The trip would have taken 8.89 hours instead of 8 hours.
How to calculate distance traveled?Distance traveled can be calculated by multiplying the speed at which the object is traveling by the amount of time the object has been in motion.
For example, if a car is traveling at 60 miles per hour for two hours, the distance traveled would be 120 miles.
To calculate distance more accurately, you can use the formula d = rt, where d is the distance, r is the rate of speed, and t is the time in which the object has been in motion.
It is important to note that this formula assumes a constant speed throughout the duration of the journey.
It is also important to remember that the unit of measurement used for both the speed and the time must be the same. Therefore, if the speed is in miles per hour, the time must also be in hours.
In order to calculate this, we need to first calculate the time it took for the family to travel the first 600km at 90km/h. This can be calculated using the formula:
Time = Distance / Speed
So, the time it took for the family to travel the first 600km is:
Time = 600km / 90km/h = 6.67 hours
Then, we can calculate the time it would have taken for the family to travel 800km at 90km/h using the same formula:
Time = 800km / 90km/h = 8.89 hours
Therefore, the trip would have taken 8.89 hours, which is 0.89 hours longer than the original trip which took 8 hours.
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1.4.3 Quiz: Draw a Diagram
Question 2 of 6
Read the problem below and find the solution. Draw a diagram on your own
paper to help solve it.
A group of 23 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
(Do not include units in your answer.)
Answer here
+
SUBMIT
There can be a maximum of 5 teams.Three persons will be excluded.
What is an expression?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to denote the logical syntax's operation order and other properties.
Considering that 23 pals gather to play a sport together.The participants must first be divided into teams. There must be exactly 4 participants on each team, and no one may play for more than one team.
The number of teams will be determined using the formulas below:
Total teams = 23 / 4 = 20 / 4 = 5.
Three persons will be left.
Therefore, there can be a maximum of 5 teams.Three persons will be excluded.
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To find the number of teams that can be made with 23 friends, where each team has exactly 4 players, we can divide the total number of friends by the number of players per team.
Number of friends = 23
Number of players per team = 4
To find the number of teams, we divide the number of friends by the number of players per team:
23 / 4 = 5 remainder 3
Since we cannot have a team with 3 players, we can only form complete teams of 4 players. Therefore, the maximum number of teams that can be formed is 5.
Therefore, the answer is 5 teams.
A p-value of 0.04 obtained from a two-tailed t-test means that there is a ____ % chance that the obtained results are due to _______. Given the conventional significance level, you would accept that the _________ hypothesis is correct.
A p-value of 0.04 obtained from a two-tailed t-test means that there is a 4% chance that the obtained results are due to chance. Given the conventional significance level, you would accept that the alternative hypothesis is correct.
The P=0.04 defines that if the null hypothesis is true and if you perform the study a large number of times and in exactly the same manner.
Drawing random samples from the population on each occasion, then, on 4% of occasions, you would get the same or greater difference between groups.
In statistical hypothesis testing, we need to express the null hypothesis, which is the no statistical difference within the groups, and the alternative hypothesis, which is the statistical difference.
Then, we determine the test statistic, which is a standardized quantitative measure of the group difference.
The null hypothesis predicts that the test statistic value will be small, but there is a slight possibility that it will be big by chance. We utilize the test statistic to compute the p-value once we determine the test statistic.
The p-value is described as the calculated probability of determining the observed result from the value of the test statistic, or larger, under the null hypothesis.
Therefore, we can conclude that the value of the definition of the p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.
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math homework help me
Answer:
D
Step-by-step explanation:
Option A has a dot on -25 and the arrows point from there to the left of the number line, going down from there. Representing x<-25.
Option B has a dot on -25 and the arrow goes to the right from there meaning it goes up. Representing x>-25
Option C has a dot on 25 and an arrow pointing to the left going down. Representing x<25
Finally, option D has a dot on 25 and an arrow pointing to the right meaning the number is going upward as intended by the question.
What is the equation in slope intercept form?
2x−y=−21
The required equation in slope intercept form is equal to y = -2x - 21.
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 and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.Based on the information provided about the line, it is represented by this equation;
2x - y = -21
Making y the subject of formula in the above equation, we have the following:
y = -2x - 21
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write an expression for the apparent nth term an of the sequence. (assume that n begins with 1.) 3, 10, 29, 66, 127,
the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.
the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.
an = 3*2^(n-1) + 1
The sequence appears to follow a pattern of 3*2^n + 1
Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1. (Note that n begins with 1, so we subtract 1 from n.)
The nth term an of the sequence 3, 10, 29, 66, 127, can be expressed as 3*2^(n-1) + 1. This follows a pattern of multiplying the previous term by 2 and then adding 1. For example, the second term 10 is 3*2^1 + 1, and the third term is 3*2^2 + 1. This pattern continues for each term in the sequence, which begins at n=1. Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.
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The numbers 840 and 8316, written as the products. of their prime factors, are 840= 2¹ × 3 × 5 × 7 and 8316= 22 x 3³ x 7 x 11. Hence, find
(i) the greatest whole number that will divide both 840 and 8316 exactly,
(ii) the smallest non-zero whole number that is divisible by both 840 and 8316.
Pls help asap
Answer:
1) 84
2) 83160
Step-by-step explanation:
Greatest common divisor and Least common multiple
840 = 2³ * 3 * 5 * 7
8316 = 2² * 3³ * 7 * 11
i) The greatest whole number that will divide both 840 and 8316 is the
Greatest common divisor. Find only the common factors.
Greatest common divisor = 2² * 3 * 7
= 84
84 is the greatest whole number that divides both 840 and 8316.
Answer: 84
ii) The smallest non-zero whole number that is divisible by 840 and 8316 is Least common multiple of 840 & 8316.
Least common multiple = 2³ * 3³ * 5 * 7 * 11
= 8 * 27 * 5 * 7 * 11
=83160
A landscaper uses boot length to estimate distances. The length of the boot is about 32 cm long. If the landscaper makes a garden that has a width of 3.5 m, approximately how many boot lengths is the width of the garden?
A. 1 boot length
B. 9 boot lengths
C. 11 boot lengths
D. 36 boot lengths
Answer:
I honestly hv iyiu u ughu ugvjug uyvbuyg uugbjug niyhnig mhyij. umnninji. oh jiuh
For every m ≥ 2, let Q(m) be the least positive integer with the following property: For every n ≥ Q(m), there is always a perfect cube k^3 in the range n < k^3 ≤ m.n Find the remainder when Σ 2017 m=2 Q(m) is divided by 1000.
The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.
448
Q(m) is the least positive integer such that for every n ≥ Q(m), there is a perfect cube k^3 in the range n < k^3 ≤ m.
For example, Q(2) = 1 since 1^3 is in the range 1 < 1^3 ≤ 2.
Similarly, Q(3) = 2 since 2^3 is in the range 2 < 2^3 ≤ 3, and Q(4) = 3 since 3^3 is in the range 3 < 3^3 ≤ 4.
We are asked to find the remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000.
To do this, we can calculate the sum of the first 2017 terms of the sequence.
Q(2) + Q(3) + Q(4) + ... + Q(2017) = 448
Since 448 is divisible by 1000, the remainder when the sum is divided by 1000 is 0.
The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.
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For the same particle as in question 1, write and evaluate an integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75.
An integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75 is 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt.
We have been given two functions representing the displacement of the particle,
x(t)=2cos(πt)
y(t)=4sin(πt)
To find the velocity vector with the help of these functions, we have to differentiate them with respect to time
i.e,
dx(t)/dt=d{2cos(πt)}/dt=-2sin(πt)
dy(t)/dt=d{4sin(πt)}/dt=4cos(πt)
and finally, the velocity vector would be written as,
v(t)=-2sin(πt) i +4cos(πt) j
Now to get the distance for the given limits we have to integrate the magnitude of the given velocity
i.e, integrate 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt
which would approximately result in a value of 3.69 units in length.
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Premises: If a child is arrested for a minor crime, he or she is either charged with the crime or released with no charges. A child released with no chargers cannot be required by the court to seek counseling. Children are almost never charged with first time they are arrested. A child, Jonathan, was arrested for a first crime and is required by the court to seek coun Conclusion: Jonathan was not charged with the crime
Necessarily true
Probably, but not necessarily, true.
Indeterminable, cannot be determined.
Probably, but not necessarily, false/
Necessarily false.
The correct option is e. (Necessarily False) It required by the court to seek counselling
Because it is given as a fact that the child was "required by the court to seek counselling" ; and there is already P -> Q statement; where P : A child is released with no charges. and Q : Child is NOT required by the court to seek counseling. Taking the negation of this [tex]$\sim Q \Longrightarrow \sim P$[/tex]
[tex]$\sim P:$[/tex]Child is released with some charge.
If your child is arrested for a criminal offence and they are under 18, the police must tell you as soon as possible. The police should not interview your child until you are present, unless a delay would mean an immediate risk of harm to someone or serious loss of, or damage to, property.
Legal Counselling is the process by which a lawyer communicates advice to a client. I cannot emphasize anymore over the fact that it is the duty of an advocate to fearlessly uphold the interests of his client by all fair and honorable means without regard to any unpleasant consequences to himself or any other.
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A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 75 mph. Another train leaves Boston for New York on an adjacent set of tracks at 4:00 P.M. and averages 65 mph. At
what time will the trains meet? (Round to the nearest minute.)
They have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.
What time will the trains meet?50t = 40(t+1)
10t = 40
They are not travelling in the same way. They would cross paths in 4 hours if they were travelling in the same direction.
Before the NY train departs for Boston, a Boston train goes 40 miles.
After they have both travelled a total of 160 miles, they will now combine.
40x+50x=160
90x=160
x=16/9
1:46:40
After they have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.
They will get together at 5:46:40.
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A school group is going on a trip to a museum. Admission is $10 per student. Eight students have guaranteed they will go, but additional students may be going. The total admission the group will have to pay can be represented by the expression 10(8 + x). The group leader simplifies this expression to 80 + x to calculate how much money they will need. Is this correct? If 6 additional students go, will they have enough money to cover the admission cost?
The value of the equation is y = 10 ( 8 + x ) = 80 + 10x , where y is the total cost of admission
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 equation be represented as A
Now , the value of A is
The cost of admission per student is c = $ 10
Let the total cost of admission be represented as y
Now , the number of students = 8 students
The number of additional students = x
So , the total cost of admission y = 10 ( x + 8 )
On simplifying the equation , we get
The total cost of admission y = 10x + 80
Now , if 6 more students go , the equation will be
The total cost of admission y₁ = 10 ( x + 6 + 8 )
On simplifying the equation , we get
The total cost of admission y₁ = 10x + 140
Hence , the equation is y = 10x + 80
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Finding the zeros of a polynomial
To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.
What is a polynomial?
A polynomial is a mathematical expression that is a sum of powers in one or more variables (indeterminates) with non-negative integer exponents and real or complex coefficients. The degree of a polynomial is the highest power of the variable. For example, the polynomial 3x^2 + 2x - 1 is a polynomial of degree 2, and the polynomial 5 is a polynomial of degree 0.
To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.
For example, to find the zeroes of the polynomial 3x^2 + 2x - 1, we set the polynomial equal to zero:
3x^2 + 2x - 1 = 0
Then we can factor the polynomial or use the quadratic formula to find the solutions:
x = (-2 +/- sqrt(2^2 - 43(-1)) ) / (2*3) = (-2 +/- sqrt(4 + 12))/6 = (-2 +/- sqrt(16))/6 = (-1 +/- sqrt(4))/3 = (-1 +/- 2i)/3
The zeroes of the polynomial 3x^2 + 2x - 1 are x = (-1 + 2i)/3 and x = (-1 - 2i)/3, which are complex numbers.
Hence, To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.
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There are 32 crates. Each crate holds 27 cans of soup. Which expressions that are NOT good ways to use compatible numbers to estimate the number of cans in the crates.a. 30 X 20b. 30 X 30c. 32 X 27d. 25 X 32e. 25 X 30
a)30*20 b)30*30 d)25*32 e)25*30 are NOT good ways to use compatible numbers to estimate the number of cans in the crates.
And the best expressions that is the good ways to use compatible numbers to estimate the number of cans in the crates is 32*27
As given in the question,
There are 32 crates. Each crate holds 27 cans of soup.
i.e. Number of total crates = 32
Number of can of soups in each crate = 27
The total number of cans of soup in every crates = 32*27
The total number of cans of soup in every crates = 864
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which pattern should replace the question mark in column 4?this question is required. * circle pattern up one
The answer to column 4 is a circle pattern that is shifted one unit up. This pattern consists of a series of overlapping circles that expand outward in a vertical direction.
To replace the question mark in column 4, you need to identify the pattern that is shifted one unit up. To do this, start by looking at the pattern in column 3 and imagining it shifted upwards one unit. This will give you the pattern for column 4. The pattern is a series of overlapping circles which expand outward in a vertical direction. To create the pattern, start by drawing a circle in the center of the column. Then, draw circles around the center circle that are slightly larger than the previous one. Repeat this process until the circles reach the edge of the column. This will create the circle pattern that is shifted one unit up. Finally, connect the circles with straight lines to create the full pattern. This pattern will replace the question mark in column 4.
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The complete question: which pattern should replace the question mark in column 4? this question is required. * circle pattern up one circle pattern down one
g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y
The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.
In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property. To determine this property, we can look at the two-dimensional transformation above, where y = ax + b. In order for the PDFs of x and y to be the same, the linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1.In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.
The complete question is : g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y = ax + b, are to be the same?
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1. Consider the graph of the function y = sin x + cos x. Describe its overall shape.
Is it periodic?
How do you know?
2. Using a graphing calculator or other graphing device, estimate the x- and y-values of the maximum point for the graph (the first such point where x > 0). It may be helpful to express the x-value as a multiple of π.
3. Now consider other graphs of the form y = A sin x + B cos x for various values of A and B.
Sketch the graph when A = 2 and B = 1, and, find the x - and y-values for the maximum point. (Remember to express the x-value as a multiple of π, if possible.)
Has it moved?
4. Repeat and sketch the graph for A = 1, B = 2.
Is there any relationship to what you found in part (2)?
5. Explain what you have discovered from completing this activity using details and examples.
It is revealed through completing the task that the graph of y = sin x + cos x is periodic, having a maximum point at x 0.94 and y 2.24. We've also noted that changing the values of A and B causes the graph to move to the left, with the highest point at x 0.44 and y 2.84. This demonstrates that the ratio of A and B determines the greatest point of the graph.
What does this activity shows?This activity has demonstrated the effect of changing the coefficients of sine and cosine functions when combined. For example, when A and B are both 1, the graph of y = sin x + cos x creates a wave-like shape with a maximum point at (π/2, 2). When A is increased to 2 and B is kept at 1, the maximum point moves to the right and increases in y-value to (2π/3, 3). When B is increased to 2 and A is kept at 1, the maximum point moves to the left and increases in y-value to (π/3, 3). This shows that when the coefficient of the sine term is increased, the maximum point moves to the right, and when the coefficient of the cosine term is increased, the maximum point moves to the left. This also shows that the maximum point of the graph y = A sin x + B cos x increases in y-value as A and B increase.
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2. If 9 men can do a piece of work in 6 days, how long will it take 12 men to do the same work?
Answer: 4.5 Days
Step-by-step explanation:
The work requires 9 men x 6 days or 54 man-days.
So 12 men will do the same work in 54 man-days/12 men
= 4.5 days.
I hope this is right sorry if its not
the cost of chesse increased by 25%. how much is the new price of the cheese that originally cost $4.20. PLEASE HELP WILL GIVE BRAINLIST FOR SOLULTIONS
Answer:
$5.25
Step-by-step explanation:
Original cost of cheese = $4.20
An increase in price of 25% means the cost increase = 25% of $4.20
25% in decimal = 25/100 = 0.25 (or 1/4)
25% of $4.20 = 0.25 x $4.20 = $1.05
or, if you are more comfortable working with fractions
25% of $4.20 = 1/4 x $4.20 = $1.05
This is only the cost increase.
Add this increase to the original cost to get the new price:
New price = $4.20 + $1.05 =$5.25
a group of students were asked if they carry a credit card. the responses are listed in the table. if a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. round your answer to three decimal places.
The probability that the student owns a credit card given that they are a freshman is 0.350 (3 d.p.)
[tex]Probability\: of\: an\: event\: occurring = \frac{Number\: of \:ways\:it\:can\:occur}{Total\:no.\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student is a freshman
Let P(B) = probability that the student owns a credit card
Use the given table to calculate the probability that the student is a freshman:
[tex]= > P(A)=\frac{60}{100} =0.6[/tex]
And the probability that the student is a freshman and owns a credit card:
[tex]= > P(A \cap B)=\frac{21}{100}=0.21[/tex]
To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of B given A is:
[tex]P(B |A)=\frac{P(A\cap B)}{P(A)}[/tex]
Substitute the found values into the formula:
[tex]P(B|A)=\frac{0.21}{0.6} =0.35[/tex]
Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35.
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The complete question is:
A group of students was asked if they carry a credit card. the responses are listed in the table. if a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. round your answer to three decimal places.
For each graph describe the domain and range using interval notation. Determine if the graph is a function. Also list increasing,decreasing, or constant intervals
The interval notation, which describes a set of numbers by using values enclosed in brackets, can be used to express the domain and range. When writing intervals, we place a square bracket around the endpoint when it is part of the set and a parenthesis around it if it is not or if the interval is unbound.
What the Finding the Domain of a Function Defined by an Equation?Our introduction to the ideas of domain and range was in Functions and Function Notation. Identifying the domains and ranges for particular functions will be practiced in this session. Be aware that while choosing domains and ranges, we must take into account what is realistically feasible or significant, such as the number of tickets sold and the year in the previous horror movie example. Additionally, we must think about what is allowed mathematically. As an illustration, if the domain and range are real numbers, we cannot include any input value that causes us to take the even root of a negative number. Alternatively, in a function denoted by a formula, we are not allowed to include any input value whose domain would cause us to divide by 0.The interval notation, which describes a set of numbers by using values enclosed in brackets, can be used to express the domain and range. When notating intervals, we use square brackets to denote inclusion of the endpoint in the set and parentheses to denote exclusion of the endpoint or unbounded intervals. The interval that is more than 0 and less than or equal to 100, for instance, must be expressed as [0,100] if someone has $100 to spend.To Learn more About domain and range refer To:
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The sum of ages of Akua and Yeboah is 23 years. Akua is 3 years older than Yeboah. Find: 1. The age of Yeboah. 2. The products of their ages.
Answer:
Step-by-step explanation:
we first have to remove the 3 years as it is the difference
then when we divide it we get the age of yeboah=10
as akua is 3 years older we add the3 to the 10= 13
the product is = 10×13=130
please help! Thank you
The unit rate of change in this situation is 0.25 mile per hour.
What is the unit rate of change in this situation?The unit rate of change in this situation is 0.25 mile per hour.This means that for every 1 hour the painting crew works, they will paint 0.25 mile of the road.This rate of change can be calculated by dividing the total distance painted (9.5 miles) by the total amount of time (hours) it took to paint it (38 hours). Therefore, 9.5 miles/38 hours = 0.25 mile/hour.This unit rate of change indicates that the painting crew is consistently painting 0.25 mile of the road per hour.This is important because it helps the crew accurately plan how long it will take to complete the 24-mile stretch of road, as well as how much paint they need to purchase and how much manpower is needed.To learn more about the unit rate of change refer to:
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Each day, Millie reads 225 pages of a book while her brother Lee reads 155 pages. Which expression can be used to find p, the total number of pages Millie and Lee read each day?
A. 72-48=r
B. 48+r=72
C.72-r=48
D.72+48=r
The expression for the total number of pages Millie and Lee read each day is 225 + 155.
How to determine the total number of pages Millie and Lee read each day?From the question, we have the following parameters that can be used in our computation:
Mille = 225 pages
Lee = 155 pages
The expression to find the total number of pages Millie and Lee read each day is given by the sum of the individual pages
i.e. p = 225 + 155
So, the expression to find p is p = 225 + 155.
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find the standard deviation for the distribution of the number of people you talk to before finding your first piece of gum.
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed.
What is standard deviation?The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range. The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.How dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed value from the mean. Any distribution will have roughly 95% of values within 2 standard deviations of the mean.To learn more about standard deviation refer to:
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Find the values of x and y in each parallelogram
The value of x and y of the first parallelogram is x = 7 and y = 9
The value of x and y of the second parallelogram is x = 3 and y = 6
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
a)
Let the first parallelogram be ABCD
Now , the opposite sides are parallel and opposite sides are congruent
So , The measure of AB = measure of CD
And , the measure of AD = measure of BC
Substituting the values in the equation , we get
3x - 5 = 2x + 2 be equation (1)
On simplifying the equation , we get
Subtracting 2x on both sides of the equation , we get
x - 5 = 2
Adding 5 on both sides of the equation , we get
x = 7
Now , 2y - 6 = y + 3 be equation (2)
On simplifying the equation , we get
Subtracting y on both sides of the equation , we get
y - 6 = 3
Adding 6 on both sides of the equation , we get
y = 9
Therefore , the value of x and y of the parallelogram is 7 and 9 respectively
b)
Let the second parallelogram be ABCD
Now , the the diagonals of a parallelogram bisect each other
Let O be the point of intersection of diagonals
So , The measure of AO = measure of CO
And , the measure of DO = measure of BO
Substituting the values in the equation , we get
2x + 5 = 11 be equation (1)
On simplifying the equation , we get
Subtracting 5 on both sides of the equation , we get
2x = 6
Divide by 2 on both sides of the equation , we get
x = 3
Now , y + 4 = 2x + 4 be equation (2)
On simplifying the equation , we get
Substitute the value of x = 3 in the equation , we get
y + 4 = 2 ( 3 ) + 4
y + 4 = 10
Subtracting 4 on both sides of the equation , we get
y = 6
Therefore , the value of x and y of the parallelogram is 3 and 6 respectively
Hence , the measures of parallelogram is solved
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Find the x-intercept of the line -5x-2y=15
Answer:
The x intercept is -3
Step-by-step explanation:
To find the x intercept, let y = 0 and solve for x.
-5x-2y=15
-5x-2*0=15
-5x=15
Divide each side by -5
-5x/-5 = 15/-5
x = -3
The x intercept is -3
Note that triangle ABD from part A is a 30 - 60 - 90 triangle.
Drag the tiles to the correct box to show how the Pythagorean theorem can be used to find
We will examine the 30-60-90 triangle concept in this session and learn everything there is to know about it, including its formula, definition, sides, area, and the rules that apply to this triangle.
What is the triangle of 30-60-90?A 30-60-90 triangle is a special sort of right triangle that always has angles that are 30, 60, and 90 degrees.
The angles of the triangles ABC and PQK in this instance are 30°, 60°, and 90°, respectively.
The side opposing the 30° angle, AB = y, will always be smaller because 30° is the triangle's smallest angle.
The side opposing the 60° angle, BC = y 3 = y 3, will be of medium length because 60° is the triangle's mid-sized degree angle.
The hypotenuse AC = 2y will be the greatest side on the side across from the 90° angle because 90° is the largest angle.
Considering that the Pythagorean Theorem is given by:
a² =b² +c²AD² + 1² = 2²AD² = 3²To learn more about triangle refer to:
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Complete question -
Howww did you fine the answer???
convert the following numbers from the given base to the other three bases listed in the table: decimal binary octal hexadecimal 369.3125 ? ? ? ? 10111101.101 ? ? ? ? 326.5 ? ? ? ? f3c7.a
Decimal: 369.3125 Binary: 101111001.0101 Octal: 571.5 Hexadecimal: 171.A8. The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows: Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8.
Decimal: 10111101.101 Binary: 10111101.101 Octal: 277.125 Hexadecimal: BD.1A
Decimal: 326.5 Binary: 10100010.1 Octal: 502.1 Hexadecimal: 142.8
Decimal: F3C7.A82 Binary: 1111001111100111.10101000010 Octal: 36367.5212 Hexadecimal: F3C7.A82
To convert a number from one base to another, we can use the following steps:
1. Identify the number and its base.
2. Convert the number to its equivalent in decimal form.
3. Convert the decimal form of the number to the desired base.
For example, to convert the number 369.3125 from decimal to binary, octal, and hexadecimal, we can follow these steps:
1. Identify the number and its base: 369.3125 is a decimal number.
2. Convert the number to its equivalent in decimal form: 369.3125 is already in decimal form, so we don't need to convert it.
3. Convert the decimal form of the number to the desired base:
Binary: 101111001.0101
Octal: 571.5
Hexadecimal: 171.A8
The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows: Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8. Similarly, the number 10111101.101 can be converted to binary, octal, and hexadecimal as follows: Binary: 10111101.101, Octal: 277.125, Hexadecimal: BD.1A. Finally, the number 326.5 can be converted to binary, octal, and hexadecimal as follows: Binary: 10100010.1, Octal: 502.1, Hexadecimal: 142.8, and the number F3C7.A82 can be converted to binary, octal, and hexadecimal as follows: Binary: 1111001111100111.10101000010, Octal: 36367.5212, Hexadecimal: F3C7.A82.
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