There are 55 senators and 235 representatives are in this state's legislature.
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.
Let's call the number of senators in the state legislature "s" and the number of representatives "r". We know the following:
s + r = 290 (the combined number of senators and representatives is 290)
r - s = 180 (the difference of the numbers is 180)
We can use the first equation to solve for one of the variables in terms of the other:
r = 290 - s
Next, we can substitute this expression for r into the second equation:
290 - s - s = 180
Simplifying the left-hand side:
290 - 2s = 180
Adding 2s to both sides:
290 = 180 + 2s
Subtracting 180 from both sides:
110 = 2s
Dividing both sides by 2:
s = 55
So there are 55 senators in the state legislature. To find the number of representatives, we can use the first equation:
r = 290 - s = 290 - 55 = 235
So there are 235 representatives in the state legislature.
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$122.62-$lal
5.) On February 3rd, Cardi B borrowed $17,500.00 at 6.5% exact interest to buy a new car. She had to pay back
a maturity value of $17,873.97 to pay off the loan. On what day did Cardi pay back the loan?
has a 10.3% ordinary
The day that Cardi B paid back the loan is given as follows:
June 3rd.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The parameter values for this problem are given as follows:
A = 17873.97, P = 17500, r = 0.065.
Hence the time in years is obtained as follows:
17873.97 = 17500(1 + 0.065t)
1 + 0.065t = 17873.97/17500
1 + 0.065t = 1.02136971429
t = (1.02136971429 - 1)/0.065
t = 0.32876483523
A year is composed by 365 days, hence the time in days is given as follows:
0.32876483523 x 365 = 120 days.
120 days after February 3rd is June 3rd.
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PLEASE HELP!!
Look at the screen shot for the question, thank you!
A function equation in slope-intercept form to model the situation are as follows;
Slope: 3.
Y-intercept: 48.
Equation: y = 3x + 48.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x represents the number of minutes.y represents the temperature.m represents the slope of a line.c represents the y-intercept of a line.Since the liquid started at a temperature of 48 degrees and drops 3 degrees per minute, an equation that model the situation is given by:
y = mx + c
y = 3x + 48
Next, we would fill in the table as follows. At x = 0, the temperature of liquid (y) is given by:
y = 3(0) + 48
y = 48.
At x = 1, the temperature of liquid (y) is given by:
y = 3(1) + 48
y = 51.
At x = 2, the temperature of liquid (y) is given by:
y = 3(2) + 48
y = 54.
At x = 3, the temperature of liquid (y) is given by:
y = 3(3) + 48
y = 57.
At x = 4, the temperature of liquid (y) is given by:
y = 3(4) + 48
y = 60.
At x = 5, the temperature of liquid (y) is given by:
y = 3(5) + 48
y = 63.
At x = 6, the temperature of liquid (y) is given by:
y = 3(6) + 48
y = 66.
At x = 7, the temperature of liquid (y) is given by:
y = 3(7) + 48
y = 69.
At x = 8, the temperature of liquid (y) is given by:
y = 3(8) + 48
y = 72.
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PLEASE HELP ME WITH THESE QUESTIONS IM SO DESPERATE
WILL GIVE BRAINLIEST
Answer:
11.55m², 181.12mm²,11ft,
Step-by-step explanation:
Simplify the expression.
and multiply A=1/2bh
Which segment of this graph shows a decreasing velocity?
A. A to B
B. B to C
C. C to D
D. D to E
E. E to F
anderson and addison leave from the same restaurant and the same time, traveling in opposite directions. if anderson travels 15 mph and addison travels 6 mph, how long until they are 126 miles apart?
After 6 hours, Anderson and Addison will be 126 miles apart.
Let's call the time they have been traveling "t" (in hours).
Anderson will have traveled 15t miles and Addison will have traveled 6t miles. The total distance between them is 15t + 6t = 21t miles.
We know that they need to be 126 miles apart, so we can set up the equation:
21t = 126
Now we can solve for t:
t = 126 / 21
t = 6
So after 6 hours, they both will be 126 miles apart.
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Find the indicated measure.
Using the inscribed angle theorem:
7. m<A = 79°
8. m<B = 90°
9. m(BC) = 152°
What is the Inscribed Angle Theorem?The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.
Applying the inscribed angle theorem, we have:
7. m<A = 1/2(158)
m<A = 79°
8. m<B = 1/2(180)
m<B = 90°
9. m(BC) = 2(76)
m(BC) = 152°
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Given that A, O & B lie on a straight line
segment, evaluate obtuse ZAOC.
C
A
(3x +94)
0
→ ZAOC =
(x +30)
(2x-4)
The diagram is not drawn to scale.
0°
D
B
The evaluation of obtuse angle ∠AOC is 124°.
What does "obtuse angle" mean?Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
3x + 94 + x + 30 + 2x - 4 = 180
Sum of angle in a triangle
6x + 120° = 180°
6x = 180° - 120°
6x = 60°
x = 10°
Now, ∠AOC = 3x + 94
3 × 10 + 94
30 + 94
124°
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question content area top part 1 suppose a 4×7 coefficient matrix for a system has four pivot columns. is the system consistent? why or why not?
If a 4x7 coefficient matrix has four pivot columns, the system is consistent and has exactly one solution.
A coefficient matrix is a matrix that represents a system of linear equations. In the case of a 4x7 coefficient matrix, the matrix has 4 rows and 7 columns.
When it comes to determining the consistency of a system of linear equations, the presence of pivot columns is a key factor.
A pivot column is a column that contains a leading 1 in the row reduced echelon form of the matrix. If a system has four pivot columns, this means that the system has 4 linearly independent equations, meaning that there is exactly one solution to the system.
Therefore, the system is considered consistent.
However, if the number of pivot columns is less than the number of unknowns, then the system is considered inconsistent, meaning that there is either no solution or an infinite number of solutions.
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a bin contains 5 red balls and 9 blue balls. the following experiment is repeated several times: remove a ball from the bin, observe its color, and replace it. what is the probability that the 5th ball drawn is red and the 8th ball drawn is blue?
The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
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The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
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Solve by graphing
4x - 4y = 22
y = -5.5
The system of equations has a unique solution. The solution is (0,-5.5).
What is the system of equations?
A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.
The system of equations is
4x - 4y = 22 ....(i)
y = -5.5 ...(ii)
Putting x = 0 in 4x - 4y = 22:
4 × 0 - 4y = 22
- 4y = 22
y = -5.5
Putting x = 1 in 4x - 4y = 22:
4 × 1 - 4y = 22
- 4y = 18
y = -4.5
The points on equation (i) are (0,-5.5) and (1, -4.5).
The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).
Plot the points and join them.
The intersection point is the solution of the system of equations.
The solution is x = 0 and y = -5.5
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Water flows at a speed of 20 cm/s along a rectangular channel into a lake. The width of the channel is 15 cm, the depth of the water is 2.5 cm. Calculate the amount of water that flows from the channel into the lake in 1 hour. Give your answer in litres.
Answer is 2.7 million liters/hour
What is speed?
Speed tells us how fast something or someone is travelling.
The flow rate of water can be calculated as the cross-sectional area of the channel multiplied by the speed of the water.
The cross-sectional area of the channel can be calculated as width x depth = 15 cm x 2.5 cm = 37.5 cm^2
The flow rate of water can be calculated as 37.5 cm^2 x 20 cm/s = 750 cm^3/s
To convert this to liters, we need to multiply by 1000 to convert cubic centimeters to cubic centimeters:
750 cm^3/s x (1000 cm^3/L) = 750 L/s
Finally, to find the amount of water that flows into the lake in 1 hour, we need to multiply the flow rate by the number of seconds in an hour:
750 L/s x (3600 s/hr) = 2700000 L/hr = 2.7 million liters/hour.
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for a given number of domains, which characteristic is common to every molecule?
Every molecule has a unique molecular formula.
A molecular formula is a chemical formula that represents a molecule and gives information about the number and type of atoms present in the molecule. This formula is unique to each molecule and distinguishes one molecule from another, even if they have the same number and type of atoms arranged in a different way.
For example, the molecular formula for glucose (C6H12O6) is different from that of fructose (C6H12O6), even though they have the same number and type of atoms. The molecular formula represents the actual number of atoms present in the molecule and their chemical makeup, which in turn determines the chemical properties and behavior of the molecule.
Thus, for a given number of domains, the characteristic that is common to every molecule is their unique molecular formula.
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→ A, B, C, D, E, F, G & H form a cuboid. AB = 3.2 cm, BC = 4 cm & CG = 7.7 cm. Find AG rounded to 1 DP. w A I AG = The diagram is not drawn to scale.
The length of AG which is the diagonal of the cuboid is; 8.5 cm
How to find the diagonal of a cuboid?A cuboid is defined as a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.
A diagonal in geometry is defined as a line segment that connects two polygonal vertices when they are not on the same edge.
The parameters are;
A, B, C, D, E, F, G & H form a cuboid. AB= 3.2 cm, BC = 1.6 cm & CG = 7.7 cm. That is l=3.2 cm, b=1.6 cm, h=7.7 cm.
A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is;
Diagonal length = √(l² + b² + h²) units.
Thus lugging in the relevant values;
Diagonal length = √(3.2² + 1.6² + 7.7²)
Diagonal Length = 8.49 cm
≈ 8.5 cm
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You roll a 6-sided die two times. What is the probability of rolling a number less than 4 and then rolling a number greater than 3? Write your answer as a percentage%.
Answer:
Step-by-step explanation:
3/6
Arnold is drawing another part of his blueprint. He draws a line that is 1/8 an inch and then draws another line next to it that is 14 of an inch. How long is this line Arnold has drawn?Arnold is drawing another part of his blueprint. He draws a line that is 1/8 an inch and then draws another line next to it that is 1/4 of an inch. How long is this line Arnold has drawn?
The length of the new line is twice the length of the old line and total length is given by the equation L = (3/8 ) of an inch
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 length of the old line be A
Now , the value of A = 1/8 of an inch
Let the length of the new line be B
Now , the value of B = 1/4 of an inch
So , the equation will be
The number of times the new line is greater than old line is given by
B / A = x
Substituting the values in the equation , we get
x = ( 1/4 ) / ( 1/8 )
x = 8/4
x = 2 times
So , the total length of the line = A + B
Substituting the values in the equation , we get
The total length of the line L = ( 1/4 ) + ( 1/8 )
The total length of the line L = 3/8 of an inch
Hence , the equation is L = (3/8 ) of an inch
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Help me because why is math so hard now
Answer:
Step-by-step explanation:
The answer will be the third one because 2/3 * (3/10 X 1) is the same as 2/3 already being multiplied to 3/10.
If you use a calculator and put 2/3 * (3/10 X 1), you will get 0.2 and if you put (2/3 * 3/10) x 1 you will also 0.2.
So (2/3 * 3/10) x 1 is equal to 2/3 * (3/10 X 1)
: Can you find any relation between the number of ide, edge and
vertice in each hape? What i the relation? What i the formula and what i it known a?
The relation between the number of ide, edge, and vertice in each shape Euler’s Formula for Polyhedron.
Polyhedron Euler's Formula
One of the most significant mathematical theorems, the Euler theorem is named Leonhard Euler and is widely recognized as such.
The link between a polyhedron's face, vertex, and edge counts is stated in the theorem.
F + V = E + 2 is the formula for Euler's equation, where F is the number of faces, V is the number of vertices, and E is the number of edges.
According to Euler's formula, many solid shapes have a number of faces plus vertices plus vertices minus vertices equal to two.
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Suppose that y(t) solves the ordinary differential equation
dy/dt = (4-3Y)/(5+2Y) Y(0)=0 Find d2y/dt2 (0)
To find the second derivative of y(t) at t = 0, we can use the chain rule. We can write the given equation as dy/dt = f(y), where f(y) = (4-3y)/(5+2y).
Then the second derivative of y at t = 0 can be calculated as: d2y/dt2 (0) = f'(y) * dy/dt (0) = f'(0)f(0) = [-3/(5+20)](4-30)/(5+2*0) = -3/5.
A differential equation is an equation that relates one or more unknown functions and their derivatives. It is mainly used in the fields of biology, physics, engineering, economics, and other sciences.
A differential equation states how a rate of change (a "differential") in one variable is related to other variables. For example, the Single Spring simulation involves a differential equation that describes the displacement of a spring in response to a force.
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Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (a) Length of time to complete an exam (b) Time of fi rst class (c) Major field of study (d) Course evaluation scale: poor, acceptable, good (e) Score on last exam (based on 100 possible points) (f) Age of student
The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.
(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).
(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).
(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).
(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).
(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).
(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).
The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.
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sketch an angle θ in standard position such that θ has the least possible positive measure, and the point \left(-2,\sqrt{3}\right) is on the terminal side of θ.
The angle has a measure of 0° and is in standard position with its vertex at the origin. On the terminal side of lies the point (-2, 3).
The vertex of an angle in standard position on a coordinate plane is at the plane's origin. The angle's terminal side is rotated anticlockwise from the starting side while the angle's initial side is on the positive x-axis. The number of degrees the terminal side has travelled away from the initial side anticlockwise is how an angle is measured in standard position. This signifies that the terminal side is exactly on the same line as the initial side because the angle has the smallest positive measure of 0°. Since the line segment from the origin to the point (-2,3) is on the terminal side of, the point (-2,3) is on that side as well.
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PROOF Complete the proof.
Given BC AD, BCLDC, ADL DC
Prove ABCD is a rectangle.
A
B
D
C
In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.
What is meant by Reflexive Property?In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.
2. AD = BC due to the congruence of a rectangle's opposite sides.
3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.
4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).
5. Since they form right angles and all right angles are congruent, ADC=BCD.
6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).
7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).
Statement Reason
1. Rectangle ABCD Given
2. AD=BC Opposite sides of a rectangle are congruent
3. DC=DC Reflexive Property of Congruence
4. <ADC and <BCD are Definition of rectangle
right angles
5. <ADC=<BCD All right angles are congruent
6. ∆ADC=∆BCD SAS Congruence Postulate
7. AC=BD CPCTC
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Throughout this module, you have learned how to gather and present information to help justify your answer. You will use this skill, along with your knowledge of constructing figures in Geometry, to construct an argument in paragraph form.
Step 1: Tips on Formulating Your Argument
Here are some tips on formulating your argument:
● Think, Think, Think. Ask yourself lots of questions about each side of the topic, then answer them based on your research findings, your opinion, and your experiences with both sides of the argument.
● Think from the other side. It is impossible to refute, or prove false, someone’s claim if you don’t know what he or she is thinking ahead of time.
● Create a list of some sort that helps you organize your thoughts. The more organized you are, the more prepared you will be and the more likely you are to win a debate!
● Cite your sources when you are speaking. Citing your sources gives your arguments more credibility. For example, you might say, "According to an article in the Math Rocks Journal ..."
● Use credible sources. Credible sources are ones readers can trust and ones that can be backed up with evidence. Not all sources carry the same weight; use sources that enhance your argument. Wikipedia is not a reliable or credible source.
● Use effective speech and grammar. Remember, you are trying to get others to side with you, so speak clearly and professionally.
● Do more research. If you haven’t caught on by now, formulating your argument takes a lot of digging. Essentially, you have to prove your
points. You can even research how to debate! Take really good notes.
Step 2: The Argument
Here are the two arguments:
Argument A: There is a need for students to understand and be able to construct geometric figures using a compass and straightedge.
Argument B: There is no need for students to use a compass and straightedge, and all geometric constructions should be done using a drawing program.
There are two opposing arguments listed above. You need to choose which one you will support as your argument. Formulating an argument takes research and time to get yourself to the point where you can defend your position thoroughly.
Step 3: What to Submit
You may use any word processing program to present your argument, but you must include the following:
1. A summary of your argument. The summary should begin with the argument statement you chose. In addition, provide at least three
reasons why the method you chose is better than the other method and at least three reasons why the other method is not better. This
summary can have a lot of opinion in it and should be persuasive and argumentative. You should submit in paragraph form.
2. A list of at least two resources used. Resources may include interviews with professionals and/or URLs of websites. Remember, you may
gather ideas from research, but you must explain the ideas yourself. Copying and pasting someone else's ideas is plagiarism. Be sure to avoid plagiarism by phrasing your argument in your own words. Reach out to your teacher if you have any questions.
An argument that supports Argument A is given below:
Geometric figures play a crucial role in many areas of mathematics and science, including engineering, architecture, physics, and computer graphics.
Why is it important to understand and be able to construct geometric figures?Being able to construct these figures accurately and efficiently is therefore an important skill for students to have. By using only a compass and straightedge, students can explore and understand the properties of different shapes and their relationships with one another.
This helps them develop their spatial reasoning abilities and improves their understanding of mathematical concepts such as congruence, similarity, and symmetry.
Furthermore, this skill can be applied to solving real-world problems, such as determining the dimensions of a building or designing a circuit board.
In conclusion, the ability to construct geometric figures using a compass and straightedge is essential for students' mathematical and scientific development and should be taught as part of their education.
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Lat week, Toby bought 11 book and 8 movie for a total of $207. Today, Toby bought 16 book and 9 movie for a total of $280. Auming neither item ha changed in price, what i the cot of a book in dollar?
Last week, Toby bought 11 book and 8 movie for a total of $207. Today, Toby bought 16 book and 9 movie for a total of $280 the cost of book is 13$.
Toby bought 11 book and 8 movie for a total of $207 so,
11B + 8M = 207
Today, Toby bought 16 book and 9 movie for a total of $280 so,
16B + 9M = 280
Solving equations simultaneously we get,
11B + 8M = 207
16B + 9M = 280
99B = 1863
B = $13
So, the cost of a book in dollar is $13.
Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.
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A charitable organization in Oxford i hoting a black tie benefit for charity and the organization member hope to bring in at leat $1,200 tandard ticket are available for 21 each wherea vip ticket are offered for 43 a piece
To reach the goal of $1,200, the organization needs to sell at least 28 standard tickets (1,200 / 42 = 28.57) or 28 VIP tickets (1,200 / 43 = 27.91). They can also combine the sales of standard and VIP tickets to reach the goal.
The charitable organization is hosting a black-tie benefit event and aims to raise at least $1,200 through ticket sales.
The standard tickets are priced at $21 each, while the VIP tickets are priced at $43 each.
To reach the goal of $1,200, the organization needs to sell a minimum of 28 standard tickets ($1,200 / $21 = 57.14).
However, if they only sell VIP tickets, they will need to sell at least 28 VIP tickets ($1,200 / $43 = 27.91).
Finally, they can also achieve their goal by selling a combination of standard and VIP tickets.
For example, they can sell 20 standard tickets and 8 VIP tickets, which would result in a total of 20 * $21 + 8 * $43 = $840 + $344 = $1,184, reaching their goal of $1,200.
In conclusion, the charitable organization has multiple options to reach their goal of $1,200 through ticket sales for their black-tie benefit event.
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In 2015, the per capita consumption of bottled water in the United States was reported to be 36.2 gallons. Assume that the per capita consumption of bottled water in the U.S. is approximately normally-distributed with a standard deviation of 10 gallons.
Find the Z-score of someone who consumed 26.2 gallons of water. Using the Empirical Rule, what is the approximate probability that someone in the United States consumed less than 26.2 gallons of water, what is the approximate probability that someone in the United States consumed between 26.2 and 36.2 gallons of water, and what is the approximate probability that someone in the United States consumed between 26.2 and 46.2 gallons of water?
The required probabilities = 0.16
The required probabilities = 0.68
What is z-score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.
As given that,
μ = 36.2
σ = 10
As per empirical Rule:
μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%
μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%
μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%
less than 26.2:
13.5% + 2.35% + 0.15% = 0.16
between 26.2 and 36.2:
68% = 0.68
The required probabilities = 0.16
The required probabilities = 0.68
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What is 65 Inches in Feet?
When 65 inches are converted to feet, the result is 5.41667 feet.
How do I convert an inch to a foot?To convert 65 inches to feet, divide 65 by 12.We can calculate 65 inches equals 5.41667 feet using a calculator or long division. As a result, 65 inches is equivalent to 5.41667 feet. It is important to note that inches and feet are both length units, so converting between the two involves moving the decimal point in the number two places to the left or right, depending on which unit you are converting to.Divide the number of inches by 12 to convert to feet, because a foot is 12 inches long. Similarly, multiply the number of feet by the number of inches.As a result, 65 inches equals 5.41667 feet, and you can convert inches to feet by dividing the number of inches by 12.To learn more about inches refer to :
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find a · b. a = 4, 1, 1 3 , b = 8, −3, −9
The dot product of a.b is 20.
What is the dot product?
The dot product (also called scalar product or inner product) of two vectors a and b in a Euclidean space is a scalar value that represents the projection of one vector onto the other and the cosine of the angle between them. The dot product of two vectors a and b is defined as:
a · b = ||a||||b||cos(θ) = a1b1 + a2b2 + ... + anbn
where a = (a1, a2, ..., an) and b = (b1, b2, ..., bn) are the components of the vectors and θ is the angle between the vectors.
Finding a · b:
Given a = (4, 1, 1) and b = (8, -3, -9), we can calculate the dot product as:
a · b = 4 * 8 + 1 * -3 + 1 * -9 = 32 - 3 - 9 = 20
Hence, the dot product of a.b is 20.
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Please help !,,,!,!,,!,,,meeee long division step by step
greatest common factor for 90 and 80
Answer:
10
Step-by-step explanation:
The GCF of 80 and 90 is 10.
two telephone calls come into a switchboard at random times in a fixed one-hour period. assume that the calls are made independently of one another. (a) what is the probability that the calls are made in the first quarter hour? 1/16 correct: your answer is correct. (b) what is the probability that the calls are made within six minutes of each other? (round your answer to four decimal places.)
The probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16
Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A statistical function known as a probability distribution explains all the potential values and probabilities for a random variable within a certain range.
The uniform probability distribution is a distribution composed by two bounds, given by a and b, in which each possible outcome within these two bounds is equally as likely.
The probability that a call is made in the first quarter is 15/60
Now the probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16
Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1
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