The circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.
We are given that:
Length of the shorter arc forming an angle of 45° with the center = 22 cm
AB = 22 cm
C is the center of the circle.
We know that the length of the arc is calculated as:
Length of an Arc = θ × (π / 180) × r
22 = 45 × (3.14 / 180) × r
22 = 0.785 r
r = 22 / 0.785
r = 28.0255
Circumference = 2 π r
Circumference = 2(3.14) (28.0255)
C = 176 cm
Therefore, we get that, the circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.
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Which of the following mathematical relationships could be found in a linear programming model? (Select all that apply.)
(a) −1A + 2B ≤ 60
(b) 2A − 2B = 80
(c) 1A − 2B2 ≤ 10
(d) 3 √A + 2B ≥ 15
(e) 1A + 1B = 3
(f) 2A + 6B + 1AB ≤ 36
The mathematical relationships that could be found in a linear programming model are:
(a) −1A + 2B ≤ 60
(b) 2A − 2B = 80
(e) 1A + 1B = 3
Explanation:
Linear programming involves optimizing a linear objective function subject to linear constraints. In a linear programming model, the objective function and constraints must be linear.
(a) −1A + 2B ≤ 60: This is a linear inequality constraint with linear terms A and B.
(b) 2A − 2B = 80: This is a linear equation with linear terms A and B.
(c) 1A − 2B2 ≤ 10: This relationship includes a nonlinear term B2, which violates linearity.
(d) 3 √A + 2B ≥ 15: This relationship includes a nonlinear term √A, which violates linearity.
(e) 1A + 1B = 3: This is a linear equation with linear terms A and B.
(f) 2A + 6B + 1AB ≤ 36: This relationship includes a product term AB, which violates linearity.
Therefore, the correct options are (a), (b), and (e).
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how many times is the letter f (any case) in the following? if fred is from a part of france, then of course fred's french is good.
The count of letter f (any case) in ' if fred is from a part of france, then of course fred's french is good', is 8.
A word, phrase, or sentence in which no letter of the alphabet appears more than once is known as a heterogram (from the prefix hetero-, meaning "different," and the suffix -gram, meaning "written"). The same idea has also been denoted by the phrases isogram and nonpattern word.
Language on Vacation: An Olio of Orthographical Oddities, written by Dmitri Borgmann in 1965, mentions the idea, however he refers to it as an isogram. Borgmann asserts that he "introduced" the term "isogram" in a 1985 essay. Although he uses the term "isogram" in the paper itself, he also offers the name "asogram" to prevent confusion with lines of constant value like contour lines.
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Which of the following terms describe the relationship between the number of notes and each syllable of a text and which do not?
-syllabic
-melismatic
-neumatic
The terms syllabic, melismatic, and neumatic are all related to the number of notes in relation to each syllable of a text. Syllabic means that each syllable of the text is sung to one note.
This is the simplest type of setting for text to music. In contrast, melismatic means that each syllable of the text is sung to many notes, creating a more intricate and ornamental melody. Neumatic is somewhere in between syllabic and melismatic, where each syllable is sung to a few notes, but not as many as in a melismatic setting.
Syllabic, melismatic, and neumatic all describe the relationship between the number of notes and each syllable of a text.
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Did you mean: a dolphin was swimming 28 meters below the ocean's surface it changed its depth to avoid a predator and ended up 21 meters below the surface
Answer:
yes
Step-by-step explanation:
What is 5 times 10 pls help me
Answer:
50
Step-by-step explanation:
something called a calculator
Identify all values of x that make the equation true
This equation has 2 solutions
x=-9
x=1
solving for SR.. help me please
A) 8cm
Step-by-step explaination:
TR = 4 + x
Also,
TR = 8 + (2x - 16)
Therefore,
4 + x = 8 + 2x - 16
4 + x = (8 - 16) + 2x
4 + x = -8 + 2x
4 + 8 = 2x - x
12 = x
SR = 2x - 16
= 2(12) - 16
= 24 - 16
= 8
Bellrose Bank charges a monthly maintenance fee of $17 and a check-writing fee of $0.05 per
check. Last year, Patricia wrote 445 checks from her account at Bellrose. What was the total of all
fees she paid on that account last year?
The amount Patricia paid as fees on on the account last year was $226.25
What makes up the total cost for Patricia?
Patricia pays a fixed monthly maintenance fee of $17 for every month last year, which means that the total annual maintenance fee last year is the monthly maintenance fee multiplied by 12 months, whereas, the annual check-writing fee is the check-writing fee per check multiplied by the number of checks issued last year.
total annual maintenance fee=monthly maintenance fee *12
monthly maintenance fee=$17
total annual maintenance fee=$17*12
total annual maintenance fee=$204.00
annual check-writing fee= check-writing fee per check*number of checks
annual check-writing fee=$0.05*445
annual check-writing fee=$22.25
total fees paid by Patricia last year=$204.00+$22.25
total fees paid by Patricia last year=$226.25
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a star is inside a square of side length 8cm the star covers 40% area of the square The same star is placed inside a rectangle with width 8cm the length of the rectangle is 60% longer than the width calculate the percentage of the rectangle that the star covers
Answer:
Step-by-step explanation:
The area of the square is:
A = side^2 = 8^2 = 64 cm^2
Since the star covers 40% of the area of the square, its area is:
a_star = 0.4 * 64 = 25.6 cm^2
Let the width of the rectangle be 8 cm. Then, the length of the rectangle is:
l = 8 + 0.6*8 = 12.8 cm
The area of the rectangle is:
A_rect = wl = 812.8 = 102.4 cm^2
To calculate the area of the star inside the rectangle, we need to know the dimensions of the rectangle that are covered by the star. Since the star is inside a square of side 8 cm, its maximum width and height are both 8 cm. Therefore, the maximum area of the star inside the rectangle is:
a_star_max = 8*8 = 64 cm^2
However, this area is larger than the area of the star itself, which is 25.6 cm^2. Therefore, the area of the star inside the rectangle is 25.6 cm^2.
The percentage of the rectangle that the star covers is:
% coverage = (area of star inside rectangle / area of rectangle) * 100
= (25.6 / 102.4) * 100
= 25%
Therefore, the star covers 25% of the rectangle.
And this one help pleaseee
Answer:
m∠5 = 54
Step-by-step explanation:
m∠1 + 126 = 180
m∠1 = 54
m∠1 = m∠5
m∠5 = 54
Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of breast cancer. The researchers studied 1813 people over the course of 5 years. During this 5-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of breast cancer over the 9-year period. After their analysis, the researchers concluded that the happy individuals were less likely to experience breast cancer. (a) What type of observational study was this? Explain. (b) What is the response variable? What is the explanatory variable?
The answers to all the subparts of the question are shown below.
What is an observational study?An observational study is used in fields such as epidemiology, social sciences, psychology, and statistics to draw conclusions from a sample to a population where the independent variable is not under the researcher's control due to ethical concerns or logistical constraints. One common observational study is about the potential effect of a treatment on subjects, where the assignment of subjects to a treated versus a control group is beyond the investigator's control.(A) What type of observational study was this?
Because all information about the individuals was gathered at one point in time, this was a cross-sectional study.(B-1) What is the response variable?
Whether or not the woman has IDC breast cancer is the response variable. The qualitative response variable is used.(B-2) What is the explanatory variable?
Whether or not the woman has IDC breast cancer is the explanatory variable.Therefore, the answers to all the subparts of the question are shown.
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The cost of a bicycle wheel was $62 last week. This week, the cost rose to $79 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
the percentage increase is 27.4%
Step-by-step explanation:
To find the percentage increase, we can use the formula:
(New cost - Old cost) / Old cost x 100% = Percentage increase
(79 - 62) / 62 x 100% = 27.41%
The percentage increase is 27.41%. Rounded to the nearest tenth of a percent, the percentage increase is 27.4%
Difference of $62 and $79 is 24.1%
62 - 79/((62 + 79)/2) = 17/70.5 =
0.24113475177305 x 100 = 24.113475177305%
the distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 477 and a standard deviation of 35.according to the standard deviation rule, approximately 95% of the students spent between $ and $ on textbooks in a semester
Approximately 95% of the students spent between $407 and $547 on textbooks in a semester, based on the standard deviation rule and the given mean and standard deviation.
To estimate the range of money spent by students on textbooks in a semester using the standard deviation rule, we can utilize the concept of the empirical rule.
According to the empirical rule, in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
Given that the mean is $477 and the standard deviation is $35, we can calculate the range for approximately 95% of the students.
One standard deviation from the mean is $477 ± $35, which gives us a range of $442 to $512.
Two standard deviations from the mean is $477 ± (2 × $35), which gives us a range of $407 to $547.
Therefore, Approximately 95% of the students spent between $407 and $547 on textbooks in a semester, based on the standard deviation rule and the given mean and standard deviation.
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A fish is swimming at a constant rate toward the ocean floor. The equation y = -7x - 3 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x s represents of seconds the fish has been swimming. Which statement best describes the depth of the fish, given this equation.
The statement that best describes the depth of the fish, given this equation, is this: C. From a starting position of 3 meters below sea level, the fish is descending 7 meters per second.
The best descriptionThe first description of this statement should indicate the depth from which the fish descends. From the equation, y is equal to -7x -3. The minus in this case is indicative of descent.
7 is the rate at which the fish travels with respect to time and 3 is indicative of the distance from sea level and the starting point from which the fish moves.
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Samir's curtain company is making curtains for a local hotel. He wants each curtain to be 36 inches long. At the fabric store, fabric is sold by the foot. If Samir's curtain company wants to make 72 curtains, how many feet of fabric will he need?
Answer:
Which two elements of drama divide the play and indicate shifts in location or scenery?
dialogue
act
character
monologue
scene
Step-by-step explanation:
The following table shows values of In x and in y. In x 1.10 2.08 4.30 6.03 In y 5.63 5.22 4.18 3.41 The relationship between In x and In y can be modelled by the regression equation In y = a ln x + b.
The relationship between In x and In y can be modelled by the regression equation In y = a ln x + b. where a = -0.4557, b = 7.0459,
In x 1.10 2.08 4.30 6.03
In y 5.63 5.22 4.18 3.41
The relationship between In x and In y can be modeled by the regression equation In y = a ln x + b.
Here, we need to calculate the value of a and b using the given table. For that, we need to calculate the value of 'a' and 'b' using the following formulae:
a = nΣ(xiyi) - ΣxiΣyi / nΣ(x^2) - (Σxi)^2
b = Σyi - aΣxi / n
where n is the number of observations.
In the above formulae, we will use the following notations:
xi = In x, yi = In y
Let's calculate 'a' and 'b':
Σxi = 1.10 + 2.08 + 4.30 + 6.03= 13.51
Σyi = 5.63 + 5.22 + 4.18 + 3.41= 18.44
Σ(xi)^2 = (1.10)^2 + (2.08)^2 + (4.30)^2 + (6.03)^2= 56.4879
Σ(xiyi) = (1.10)(5.63) + (2.08)(5.22) + (4.30)(4.18) + (6.03)(3.41)= 58.0459
Using the above formulae, we get,
a = nΣ(xiyi) - ΣxiΣyi / nΣ(x^2) - (Σxi)^2= (4)(58.0459) - (13.51)(18.44) / (4)(56.4879) - (13.51)^2= -0.4557
b = Σyi - aΣxi / n= 18.44 - (-0.4557)(13.51) / 4= 7.0459
Thus, the equation of the line in the form:
In y = a ln x + b
In y = -0.4557 ln x + 7.0459.
Hence, a = -0.4557, b = 7.0459, and the regression equation In y = a ln x + b.
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$10,000 for 5 years at 4% interest
Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
As given in the question,
Simple Interest:
The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.
Principal amount:
Principal amount is the money that is taken as loan or borrowed.
Formula of Simple Interest:
Simple interest = Principal amount × Rate × Time
Since,
Principal amount = $10,000
Rate = 4% per year
Time = 5 years
Then,
Simple interest = 10,000 × 4 × 5
Simple interest = $ 12000
Total value after 5 years = $ 12000
Principal amount = $ 10000
Interest Earned = (Total value) - (Principal amount)
Interest Earned = $ 12000 - $ 10000
Interest Earned = $ 2000
Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
The complete question is:
Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?
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Za 30 dag żurawiny zapłacono 9,75zł. Oceń prawdziwość każdego zdania.
Step-by-step explanation:
Odpowiedź:
9.75zł :3 = 3.25zł
3.25zł x 4 = 13zł - Prawda
3.25zł x 10 = 32.50zł - Prawda
Liczę na najlepsze.
The map shows the locations of several different places. Each unit on the grid represents 1 block. Mr. Johnson wants to open a fruit stand, but he wants it to be at least 3 blocks from any of the other places shown on the map. Select the locations where Mr. Johnson could open his fruit stand. Check all that apply.
a. (-4,4)
b. (2,1)
c. (-4,0)
d. (-1,-2)
Recently, a certain bank offered a 10 -year CD that earns 2.97% compounded continuously. Use the given information to answer the questions. (a) If $10,000 is invested in this CD, how much will it be worth in 10 years? approximately $ (Round to the nearest cent.)
If $10,000 is invested in a 10-year CD that earns 2.97% interest compounded continuously, it will be worth approximately $13,522.18 after 10 years.
In continuous compounding, the formula to calculate the future value (FV) of an investment is given by the equation FV = P * e^(rt), where P is the principal amount, r is the interest rate, and t is the time in years. Given that $10,000 is invested for 10 years at an interest rate of 2.97% (or 0.0297 in decimal form), we can calculate the future value as follows:
FV = $10,000 * e^(0.0297 * 10)
Using a scientific calculator or an online tool, we find that e^(0.297) is approximately equal to 1.344392. Therefore:
FV = $10,000 * 1.344392 ≈ $13,443.92
Rounding this amount to the nearest cent, the investment in the 10-year CD will be worth approximately $13,522.18 after 10 years.
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How many of the first million positive integers share no common factors greater than 1 with 2020
9514 1404 393
Answer:
396,040
Step-by-step explanation:
Factors of 2020 are 2, 5, 101.
There are 1,000,000 / 1010 = 990 multiples of 2 and 5 and 101.
There are 1,000,000 / 505 -990 = 990 multiples of 5 and 101 only.
There are 1,000,000 / 202 -990 = 3,960 multiples of 2 and 101 only.
There are 1,000,000 / 10 - 990 = 99,010 multiples of 2 and 5 only.
There are 1,000,000 / 101 -990 -990 -3960 = 3,960 multiples of 101 only.
There are 1,000,000 / 5 -990 -990 -99,010 = 99,010 multiples of 5 only.
There are 1,000,000 / 2 -990 -3960 -99,010 = 396,040 multiples of 2 only.
So, the total number of multiples of any factor of 2020 is ...
990 +990 +3960 +99,010 +3960 +99010 +396040 = 603960
Then the number of integers in the first million that do not share any common factors greater than 1 with 2020 is ...
1,000,000 -603,960 = 396,040
What is the rule of SAS criteria?
We have defined the criteria for SAS congruency of triangles.
What is SAS?
The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."
According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.
Hence, we have defined the criteria for SAS congruency of triangles.
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Which equation has only x=3 and x = -3
Answer:
/x/=3 then x value has 3 and -3
Answer:
The required equation has only two solution x = 3 and x = -3 is x2 -9
Step-by-step explanation:
List 2 possible solutions for the inequality x < 9.
Answer: Any number less than 9.
Step-by-step explanation: The inequality is x is less than 9, that’s what < means, so you can say x is 8, 7, 6, 6.9, etc, x is anything less than 9.
City A had a population of 175,000 residents in 2018. The population is increasing at a rate of 10% per year. City B has a population that can be modeled B(t) = 350,000(0. 97)t where t represents the number of years since 2018.
What is the initial population of City A?
What is the growth rate of City A?
What function model for the population of City B?
Does the model for B(t) represent an exponential growth or decay?
The initial population of City A is 175,000.
What is the growth rate of City A?The growth rate of City A is 10%.
What function model for the population of City B?The function model for the population of City B is:B(t) = 350,000(0.97)t
Does the model for B(t) represent an exponential growth or decay?The model for B(t) represents an exponential decay, as the base (0.97) is less than 1.Explanation:Given,The initial population of City A was 175,000 in 2018.The growth rate of City A is 10% per year.
Therefore,The population of City A after n years can be represented as:P(n) = 175,000(1 + 0.1)n
Now,The function model for the population of City B is:B(t) = 350,000(0.97)t where t represents the number of years since 2018.The model for B(t) represents an exponential decay, as the base (0.97) is less than 1.
So, the initial population of City A is 175,000.
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The two parallelograms in the sketch below are congruent. Which sequence exhibits their congruence? A reflection across the y-axis followed by a translation 10 units left A reflection across the x-axis followed by a translation 10 units up A reflection across the y-axis followed by a translation 10 units right A reflection across the x-axis followed by a translation 10 units left
A reflection across the y-axis followed by a translation 10 units right
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the z-scores first, and then use those to calculate the probability.
For an a normally distributed the length of a pregnancy, with mean of 280 days and a standard deviation of 13 days,
a) the probability that he was NOT the father is equals to the 0.9762.
b) The probability that he could be the father is equals the 0.0238.
We have an expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed. Let variable X has normal distribution, Mean, μ = 280 days
standard deviations, σ = 13 days
An alleged father was out of the country from 240 to 306 days before the birth of the child. So, the variable value varies X < 240 or X> 306. Using Z-Score formula for normal distribution,
\(z= \frac{x -μ}{σ}\)
For x = 240
=> z =( 240 - 280)/13
= -40/13 = - 3.07
For x = 306
=> z = (306 - 280)/13
= 26/13 = 2
a) Probability that he not be the father , P ( 240< x < 306) or P(E)
= \( P ( \frac{240 - 280}{13 }< \frac{x - \mu}{\sigma} < \frac{306 - 280}{13})\)
= P (- 3.07 < z < 2 )
= P( x< 2) - P(z< - 3.07)
Using the normal distribution table value of probabilities for z < 2 and z< - 3.07 are determined, = 0.9762
= P(240<x <306)
b) Probability that he could be the father,
\(P( \bar E) \) = 1 - P(E)
= 1 - 0.9762
= 0.0238
Hence, required value is 0.0238.
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Mr. Hunt gave out award ribbons to everyone who made honor roll. An image of the award ribbon is shown on the plane below. The award ribbon was pink and had an image of the school's logo
covering part of the ribbon. In the diagram, each grid square measures 1 inch by 1 inch.
The total area of the ribbon is equals to 46 sq. inches with a 4 square inches of school logo in between.
What is a Quardilateral ?The four-sided polygonal shape known as a quadrilateral has four edges and four corners. The Latin words quadri, a variation of four, and latus, meaning "side," were used to create the term.
Its sides are AB, BC, CD, and DA.There are four of them: Indicators A, B, C, and DThe angles are ABC, BCD, CDA, and DAB.Angles A and B are near one other.The polar opposite angles are A and C.They are the opposing parties, AB and CD.The neighboring sides are ABC.A 4-sided planar figure is called a quadrilateral. The following are some crucial characteristics of quadrilaterals:There are 4 vertices, 4 angles, and 4 sides in every quadrilateral.Its inner angles add up to 360 degrees.In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.
The total area of the ribbon = area of the top square + area of the bottom trapizium
Area of the square = 4*4 = 16 sq. inches
Area of the trapizium = (1/2)*(sum of parallel sides)*height = (1/2)*(4+8)*5 = 30 sq. inches.
The total area of the ribbon is equal to 30 + 16 = 46 sq. inches with a 4 square inches of school logo in between.
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Which expression is equivalent
Answer:
the first one
Step-by-step explanation:
A code ue for 1 for A, 2 for B, 3 for C and o on upto 26 for Z. Coded word are written without pace to confue the enemy o 18 could be AH or R. Decode the following meage
The code 1814151418 decodes to RADE using a simple substitution cipher, where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which is the code that maps each letter to a number
The code provided indicates that each number corresponds to a letter in the alphabet. Since 1 is A, 2 is B, and so on, the code 1814151418 would decode as RADE. This is an example of a simple substitution cipher, a type of encryption where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which in this case is the code that maps each letter to a number. Knowing this, it is a simple task to decode any message that has been encrypted with this code.
The code 1814151418 decodes to RADE using a simple substitution cipher, where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which is the code that maps each letter to a number
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