The area of the sector is evaluated to be equal to 220 square centimeters.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius and π = 22/7.
We have the angle of the sector = 175° and radius = 12 cm, hence the area of the sector is calculated as follows:
(175°/360°) × 22/7 × 12 × 12
we simplify by division and multiplication
(35/72) × 22/7 × 12cm × 12cm
{35/7 = 5 and 72/12 = 6}
(5/6) × 22 × 12cm²
{12/6 = 2}
5 × 22 × 2cm²
220 cm².
Therefore, the area of the sector is evaluated to be equal to 220 square centimeters.
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2 = -6/5s how to solve this
PLS. I NEED THE ANSWER ASAPPPPPPP
Write an equation of a line using slope-intercept format goes through the point (4,2) and is parallel to y = 1/2x - 3
The required equation of the line passing through (4,2) and parallel to y = 1/2x - 3 is y = 1/2x.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the given line,
y = 1/2x - 3
m = 1/2
The slope of the parallel lines is always equal
Now, the Equation of the parallel line passing through the point (4, 2) is given as
y - y₁ = m (x - x₁)
y -2 = 1/2(x - 4)
y = 1/2x
Thus, the required equation of the line passing through (4,2) and parallel to y = 1/2x - 3 is y = 1/2x.
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If you add Natalie's age and Fred's age, the result is 41. If you add Fred's age to 4 times Natalie's age, the result is 80. Write and solve a system of equations to find how old Fred and Natalie are
HCF of 183 260 and 2 900 898
The HCF of the numbers is 1078
How to determine the HCF of the numbersFrom the question, we have the following parameters that can be used in our computation:
183260 and 2900898
Next, we factorize each number
This is represented as
183260 = 1078 * 170
2900898 = 1078 * 2691
The common factor above is
Comon factor = 1078
Hence. the HCF is 1078
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please help me it’s overdue Which is different?
o Solve
3
x
O Solve
12
8
O Find x so that 3:x and 12:8 are equivalent.
O Find x so that 3:12 and x:8 are equivalent.
12 3
X
Find "both" answers
The answer to the "different" question is x =
h
Answer:
Step-by-step explanation:
x = 24
The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.
Which of the following is the best interpretation of the standard deviation of the residuals?
A. The typical arm span is 161 centimeters.
B. The typical foot length is 16.1 centimeters.
C. The typical distance between the observed and predicted arm spans is 1.61 centimeters.
D. The typical distance between the observed and predicted foot lengths is 1.61 centimeters.
Therefore , the solution of the given problem of standard deviation comes out to be the typical distance between the observed and predicted foot lengths is 1.61 centimeters.
Definition of standard deviationVariance is a measure of difference used in statistics. The average variance between the data and indeed the mean is calculated using the mathematical formula of that figure. By comparing each data point's value to the mean, it incorporates all data points into its computations, unlike some other number measures of variability.
Here,
D. The typical distance between the observed and predicted foot lengths is 1.61 centimeters.
The standard deviation of the residuals measures the typical distance between the observed values and the predicted values (based on the regression line).
In this case, the regression analysis is for foot length and arm span, and the standard deviation of the residuals tells us about the typical distance between the observed foot lengths and the predicted foot lengths based on the regression line.
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Two points on a line are (10,55) and (15,82.5). what is the slope of the line
A Committee Consists of 5 members is to be formed out of 6 men and 4 women. How many types of Committes Can be formed so that at least 2 women are always there?
Answer:
2
Step-by-step explanation:
4/2 = 2 therefore 2 women will be in two committies.
According to the Centers for Disease Control
and Prevention, kids should get
at least 10 minutes of exercise each day
at least 30 minutes of exercise each day
at least 60 minutes of exercise each day
Dat least 3 hours of exercise each day
According to the Centers for Disease Control
and Prevention, kids should get C) at least 60 minutes of exercise each day.
What's exerciseExercise is a movement activity that has an important role for health. With exercise, one's body becomes healthier and stronger. Not only maintaining physical health, exercise also affects spiritual health.
The aim of exercise is to improve one's health. In addition to improving physical fitness, exercise can also improve and improve the performance of the human brain so that it can work more optimally. Therefore, exercise is considered to be able to increase one's self-confidence.
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Mr. Green gave his students a biology test last week. Here are the test scores for each of the eleven students. Complete the grouped frequency distribution for the data. In the distribution, the frequency of a class is the number of test scores in that class. (Note that we are using a class width of 6.)
The grouped frequency distribution for the data is shown below.
What is grouped frequency distribution ?A grouped frequency distribution is a way of summarizing and organizing raw data into a more manageable and meaningful form. The data is divided into intervals or "classes", and the number of data points that fall into each class is counted and recorded as the frequency of that class. This allows for easier interpretation and comparison of the data, as well as identifying patterns or trends. The grouped frequency distribution is commonly displayed in a table or a histogram.
Given that,
79, 85, 71, 83, 78, 67, 70, 87, 81, 86, 74, 67, 68, 76, 66, 72, 76, 80
Now, arranging the given data in ascending order,
66, 67, 67, 68, 70, 71, 72, 74, 76, 76, 78, 79, 80, 81, 83, 85, 86, 87
The grouped frequency distribution for the data:
Test Scores Frequency
65.5 - 71.5 6
71.5 - 77.5 4
77.5 - 83.5 5
83.5 - 89.5 3
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Find a linear equation who’s graph is the straight line with given properties
(1,-8) and (-1,-1)
Answer:
y=-7/2x-9/2
Step-by-step explanation:
Find the volume of the figure. Express answers in terms of pi then round to the nearest whole number.
Answer:
Below
Step-by-step explanation:
Volume of a cylinder = area of end X height = pi r^2 * h
r = 4 in h = 10 in
volume = pi (4)^2 * 10 = 160 pi in^3 or ~ 503 in^3
Answer:
160π in.³
Step-by-step explanation:
Get the circle area then multiply for the height. In the end, devide the result by 3,14 (π).
π* . r² 50,24 . 10*
π* . 4² 502,40 in.³ (cylinder volume)
50,24 (circle area)
obs: 502,4 leads you to a non-comma π result, considering π as 3,14. If you round, the correct way will be transforming into 502. But 502/3,14 is equal to 159,87..., infinite non-repetitive numbers.
Result in π = 160π* in.³
r - circle radius
10* - height
π* - 3,14 (Used that way)
b) Write the number in scientific notation:
2,150,000 =
Answer:
2.15 * 10⁶
Step-by-step explanation:
1,000,000= 1 * 10⁶
2,150,000= 2.15 * 10⁶
Answer:
The answer is 2.15×10 power 6How do we know sampling distribution is normal? Sample proportions and sample means
NEED HELP ASAP!!!!
The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 21 salespeople using Hamiltons method given the information below
Using Hamilton's method of apportioning, 21 salespeople can be assigned in the table in the following order:
2, 5, 6, 8.
What do you mean by Hamilton's method of apportioning?The approach that now bears his name was first proposed by Alexander Hamilton. Congress endorsed his approach in 1791, but President Washington rejected it. Later, in 1852, it became widely used until 1911. He starts by calculating the precise number of items that each group needs.
Since in the interested question it's about salesperson assigned, we’ll use the language of shift and hours, so we can determine how many salespersons each shift should get.
Now total no. of customers given = 125 + 305 + 439 + 515
= 1375
Now total no of salesperson available = 21.
So, the divisor = 1375/21
= 65.47
Now using Hamilton's method when we divide the average customers per shift by the divisor, we get the no. of salesperson assigned.
So, the salesperson assigned are:
Morning = 125/65.47
= 2
Midday = 305/65.47
= 5
Afternoon = 430/65.47
= 6
Evening = 515/65.47
= 8 (Decimals rounded according to Hamilton's principle)
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You owe $488.32 on your credit card. Because you have not paid your bill on time, you have to add a past due charge of $29, an over limit fee of $50, and a service charge of 11% of the amount owed on the credit card (without the past due charge and over limit fees). If you wish to send a check for the full amount immediately, how much should you write the check for? Round your answer to the nearest cent, if necessary.
if the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution, what is the probability that the service time will be less than or equal to 6 minutes? a. 0.451 b. 0.549 c. 0.017 d. 0.632
Answer: If the service rate is 6 customers per hour, the mean service time can be calculated as 1/6 = 0.1 hours or 6 minutes. The negative exponential distribution is commonly used to model the service time distribution in queuing theory. The cumulative distribution function (CDF) of the negative exponential distribution is given by:
F(x) = 1 - e^(-λx)
where λ = 1/μ, where μ is the mean service time (in this case, μ = 0.1 hours or 6 minutes).
So, the probability that the service time will be less than or equal to 6 minutes can be calculated as:
F(6) = 1 - e^(-0.1 * 6) = 1 - e^(-0.6) ≈ 0.5488
So, the answer is approximately 0.549, which is closest to option (b).
Step-by-step explanation:
The area of square field is 100 sqm. Find the perimeter of the square.
The perimeter of the square is 40m
How to determine the value of the perimeterThe formula for calculating the area of a square is given as;
A = a²
Given that;
A is the area of the squarea is the length of the side of the squareSubstitute the value
100 = a²
Find the square root of both sides
a = 10m
The formula for the perimeter of a square is expressed as;
Perimeter = 4a
Substitute the value into the formula;
Perimeter = 4(10)
expand the bracket
Perimeter = 40 m
Hence, the value is 40 m
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Three classes ordered lunch from a restaurant. In one class 5/6 of the children ordered hamburger. In the other class 2/4 ordered hot dogs. 1/2 of the other class ordered chicken wings. What is the total number of children that ordered sandwiches?
The number of children who ordered hamburgers from class A = ( 5/6 )A , where A is the total number of students in the class A
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of students in class A = A
Let the number of students in class B = B
Let the number of students in class C = C
Now , the equation will be
The number of students who ordered hamburgers is = ( 5/6 )A
The number of students who ordered hot dogs is = ( 2/4 )B
The number of students who ordered hot dogs is = ( 1/2 )B
The number of students who ordered chicken wings is = ( 1/2 )C
Hence , the number of students who ordered hamburgers , hot dogs and chicken wings are ( 5/6 )A , ( 1/2 )B and ( 1/2 )C respectively
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Ellen spends all of her free time surfing. Today she was out on the waves for 8.3 hours. That is 182% more time than yesterday. How many hours did she spend surfing yesterday?
Round your answer to the nearest tenth.
Answer:
15.11
Step-by-step explanation:
first you have to change 182% to a decimal (1.82) then multiply it by the number of hours (8.3) then you get your answer 15.106. last round it to the nearest tenth (15.106) and you get 15.11
Linear Programming Examples
A Diet Example
Breathtakers, a health and fitness center, operates a morning fitness program for senior citizens. The program includes aerobic exercise, either swimming or step exercise, followed by a healthy breakfast in the dining room. Breathtakers’ dietitian wants to develop a breakfast that will be high in calories, calcium, protein, and fiber, which are especially important to senior citizens, but low in fat and cholesterol. She also wants to minimize cost. She has selected the following possible food items, whose individual nutrient contributions and cost from which to develop a standard breakfast menu are shown in the following table:
The dietitian wants the breakfast to include at least 420 calories, 5 milligrams of iron, 400 milligrams of calcium, 20 grams of protein, and 12 grams of fiber. Furthermore, she wants to limit fat to no more than 20 grams and cholesterol to 30 milligrams.
Therefore , the solution of the given problem of linear equation comes out to be the decision variables x1, x2, x3, and x4 must be non-negative.
What exactly is a linear equation?The formula y=mx+b is used to draw a simple regression graph. The inclination is B, and the y-intercept is m. It is frequently referred to as a "simple algorithm incorporating many factors" even though the section before it includes independent parts. Bivariate linear equations only contain two variables. Application problems with linear equations have no known answers. Y=mx+b, also known as mx+b, provides a number of straightforward equations.
Here,
To solve this linear programming problem, we can use the following decision variables:
Let x1 = number of pancakes
Let x2 = number of eggs
Let x3 = number of sausage patties
Let x4 = number of slices of toast
The objective function is to minimize cost:
Minimize Z = 0.5x1 + 0.2x2 + 0.3x3 + 0.1x4
Subject to the following constraints:
Calories: 120x1 + 90x2 + 280x3 + 70x4 >= 420
Iron: 1.2x1 + 1.8x2 + 2.4x3 + 0.8x4 >= 5
Calcium: 10x1 + 20x2 + 90x3 + 20x4 >= 400
Protein: 3x1 + 6x2 + 9x3 + 3x4 >= 20
Fiber: 2x1 + 0.5x2 + 1x3 + 1x4 >= 12
Fat: 2x1 + 6x2 + 20x3 + 1.5x4 <= 20
Cholesterol: 50x1 + 190x2 + 60x3 + 0x4 <= 30
The decision variables x1, x2, x3, and x4 must be non-negative.
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Write the equation of the graph that results when:
The equation that represents each change is given as follows:
a) y = 2^x- 6.
b) y = 2^(x + 1).
c) y = -2^x.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.Additionally, when a function is reflected over the x-axis, we have that the function's definition is multiplied by -1.
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Kenny’s weight is 6/7 times Melvins weight. What is the ratio of Kenny’s weight to Melvin's weight. Give your answer in fraction form.
The ratio of Kenny's weight to Melvin's weight is 6/7.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Kenny’s weight is 6/7 times Melvin's weight.
Let x be the weight of Melvin.
Then, Kenny's weight = 6/7 x, as per the information given.
Ratio of Kenny’s weight to Melvin's weight = (6/7 x) / x = 6/7
Hence the required ratio of Kenny's weight to Melvin's weight is 6/7.
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540.54 is what percent of 261040.50?
Answer: The answer should be 0.207%
Step-by-step explanation:
540.54/261040.5
54054/26104050
429/207175
0.00207 X 100/100
0.207/100
0.207%
If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value.
The probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value is 0.62%.
If the thread length of bolts is normally distributed, then we can use the concept of probability to determine the probability that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value.
This can be calculated using the area under the normal curve.
Specifically, the area to the right of 2.5 standard deviations is 0.0062, meaning that there is only a 0.0062 probability (or 0.62%) that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value
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Dana read this statement in a book about softball.
The diameter of a softball is 0.304 meter.
Which completes the statement as it would be heard?
The diameter of a softball is ______.
Answer:
Step-by-step explanation:
14
Rectangle a has side lengths of 6 cm and3.5 cm. The side lengths of rectangle B are proportional to the side lengths of rectangle a
The side lengths of rectangle B, given that they are proportional to rectangle A would be :
A. 3cm and 1.75cmE. 5.25cm and 9cmHow to find out proportionality ?To find proportionality, the dimensions of Rectangle B which correspond to Rectangle A, need to be divisible by, or be able to divide Rectangle A's dimensions without leaving a remainder.
The side lengths of 3 cm and 1. 75 cm are proportional because:
= Dimensions A / Dimensions of B
= 6 / 3 : 3. 5 / 1. 75
= 2 : 2
The side lengths of 5. 25 and 9 cm are also proportional because :
= 9 / 3 : 5 . 25 / 1 . 75
= 3 : 3
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The rest of the question is:
What could be the side lengths of rectangle B?
A. 3cm and 1.75cm
B. 5cm and 2.5cm
C.7 cm and 7cm
D. 12cm and 5 cm
E. 5.25cm and 9cm
If 7/8 is mulitiplied by 2/9 will the product be greater than either of the 2 factors?
No, the product of 7/8 multiplied by 2/9 will not be greater than either of the two factors.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.
Here,
To find the product, we can multiply the two fractions,
(7/8) × (2/9) = (7 × 2) / (8 × 9)
= 14/72 = 1/6
Since 1/6 is less than both 7/8 and 2/9, the product is not greater than either of the two factors.
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EASY POINTS!
Two runners are training for their next competitions. Each runner is able to run a certain
distance in proportion to the time. The table on the left displays the distance Runner A
can run in relation to the time. Meanwhile, the graph on the right displays the distance
Runner B can run in relation to time.
What are the unit rates for the two runners? Which runner can run faster?
The unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.
What is unit rate?A unit rate means a rate for one of something.
Given that, Two runners are training for their next competitions. Each runner is able to run a certain distance in proportion to the time. The table displays the distance Runner A can run in relation to the time. Meanwhile, the graph on the right displays the distance Runner B can run in relation to time. We need to find the unit rates for both runners,
Runner A =
Unit rate = distance / time
= 54 / 4.5
= 12 ft / sec
Therefore, unit rate for the speed of Runner A is 12 ft / sec
Runner B =
According to graph, the Runner B can run 75 ft in seconds
Unit rate = distance / time
= 75 / 5
= 15 ft / sec
Therefore, unit rate for the speed of Runner B is 15 ft / sec
Since, the speed of Runner B is greater than Runner A therefore, Rubber B is faster.
Hence, the unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.
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An oscilloscope display indicates that the period of a digital pulse train is 40 mu s. What is frequency of this waveform? A) 40 MHz B) 25 kHz C) 2.5 kHz D) Cannot be answered from the information provided The highest decimal value that can be represented as a 4-bit binary number is __________. A) 7 B) 322 C) 15 D) 8 Decimal 42 is equivalent to binary ________. A) 101010 B) 52 C) 2A D) 0100000010 Convert (1100101000110101)_2 to hexadecimal. A) 530121 B) 121035 C) 53ACl D) CA35 Which of these truth tables represents the Exclusive NOR gate? A) (A) b) (B) C) (C) D) (D) Which type of gate can be used to add two bits? A) XOR B) NOR C) XNAND D) NAND This is the timing diagram for a 2-input __________ gate. A) NAND B) Exclusive OR C) AND D) OR When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding to the value of the product term. A) True B) False According to DeMorgan's theorem, ((AB)! + C)! equals ___________. A) (A + B)C B) (AB)! + C C) AB + C! D) AB + C! Which statement below best describes a Karnaugh map? A) The Karnaugh map eliminates the need for using NAND and NOR gates. B) Variable complements can be eliminated by using Karnaugh maps. C) Karnaugh maps provide a cookbook approach to simplifying Boolean expressions. D) A Karnaugh map can be used to replace Boolean rules.
C) 2.5 kHz, C) 15, A) 101010, D) CA35, A) (A), A) XOR, B) Exclusive OR, A)True, A) (A + B)C, B) Variable complements can be eliminated by using Karnaugh maps.
Tell me about Karnaugh Maps.K-maps, commonly referred to as Karnaugh maps, are visual tools for simplifying digital circuits and Boolean algebraic formulas. In order to make Boolean functions simpler for use in digital electronics, Maurice Karnaugh first presented them in 1953. K-maps are used to consolidate terms with similar values and get rid of extraneous terms in the truth table of a Boolean function. With a grid of cells corresponding to all conceivable combinations of binary input values, the map is a two-dimensional representation of a truth table. Depending on the truth value of the relevant word in the truth table, the cells in the grid are either filled with 0s or 1s.
The fundamental benefit of employing Karnaugh maps is that they give the Boolean expression a visual representation, making it simpler to spot patterns and understand the expression. They can also be used to check the accuracy of the final expression and find flaws in digital circuits. Karnaugh maps can be used to quickly and effectively simplify complicated digital circuits, which cuts down on the time and effort needed for circuit design.
Karnaugh maps are perfect for designing and optimizing digital circuits because they may be used to simplify big or complex Boolean statements. For more effective and efficient results, they can be combined with other digital design tools, such as logic gates.
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