for the estimate of the drug that would lower a typical patient's systolic blood pressure (using a 90% confidence level) is; 53.3 ≤ x-bar ≤ 58.3.
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What is 3 divided by 80?
Answer: 3/80 = 0.0375
Another karaoke location, Sounds of the Sea, is charging $15 for 5 songs. Construct a graph to model the relationship between cost and number of songs.
The function that represent the proportional relationship between cost and number of songs is y = 3x and it's graph is attached below
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variableTo find the relationship between cost and number of songs, we can write a proportional relationship for this
y = mx
m = constant of proportionality
15 = m(5)
m = 15 / 5
m = 3
The constant of proportionality is 3
The function to represent the relationship between the cost and number of songs is
y = 3x
The graph of the function is attached below
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kyra's math instructor told the class to refer to the unit conversion charts in the textbook when completing the homework assignment. however, she discovered that these charts weren't in the assigned chapter. where will kyra most likely find the unit conversion charts in her math textbook?
Kylie will most likely find the unit conversion charts in the appendix of her math textbook.
The correct answer option is option C
What is an appendix?An appendix can be defined as a text that is added to the end of a book or an article which provides additional information that was best left as an addition or complement at the end rather than being included somewhere in the book or article, that is, appendix is an information supplementing the texts. The plural form of appendix is appendicitis.
Foreword: This is an introductory section preceding the main text of a book or other document, also known as a preface or introduction.
Introduction: An initial section of a book or article, which introduces the subject material.
Glossary: This is a list of terms in a particular domain of knowledge with their definitions.
Complete question:
Kylie's math instructor told the class to refer to the unit conversion charts in the textbook when completing the homework assignment. However, she discovered that these charts weren't in the assigned chapter. Where will Kylie MOST likely find the unit conversion charts in her math textbook?
A. Foreword
B. Introduction
C. Appendix
D. Glossary
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O A circle has a diameter of 8 meters. Find the approximate area of the circle. Use 3.14 for pi.
Answer:
The approximate area of the circle is:
50.24m²
Step-by-step explanation:
Circle area = 3.14 * (diameter/2)²
In this case:
Circle area = 3.14 * (8/2)²
Circle area = 3.14 * 4²
Circle area = 3.14 * 16
Circle area = 50.24 meters²
Suzy is competing in a long-distance au
bicycle race. In the first 6 hours, she completed 132 miles of the race. If she
plans to ride 7 hours per day, how many
days will it take for her to complete the
616-mile race at the same rate?
A 2
B 4
C 6
D 8
Rejecting the null hypothesis when it is true is called a ________ error, whereas not rejecting a false null hypothesis is called a ________ error.
a. Type II; Type I
b. Type I; Type II
c. minor; major
d. significant; nonsignificant
The correct option is b.Type I; Type II.
Rejecting the null hypothesis when it is true is called a type I error, whereas not rejecting a false null hypothesis is called a u type II error.
A type I error occurs when a null hypothesis that is true in the population is rejected. A false positive is an example of this type of error. A type II error occurs if a null hypothesis that is actually false in the population is not rejected. This type of error is known as a false negative.A type II error differs from a type I error in that a type I error rejects the null hypothesis when it is true (i.e., a false positive). The likelihood of making a type I error is equal to the level of significance set for the hypothesis test.
Thus, for the given question, option. b is the correct answer for the blanks in the question.
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the purpose of a short-term measurement is to substitute for a long-term measurement. for this purpose, which do you think is more relevant, the confidence interval or the prediction interval? explain.
Prediction interval is more relevant than confidence interval.
Given,
Short term measures;-
Short-term actions and choices undoubtedly serve as significant beginning points for both concrete accomplishments and symbolic commitments. Several short-term actions appear to have the best potential of moving in the direction of wise growth over the long run, taking into account the obstacles, strengths, and weaknesses that have been identified.
Long term measures;-
Long-Term Performance Measures refers to the performance indicators created and used by the Committee to assess the Company's performance in order to determine the number of shares of Common Stock that will be paid to the Participant at the conclusion of a Restriction Period.
Here,
Prediction intervals must take into consideration both the random variation of the individual values and the uncertainty in predicting the population mean. Consequently, a prediction interval is always larger than a confidence interval. Additionally, as the sample size grows, the prediction interval won't condense to a single value.
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There are 60 seconds in a minute and 60 minutes in an hour. How many seconds are in one hour?
Answer:
3600
Step-by-step explanation:
we just have to multiply 60 by 60.
if a situation is repeated again and again, the observed proportion of successful outcomes will tend to approach the theoretical probability that any one of the outcomes will be a success
The outcome of this question is determined by the number of alternative possibilities and their probability.
If there are only two conceivable outcomes, one of which is success and one of which is a failure, the theoretical chance of success is 50%. The theoretical probability of success is the sum of the probabilities of the two successful outcomes if there are three alternative outcomes.
If you know anything about probability, you're undoubtedly aware that the theoretical likelihood of any given result occurring in a given circumstance is always the same. Finally, the theoretical likelihood that any of the outcomes will be successful if a circumstance is repeated is the sum of the probabilities of each successful outcome divided by the entire number of alternatives.
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The correct question is-
What is the theoretical probability that any one of the outcomes will be a success if a situation is repeated again and again?
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Ben plays $119.00 to get his dog Sookie groomed if the sales taxes rate is 8.25% calculate the total cost Ben will pay
Total cost ben would pay for the dog will be $128.8175.
What is Percentage ?The proportion of value in relation to the original value is measured using the percentage concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage. Additionally, it is used in schools and colleges to show the grades that pupils have earned. A percentage formula can be used to assess the pupils' grades. In general, the definition of a percentage is any ratio of a value to the total value multiplied by 100. The percentage is denoted by the sign %.
Ben paid for dog = $119.00
Grooming to be done = 8.25% of $119.00
Total cost of grooming = $9.8175
Total cost after grooming for dog = $119.00 + $9.8175
= 128.8175 is the actual cost of dog.
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a regression was run to determine if there is a relationship between hours of tv watched per day (x) and number of situps a person can do (y). the results of the regression were:
The estimated number of situps is 31.486.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
Given that a= -1.24 and b=33.966, the regression equation is y= axe + b y= -1.24x + 33.966.
Here, "y" stands for the maximum number of situps an individual may perform, and "x" stands for the daily television viewing hours.
The estimated number of situps for a person who watches x=2 hours of TV is y=-1.24*2 + 33.966 y= -2.48 + 33.966 y= 31.486
Hence, The estimated number of situps is 31.486.
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1. From the window of one building, the angle of elevation to the top of a second building
is 41° and the angle of depression to the bottom is 54°. The buildings are 56 m apart.
a. How tall is the second building?
b. How high up is the window?
Answer:
a) the second building is 118.69 m tall
b) the height of the window from the ground is 70.077 m
Step-by-step explanation:
Attached is a sketch of the building. Look over the sketch before reading the explanation.
Use SOH CAH TOA.
Let [tex]O_{1}[/tex] be the height of the window from the ground.
Therefore we can say that [tex]O_{1}+O_{2}[/tex] is the height of the second building.
We can say that
[tex]O_{1}=tan(x_{1} )*A_{1}[/tex]
Therefore
[tex]O_{1}=tan(54)*56[/tex]
[tex]O_{1}=70.077[/tex]
[tex]O_{2}=tan(x_{2} )*A_{2}[/tex]
[tex]O_{2}=tan(41)*56[/tex]
[tex]O_{2} =48.68[/tex]
[tex]70.007+48.68=118.69[/tex]
type the correct answer in each box. use numerals instead of words. the zeros of the function f(x)=-(x+1)(x−3)(x+2) are -1, 3, and , and the y-intercept of the function is located at (0,).
zeros of function f(x)=-(x+1)(x−3)(x+2) are -1, 3, and -2 and it is located at ( 0, -1) , ( 0, 3) and ( 0, -2)
The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0.
according to the question
f(x)=-(x+1)(x−3)(x+2) are -1, 3, and -2
and it is located at
( 0, -1)
( 0, 3)
and ( 0, -2)
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Helppp I need an answer fast
Answer:6
Step-by-step explanation: PQRS is 2x the size of ABCD
A 2. 8 kg rectangular air mattress is 2. 00 m long, 0. 500 m wide, and 0. 100 m thick. What mass can it support in water before sinking?.
The mass that can rectangular air mattress can support in water before sinking is 97.2 kg
Consider the rectangular air mattress
The length = 2 meter
The width = 0.500 meter
The thickness = 0.100 meters
The volume = Length × width × thickness
The volume = 2 × 0.500 × 0.100
= 0.1 cubic meters
We know,
Total weight = Volume × Density × g
The density of water = 1000 kg/ meter square
Total mass = 0.1 × 1000 × 9.81
= 981 N
The the equation of mass will be
(2.8 + m) × 9.81 = 981
2.8 + m = 100
m = 100 - 2.8
m = 97.2 kg
Therefore, it will support 97.2 kg water before sinking
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2
52
3
5
4
47°
W
m/1 =
m/2 =
m/3=
m/4=
m25 =
Answer:55.9074
Step-by-step explanation: