Santiago can make 7 dumplings
To find out how many dumplings Santiago can make, we need to divide the total amount of dough (5 11/16 cups) by the amount of dough used per dumpling (13/16 cups).
To do this, we can first convert the fractions to have a common denominator. In this case, the denominator of 13/16 is 16, so we can convert 5 11/16 to have a denominator of 16 as well:
5 11/16 = (5 * 16) + 11/16 = 80 + 11/16
Now we can divide:
(80 + 11/16) ÷ (13/16) = (80 + 11) ÷ 13 = 91 ÷ 13
So Santiago can make 91/13 dumplings. This can be simplified further to 7 dumplings. So Santiago can make 7 dumplings with 5 11/16 cups of dough.
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A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form \frac{a\pi+b\sqrt{c}}{d\pi-e\sqrt{f}}, where a, b, c, d, e, and f are positive integers, a and e are relatively prime, and neither c nor f is divisible by the square of any prime. Find the remainder when the product abcdef is divided by 1000.
The remainder when 2 is divided by 1000 is 2
Let O be the center of the circle, R be the length of the radius, and let the chord be AB with midpoint M. Let x be the distance from O to M, then the length of the radius OM is R/2 and the length of the chord AB is 2x.
Since the chord is perpendicular to the radius at the midpoint, we know that the radius bisects the chord. Therefore, the two segments MO and MB are congruent and have length x.
The area of the larger region is the area of the sector OMB, which is (1/4) of the area of the circle. The area of the smaller region is the area of the triangle OMA, which is (1/2) of the area of the sector OMA.
The ratio of the larger region to the smaller region is (1/4) : (1/2) = 2 : 1.
So, the area of the larger region is twice the area of the smaller region.
We can see that abcdef = 21111*1 = 2, the remainder when 2 is divided by 1000 is 2. Thus, the answer is \boxed{002}.
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Translate and solve: -5 times b is no less than 35.
Note: Write your solution in interval notation,
The solution in interval notation b ∈ (-∞ , -7)
-5 times b is no less than 35.
5b ≥ 35
n order to isolate the variable in this linear inequality, we need to get rid of the coefficient that multiplies it.
-[tex]\frac{5b}{5} = \frac{-35}{5}[/tex]
This can be accomplished if both sides are divided by .
Notice that the inequality sign has changed.
b ≤ -7
We need to reduce this fraction to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
In our example, this is the common factor:5
b ∈ (-∞ , -7)
We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.
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A veterinarian weighs three cats. The
American Shorthair weighs 13.65 pounds.
The Persian weighs 13.07 pounds, and
the Maine Coon weighs 13.6 pounds.
List the cats in order from least to
greatest weight.
Answer:
Least to greatest.
Persian, Maine Coon, and American Shorthair
A plane slices a double-napped cone parallel to the slanted edge of the cone. Which conic section is formed?
Circle
Ellipse
Hyperbola
Parabola
It is both of the pair of intersecting lines and degenerate hyperbola.
What is conic section?A conic section, conic or quadratic curve is a curve formed by the surface of a cone crossing a plane. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, however it was frequently referred to as a fourth type. Parabolas, ellipses, circles, and hyperbolas are the four main forms of conics. Examine the diagrams below to discover how a conic is defined geometrically. The plane does not travel through the vertex of a non-degenerate conic.
Here,
It consists of a pair of intersecting lines as well as a degenerate hyperbola.
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Reggie made a scale drawing of a house. In real life, the garage is 3 meters wide. It is 6 millimeters wide in the drawing. What is the drawing's scale factor?
Answer:
1:50
Step-by-step explanation:
The drawing's scale factor is
1:50
Explanation:
In drawing, width of the garage is 6 cm and in actual width of the garage is 3m or 3×100=300 cm.
Hence, the drawing's scale factor is 6:300 and dividing by 6, it is 1:50
Type the correct answer in each box. The coordinates of the point that corresponds to an angle of radians in the unit circle are (, ).
On solving the provided question, we can say that coordinates of the point in the unit circle S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] ) => S= ( 0 , -1 )
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
S = (0, -1 )
coordinates of the point in the unit circle
S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] )
S= ( 0 , -1 )
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dividing decimals up to 2 decimal places
1.0.2÷6.11
Answer:
its 6.11
6.11 ÷ 1 = 6.11
Calculated to 2 decimal places.
6. 1 1
1 6. 1 1
− 6
0 1
− 1
0 1
− 1
0
Can you help me with this
The linear function that passes through (3,1) and has a slope of -1/2 is defined as follows:
y = -0.5x + 2.5.
The graph of the linear function is given by the image presented at the end of the answer.
How to define the linear function?The linear function for this problem is defined in slope-intercept format, as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value assumed by the output variable y when the input variable x assumes a value of zero.The slope of the function in this problem is given as follows:
m = -1/2 = -0.5
Hence:
y = -0.5x + b.
The line passing through point (3,1) means that when x = 3, y = 1, and thus the intercept b is obtained as follows:
1 = -0.5(3) + b
1 = -1.5 + b
b = 2.5.
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Aubrey's Pie Shop recently sold 6 cherry pies and 14 other pies. What is the experimental probability that the next pie sold will be a cherry pie?
Answer:
Step-by-step explanation:
Aubrey's Pie Shop recently sold [tex]20[/tex] pies in total, [tex]6[/tex] of them being cherry pies, so the experimental probability is [tex]\dfrac{6}{20} = \dfrac{3}{10} = 30\%[/tex] chance of the next one being a cherry pie.
How many nine-digit numbers can be made using each of the digits 1 through 9 exactly once with the digits alternating between odd and even
Using combination, 5184 nine-digit numbers can be made using each of the digits 1 through 9 exactly once with the digits alternating between odd and even.
What exactly is a permutation?An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.
If the first letter is even, there are 4 first digit possibilities (not 5 because it can't start with 0), 4 third digit possibilities, 3 fifth digit possibilities, etc., making the total 4!
If an odd number is the first letter, there will be 5!*4! different ones.
Add the two together now.
4*4!*4! + 5!*4!=5184
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The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w. The force on a sail with an area of 500 ft^2 is 64. 8 pounds when the wind speed is 18 mph. What would be the force for a sail with an area of 250 ft^2 with a wind speed of 35 mph
Answer:
122.5 pounds.
Step-by-step explanation:
f = kaw^2
So, k = f/aw^2
From the given data:
k = 64.8/(500*18)
= 0.0004
When a = 250 and w = 35:
f = 0.0004*250*35^2
= 122.5
Help me pls I’m struggling and I can’t solve it
The perimeter of the rectangle is 4y + 6 (cm).
How can the perimeter equation be found?All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.
The diagram shows a rectangle. All measurements are in centimetres an expression in terms of y, for the perimeter of the rectangle.
The perimeter of the rectangle is
2(y+3)+24
=2y + 6 + 2y = 4y + 6 (cm)
{ the perimeter:
2 * width + 2 * Length}
The perimeter of the rectangle is 4y + 6 (cm).
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Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B
i got 2/4 of the marks pls help
Answer:
Step-by-step explanation:
Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled
The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number. What is the original number?
48
39
57
Answer:
39
Step-by-step explanation:
Does (1, 10) make the inequality y ≤ 5x + 4 true?
yes
no?
Answer:
No, it is not true
Step-by-step explanation:
y ≤ 5x + 4
We know a point is (1,10), we need to put the 1 in for x and the 10 in for y to see if the inequality is true or not!
10 ≤ 5(1) + 4
10 ≤ 5 + 4
10 ≤ 9
This is not True!
Answer: nope
Step-by-step explanation:
Why infinity is open interval?
The number line is drawn to find the open end point interval is infinity.
Number Line of an Open endpoint to the endpoint of number line =?
Selection of Open endpoint to the endpoint of the number line is fit for the following intervals as such determined below :
basically the intervals are mentioned as follow
( ), [ ], ( ], [ )
An open interval is mentioned (a, b), is an interval that does not contain its endpoints. When an interval involves infinity or negative infinity, hence the following rules for whether it is an open or closed interval. (a, and
(-a , a) are open intervals.
For instance [a,∞) doesn't contain all of its endpoints as mentioned . It's a real number where The interval has only one endpoint - a, so it contains all of its endpoints (however it only has one).
Secondly, the definition forgot to add that (−∞,∞) is also open
Take numbers as follows:
Final Answer as followed in intervals
(-2, 2)
[-2, 2]
(-∞, 2]
[2, ∞)
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knowing the difference between an experimental group and a control group is most relevant to understanding the nature of: group of answer choices random sampling. replication. hindsight bias. independent variables.
The experimental group is given the experimental treatment, and the comparison group is statistically significant.
Which three attitudes are the basis of the scientific viewpoint?Curiosity, scepticism, and humility are described by historians of science as the three attitudes that form the bedrock of the scientific viewpoint. Larger, more representative sample sizes aid in the production of accurate and valid data.When random sampling is used, every member of the population has an equal chance of being chosen, resulting in the collection of a representative sample. The odds of generalising the study's findings to the population increase with the use of a random sample. The study's margin of error is reduced with higher study sample sizes.) Researcher control over the possibility of reporting false-negative or false-positive findings is made possible by larger sample sizes. Results will be more precisely predicted with a larger sample size.To learn more about random sampling refer to :
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Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A, a 50%
chance of getting a job offer from company B, and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
The probability of Johnny not getting a job offer from either company is 0.8
Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A,
A = 0.6
a 50% chance of getting a job offer from company B,
B = 0.5
and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
Suppose, probability of an event A occurring is P(A)
and that of is B IS P(B)
P(A) = 0.6
and
P(B)= 0.5
probability of either or P(AUB)=0.3
Now we need to find the probability of neither nor, which is
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = P(A) + P(B) -P(A∪B)
= 0.6 + 0.5 - 0.3
= 0.8
Now the events are mutually exclusive, so
Therefore, the probability of neither nor is 0.8
The probability of Johnny not getting a job offer from either company is 0.8
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Angle A and Angle B are complementary angles. The measure of Angle A is twice the measure of Angle B.
Write and equation to represent the complementary angle relationship between Angle A and Angle B. Use the equation to find
the measure of Angle A and B. Show all of your work.
Answer:
Acc.to question,
A+B=90° (since,they are complementary angles)
or,A+ A/2=90°(since,A is. twice the measure of B)
or,3A/2=90°
or,A=(90°×2)/3
:.A=60°
Also,
B=A/2=60/2=30°
A sine function has the following key features:
Period = 4
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
The sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].
What is sine function?
The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.
The general sine function is
[tex]y = Asin(b(x+c)+D[/tex]
Where
Amplitude = A
Period = [tex]\frac{2\pi }{B}[/tex]
Phase shift = c
Vertical shift = D
Given:
A = 4 (amplitude)
[tex]\frac{2\pi }{B} = 4[/tex] (period)
[tex]B = \frac{\pi }{2}[/tex]
Since midline: y = 1
And we know that graph of [tex]4sin(\frac{\pi }{2}x)[/tex], midline to be y = 1.
It must have vertical shift D = 1.
Since, y - intercept (0, 1)
⇒ x = 0, y = 1
⇒ It has no phase shift ⇒ c = 0
Since it satisfy [tex]y = 4sin(\frac{\pi }{2}(x+c))+D[/tex]
The graph of the sine function is attached below.
Hence, the sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].
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How to determine the number of solutions in a linear system without solving?
To determine the number of solutions in a linear system without solving it, check their slopes. If the slopes are different, there is one solution; if the slopes are the same but the equations are different, there is no solution; if the equations are exactly the same, the solutions are infinite.
The 3 possible solutions of a system of equations are:
- Unique or one solution
- Infinite solutions
- No solution
In case of a system of linear equations, we can determine the type of its solution as follows:
- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equations will have one solution.
Example:
y = -3x - 2
5x + 2y = 15
The slopes of the line equations are different, hence the solution is unique
- If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.
Example:
2x + 2y = 8
y = -x -5
These are parallel lines, hence, there is no solution
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
Example:
2x + 2y = 8
4x = -4y + 16
Those two equations are exactly the same. Hence, the solutions are infinite.
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What are 3 problem solving skills?
The major part of problem solving skill are explained below.
In order to find the ways, we must know the definition of problem solving.
The term problem solving is defined as the act of defining a problem; determining the cause of the problem identifying, prioritizing, and selecting alternatives for a solution and implementing a solution.
Therefore, the major skills included in the problem solving are defined as
=> identifying the problem,
=> analyzing possible solutions, and
=> deciding on the best course of action
Basically, this skill is important because it enables us to identify and exploit opportunities in the environment and exert control over the future.
Other that that problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations.
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What is unsolvable problem with an example?
Therefore , the solution of the given problem of algorithm comes out to be the halting problem can be demonstrated to be indecidable and so unsolvable.
Define the algorithm.A method for performing calculations or solving problems is known as an algorithm. Algorithms act as a thorough set of instructions that step-by-step direct hardware- or software-based processes through a series of planned activities. In every aspect of IT area, algorithms are utilized regularly.
Here,
The halting problem is one of the most popular unsolved issues. It poses the following inquiry:
Does M halt when it is given the input w for an arbitrary Turing machine over the parameters alphabet = a, b and an arbitrary string w over
The halting problem can be demonstrated to be indecidable and so unsolvable.
Therefore , the solution of the given problem of algorithm comes out to be the halting problem can be demonstrated to be indecidable and so unsolvable.
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What are the real roots of the equation x2 3 x1 3 − 2?
The real roots of the equation x^(2/3) + x^(1/3) - 2 = 0 are 1 and -8.
The equation x^(2/3) + x^(1/3) - 2 = 0 does not have any real roots. Since the exponents are not integers, x^(2/3) and x^(1/3) are not defined for negative values of x, and so the equation has no solutions for real values of x.
But,
Let y = x^(1/3)
The equation x^(2/3) + x^(1/3) - 2 = 0 will become y² + y - 2 = 0.
Solving for the roots of this equation,
y² + y - 2 = 0
(y + 2)(y - 1) = 0
y = -2 ; y = 1
Substitute the value of y and solve for x.
y = x^(1/3)
-2 = x^(1/3) ; 1 = x^(1/3)
x = -8 ; x = 1
Therefore, the real roots of the equation is 1 and -8.
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A class of 20 students is visiting the fair today. Each student is 16 years old or younger and will participate in either the Hay Bale Toss or the Pie Eating Contest. If all 20 students joined the same event, how would the shape of the histogram change compared to the original
In either the Hay Bale Toss or Pie Eating Contest, the graph's range of 0-19 will be extended by 20.
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices.
In either the Hay Bale Toss or Pie Eating Contest, the graph's range of 0-19 will be extended by 20. 20 students attended the fair, total. Group age = 0 to 16
This age range is located in the histogram's first interval, which is 0–19. The graph for the pie eating competition would remain the same if all 20 pupils had participated in the hay bale toss, with the bar representing 0–19 rising from 40 to 60.
The graph of the Hay Bale Toss would remain same if all 20 pupils had participated in the Pie Eating Contest, increasing the bar of 0-19 from 20 to 40.
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A track team has 7 people eligible to run the
800-meter run. A team member can only run
the race once, and 4 people are needed to run
the race. How many different ways can the 4
people be selected, if order doesn't matter?
In 35 differnt ways (Combination) the 4 players can be selected from a team of 7.
What is permutation and Combination ?Combinations are decisions that are made by choosing some or all of a group of things, regardless of how they are arranged.
Utilizing the combinations formula, it is simple to determine how many distinct groups of r items each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.
A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. In order to determine the number of configurations for seating 3 people in 5 seats, we thus multiply the alternatives at our disposal.
Permutations are several ways to arrange things in a certain sequence. It may alternatively be stated as the linear reordering of elements in an already ordered collection.
Here we have to select 4 people from a team of 7, so its a combination
So the number of ways are = [tex]\x^{7}C\x_{4} = \frac{7!}{4!\ 3!} = 35[/tex].
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Find the surface area, volume, and radius and select all the correct measurements,
Answer:
surface area ---> i
volume ---> b
radius ---> d
Step-by-step explanation:
surface area= 4πr² =4x3.14x14²=2461.76cm²
volume= (4÷3)πr³= (4÷3)x3.14x14³=11488.21cm³
radius = half the diameter = 14cm
The graph below models the value of a $20,000 car fyears after it was purchased.
20000
18000
16000
14000
12000-
10000
8000
6000
4000
2000-
Dollars
Value of Car
52:25
2 4 6 8 10 12 14 16 18 t
Years
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
A. Each car value y, is associated with exactly one time, t.
B. Each time, t, is associated with exactly one car value, y.
C.The rate at which car decreases in value is not constant.
Your answer should be B. Each time, t, is associated with precisely one car value, y.
The number of pages in an Algebra 1 book is 99 less than the number of pages in a geometry book. Write and solve an equation to find the number n of pages in the geometry book. (big ideas)
On solving the provided question we can say that *629 = n - 99 is an equation. The textbook contains 728 pages*.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
In other words, the geometry book is 99 pages LONGER than the algebra book, which is 99 pages SHORTER. The solution can be obtained using this equation. I'm sorry, but 530 is not the solution.
629 = n - 99 is an equation. The textbook contains 728 pages*.
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Additive Relationships
What is the value of y when x=100y=?
The value of y in the equation is y = x / 100.
How to make a variable the subject of the formula?Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.
Therefore, let's make y the subject of the formula in the equation x = 100y.
Hence, we will find y in terms of x.
Therefore,
x = 100y
divide both sides of the equation by 100
100y / 100 = x / 100
y = x / 100
Therefore,
y = x / 100
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