By using the concept of division, it can be calculated that
The statement given in the fourth option
Two pizzas are shared equally among zero people do not have a solution
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on division.
For the first option
Number of pizzas = 6
Number of person = 3
Number of pizzas each person get = 6 [tex]\div[/tex] 3 = 2
This problem has a solution.
For the second option
Number of pizzas = 3
Number of person = 2
Number of pizzas each person get = 3 [tex]\div[/tex] 2 = 1.5
This problem has a solution.
For the third option
Number of pizzas = 0
Number of person = 3
Number of pizzas each person get = 0 [tex]\div[/tex] 3 = 0
This problem has a solution.
For the fourth option
Number of pizzas = 2
Number of person = 0
Number of pizzas each person get = 2 [tex]\div[/tex] 0
Now anything divided by zero is not possible
This problem do not have a solution.
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solve for x
2 | 3x + 1 | -4 =6
Step-by-step:
2 | 3x + 1 | -4 = 6
2 | 3x + 1 | = 10
| 3x + 1 | = 5
| 3x + 1 | = ±5
Solve for both: 3x + 1 = -5 AND 3x + 1 = 5
3x + 1 = - 5
3x = - 6
x = -2
3x + 1 = 5
3x = 4
x = 4/3
x = -2, 4/3
Answer:
3
Step-by-step explanation
What is the value of. (3/4)2
Answer:its 14
Step-by-step explanation:
Answer: 1 1/2 / 1.5
Step-by-step explanation: So, if you divide 3 by 4, you should get 0.75, then you would multiply that to get 1.5 or 1 1/2 (as a fraction) I think this is the question you asked, but if so, I hoped this helped!
an accident reconstructionist takes the measurements of the yaw marks at the scene of an accident. what is the radius of the curve if the middle ordinate measures 4.8 feet when using a chord with a length of 42ft? round your answer to the nearest tenth of a foot (one place after the decimal).
26.3 feet is the radius of the curve if the middle ordinate measures 4.8 feet when using a chord with a length of 42ft.
The radius of the curve is 26.3 feet.
1. Use the equation: 2r = chord length/sin of the angle between the chords.
2. Plug in the chord length Just use the chord length formula as follows: Chord length is equal to 2(r2-d2), where r is the circle's radius and d is the chord's perpendicular distance from its center.(42ft) and the middle ordinate (4.8ft) and solve for r.
3. 2r = 42/sin (4.8/2) = 42/ sin 2.4 = 26.3
4. Round answer to the nearest tenth of a foot (one place after the decimal): 26.3 feet.
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50 points decreased by 26%
step by step
Answer:
37
Step-by-step explanation:
50*26%
50-(50*26%)
suppose that all license plates in a state have three letters and then four digits. if a plate is chosen at random, what is the probability that all three letters and all four numbers on the plate will be different? (round your answer to three decimal places.)
The probability that a randomly chosen plate contains the number 2222 is 0.000028 approximately.
The probability that a randomly chosen plate contains the sub-string HI is 0.002548 approximately.
Given that:
The license plate was in the form of 3 letters followed by 3 digits or 2 letters followed by 4 digits.
Part (A)
Let A be the way the symbol is three letters followed by three numbers, and B be the way two letters followed by four numbers.
Repetition is allowed here. There are 26 alphabetic characters and 10 unique digits.
If 3 letters followed by 3 numbers, the selection method is:
26 × 26 × 26 × 10 × 10 × 10
⇒ (26)² ×(10)⁴ = 6760000
The number of possibilities is 17576000 + 6760000 = 24336000
contains the digits 2222.
That is, the first two letters can be any alphabet, but the remaining digits he must be 2222. Disk contains number 2222:
(26) ² = 676
Probability that randomly selected disk contains number 2222:
676/24336000 ≈ 0.000028
Part (B):
Selected disk contains substring HI Number of possibilities:
3 letters followed by 3 digits, the disc has Un
26 × 1 ×10³ × 1 × 26 ×10³
2 letters followed by 4 digits, the number of possible ways is as follows.
1 × 10⁴
So the total number of ways a randomly chosen plate contains the substring HI is:
620000/24336000 ≈ 0.002548
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an insurance company conducted an opinion poll for a new health policy. in a sample of 200 participants, 117 of them supported this policy. does this provide strong evidence that more than a half of americans are supporting the new health policy? compute the value of the test statistic (round off to first decimal place).
Therefore , the p- value is 0.008 , thus half of population is supporting.
Describe the hypothesis .A hypothesis is a proposed explanation for a phenomenon. The scientific method states that a theory cannot be deemed scientific unless it has been put to the test. The majority of scientific ideas are founded on historical findings that are insufficiently explained by current knowledge.
Here,
test statistics Z=
Z = [tex]\frac{p-p'}{\sqrt{p'(1-p')/n} }[/tex]
for
H0 : p= 0.5
And
Ha: p>0.5
Z =(0.585-0.5) / ((0.5)(0.5)/200)
Z=2.4
Since p =x/n=117/200=0.585
Thus
p- value= P(Z>2.4)=1-Ф(2.4)=1-0.992 =0.008
Therefore , the p- value is 0.008 , thus half of population is supporting.
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A phone company offers two monthly plans. Plan A costs $16 plus an additional
$0.18 for each minute of calls. Plan B costs $28 plus an additional $0.14 for each minute of calls.
The total cost and the number of minutes of the plan will be $70 and 300 minutes, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A telephone organization offers two month-to-month designs. Plan An expense of $16 in addition to an extra $0.18 for every moment of the call. Plan B costs $28 in addition to an extra $0.14 for every moment of the call.
Let 'y' be the total amount and 'x' be the number of minutes. Then we have
y = 0.18x + 16 ...1
y = 0.14x + 28 ...2
From equations 1 and 2, then we have
0.18x + 16 = 0.14x + 28
0.18x - 0.14x = 28 - 16
0.04x = 12
x = 12 / 0.04
x = 300
Then the value of the variable 'y' will be given as,
y = 0.18(300) + 16
y = 54 + 16
y = $70
The total cost and the number of minutes of the plan will be $70 and 300 minutes, respectively.
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Plssss need help
Don’t understand
On a multiple-choice test of
92 questions, a student gets 16 questions wrong. To the nearest tenth of a percent, what percent of the questions did the student solve correctly?
Evaluate 11.5x + 10.9y when x = 6 and y =7
[tex]11.5x+10.9y[/tex] when x is 6 and y is 7
Substitute:
[tex]11.5(x)+10.9(y)[/tex]
[tex]11.5(6)+10.9(7)[/tex]
Solve:
[tex]11.5\times6=69\\10.9\times7=76.3[/tex]
[tex]69+76.3[/tex]
[tex]=\fbox{145.3}[/tex]
alina wants to make keepsake boxes for her two best friends. she doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with a limited amount of material. for eliza, alina wants to make a rectangular box whose base is twice as long as it is wide. this box will be lined on the entire inside with velvet and in addition the outside of the top of the box is to be lined in velvet. if alina has 300 square inches of velvet, how can she make eliza's box so that it holds as many keepsakes as possible? find the width (w), length (l), and height of the box in inches. (round your answers to three decimal places.)
The width, length and height of the box is 12.247 inch, 24.494 inch, 73.482 inch respectively.
We have given that Alina wants to make a rectangular box whose base is twice as long as it's wide and alina has 300 square inches of velvet.
i.e A = l × w
it s given that l = 2w
∴ A = 2w²
⇒ 300 = 2w²
w² = 150
w = 12.247 inch
i.e. l = 2w
l = 2(12.247)
l = 24.494 inch
Therefore length of the box is 24.494 inch and width is 12.247 inch.
Now we have to find height of the box.
For the height of rectangle we know the formula
i,e, Height = [tex]\frac{P}{2}[/tex] - w
where P is perimeter
we will first find perimeter of rectangle.
Therefore P = 2(l + w)
P = 2(24.494 + 12.247)
P = 2(36.741)
P = 73.482 inch
Hence the height of the rectangle is 73.482 inch.
Therefore the Eliza's box that Alina make has width 12.247 inch, length 24.494 inch and height 73.482 inch.
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in the five whys, why is it important to continue to ask why after asking why the problem occurred? g
The reason asking why the problem occurred This frequently identifies problems with the organization or places where processes need to be addressed.
What is 5 Whys?The process is remarkably straightforward: whenever an issue arises, you ask "Why?" five times to get to the bottom of it. Then, when a remedy emerges, you put it into action to stop the problem from happening again.
The nice thing about 5 Whys is that it challenges you to move beyond blaming and question why that occurred.
This frequently identifies problems with the organization or places where processes need to be addressed.
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sergio read the first 18 pages of a novel in 2 hours what is the unit rate at which he is reading plss help asap tysm <3
The answer will be (9)
Step-by-step explanation:
The first step to dividing fractions of 18 divide 2 than (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators.
If Sergio read 18 pages of novel in 2 hours, than he's only reading 9 pages at a time than the next!
true or false: a) every unitary operator u : x ! x is normal. b) a matrix is unitary if and only if it is invertible.
True, Every normal unitary operator u: x! x exists.
False, An if only if it is invertible, a matrix qualifies as unitary.
What is the matrix?
A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix, are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
Here, we have
a. Every unitary operator U:X→X is normal as an operator A is unitary if A*A = AA* = I and an operator is normal if A*A = AA*.
Hence, every unitary operator u: x → x is normal.
b. A unitary matrix is always invertible but an invertible matrix need not be unitary. An invertible matrix A is unitary if A⁻¹ = A*
Hence, it is not true.
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a factory has two assembly lines, A and B that make the same bottles. on monday only assembly line A was functioning and it made 600 bottles. on tuesday both assembly lines were functioning fit the same amount of time. line a made 270 bottles per hour and line b made 330 bottles per hour. line b made as many bottles on tuesday as line A did over both days. write and equation that can be used to find the numbers of hours,h,that the assembly lines were functioning in both days
A manufacturing plant has two assembly lines for producing glass bottles. The manager
was concerned about whether the proportion of defective bottles differs between the two
assembly lines. She gathered two independent samples and found the following data:
n 1 =100, ^p 1 =.1,n 2 =100, ^p 2 =.13.
(a) Set up the appropriate null and alternative hypotheses.
(b) Compute the value of the test statistic.
(c) Draw a conclusion as to whether there is a difference between the two assembly lines
Statistics can promote limitations in perception in all of the following ways except by __________. A. Defining the relationship between variables in a subjective manner b. Providing information about participants that leads to a biased point of view c. Considering alternative perspectives when defining variable relationships d. Creating personal labels for individuals that relate to participants within a study please select the best answer from the choices provided a b c d.
Statistics can promote limitations in perception in all the following ways, except by Option C. Considering alternative perspectives when defining variable relationships.
However, option C does not promote limitations in perception, as it encourages a more open-minded approach to interpreting the data. Statistics can promote limitations in perception in all the following ways, except by Option C. Considering alternative perspectives when defining variable relationshipsOption C encourages a holistic approach to analyzing statistics, rather than promoting limitations in perception. It encourages the analyst to consider different perspectives when interpreting the data, thus allowing a more comprehensive understanding.
This open-minded approach is essential in order to form valid conclusions. When taking into account multiple perspectives, the analyst is able to come to a more informed conclusion, rather than relying on a single-perspective interpretation. Option C does not promote limitations in perception, as it encourages a more open-minded approach to interpreting the data.
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A number cube was rolled as part of an experiment. The results are displayed in the table below.
Number
1
2
3
4
5
6
Frequency
4
6
5
7
3
5
What is the best explanation of how to find the experimental probability of rolling a 3?
Group of answer choices
A. To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary.
B. To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials. Simplify if necessary.
C. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three. Simplify if necessary.
D. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the number three. Simplify if necessary.
The option that has the best insight of how to find the experimental probability of rolling a 3 is option A
A. To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary.
What is an experimental probability?An experimental probability is a probability based on real or actual experiment, such that the result depends on the accuracy of the record of the occurrences during the experiment.
The result from the experiment is presented as follows;
Number [tex]{}[/tex] Frequency
1 [tex]{}[/tex] 4
2 [tex]{}[/tex] 6
3 [tex]{}[/tex] 5
4 [tex]{}[/tex] 7
5 [tex]{}[/tex] 3
6 [tex]{}[/tex] 5
The probability of an event is the ratio of the number of possible outcome to the number of required outcome.
Therefore: The probability of rolling a three is the ratio of the frequency of an outcome of threes to the sum of the frequency of all the events.
The correct option from which the best details of finding an experimental probability can be obtained is the option that states that the experimental probability of rolling a three is the ratio of the count of the number of times three occurs to the total number of trials, which is the frequency of rolling a three to the sum of all the frequencies in the experiment.
Mathematically, we get;
The probability of an event E, P(E) = [tex]\frac{Number\, of \, outcomes \, three}{Total \, number \, of \, outcomes}[/tex]
Therefore
[tex]P(3) = \dfrac{Number\, of \, times \, three\, occurs }{Total\, number \, of \, trials} = \dfrac{Freqiuency\ of \ 3s }{Sum\ of \ ther \ frequencies}[/tex]
[tex]P(3) = \dfrac{5}{4+6+5+7+3+5} =\dfrac{1}{6}[/tex]
The correct option is option A
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Factorise - 3 x square y - 3 x + 9 x y
square
The factorization of the given expression is -3x(xy+3y-1).
The given expression is -3x²y-3x+9xy².
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The factorization of the given expression is as follows
-3x²y-3x+9xy²
= -3x(xy-1+3y)
= -3x(xy+3y-1)
Therefore, the factorization of the given expression is -3x(xy+3y-1).
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Find the probability that a randomly selected car from this sample had 222 doors or 444 doors.
A car is selected from random sample of 100 cars,
a) The events for which the selected car has 2 doors and 4 doors are mutually exclusive event ;
i.e P(A ∩ B) = 0.
b) The probability that a randomly selected car from this sample had 2 doors or 4 doors is 0.77..
Mutually exclusive event :
A and B are mutually exclusive if they cannot occur at the same time. This means that A and B have no common result and P(A and B) = 0.
We have given a Venn diagram which consists the cars have sunroof , 2 doors and 4 doors.
Firstly we need to understand the Venn diagram properly for determining the required probability values.
From Venn diagram ,
Total number of cars in sample = 100
Cars with sunroof only = 13
Number of cars with 2 doors only = 14
Number of cars with 4 doors only = 25
Number of cars with sunroof and 2 doors = 18
Number of cars with sunroof and 4 doors = 20
a) let us consider two events A and B
A : car with two doors
B : car with four doors
As we see in Venn diagram,
the number of cars with 4 doors and 2 door, n(A∩B) = 0 => P(A and B) = 0
so, by definition of mutually exclusive event
A and B are are mutually exclusive events.
b) Probability that car with 2 doors, P(A)
= favourable outcomes for A / total outcomes
= 14+18/100 = 32/100
Probability that car with 4 doors, P(B)
= favourable cases for B/ total outcomes
= 25+20/100 = 45/100
Probability that randomly selected car from this sample had 2 doors or 4 doors = P( A or B)
= P(A) + P(B) = 77/100 = 0.77
Hence, the required probability is 0.77..
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Complete question:
Two-way tables, Venn diagrams, and probability Sunroof 13 10 18 20 14 25 2 doors 4 doors In this sample, are the events "2 doors" and "4 doors" mutually exclusive? Choose 1 answer A Yes O No Find the probability that a randomly selected car from this sample had 2 doors or 4 doors. O of 4
find the slope of the line passing through the origin which forms an angle 7pi/8 with a positive x axis
The slope of the passing line through the origin is 112.5°.
The slope of a line is given as a tangent ratio.
In this case we have the angle, so the slope would be given as
tan(7π/8).
Therefore,
The angle the line makes with the horizontal is given in radians here:
7π/8
In this degrees, we can use:
180° = π radians
1 radian = 180°/π
5π/8 radians = 5π/8 × 180° /π
=5π/8 × 180°/π
=112.5°
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a researcher wishes to estimate within $300 the true average amount of money a county spends on road repairs each year. if she wants to be 90% confident, how large a sample is necessary? the standard deviation is known to be $900.
The sample size should be 24.
What is the sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.
Here, we have
Given
Margin of error = 300
confidence level = 0.9
standard deviation = 900
Assuming the standard deviation to be of population
ME = Z(0.1/2) × σ/√n
300 = 1.645 × 900/√n
n = {(1.645 × 900)300}²
n = 24
Hence, the sample size should be 24.
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Jesse estimates that it will cost $300,000 to send his newborn son to a private college in 18 years. He currently has $65,000 to deposit in an account. What simple interest rate would he need so that $65,000 grows into $300,000 in 18 years? round to the nearest percent.
The simple interest rate would be 20%. The result is obtained by using the simple interest formula.
How to count the interest?The interest of an amount of money can be counted by the following formula.
I = P₁ - P
I = P × r × t
Where
I = interestP = principal amount (initial balance)P = final balancer = simple interest ratet = time periodJesse now has $65,000 and he deposit it in an account. After 18 years, he wishes the balance will grow into $300,000. Determine the simple interest rate!
First, let's find the interest.
I = P₁ - P
I = $300,000 - $65,000
I = $235,000
The simple interest rate is
I = P × r × t
235,000 = 65,000 × r × 18
r = 235,000 / 1,170,000
r = 0.201
r ≈ 20%
Hence, the simple interest rate he would need to deposit his money is 20%.
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during rush hour. from 8 a.m. to 9 a.m., traffic accidents occur according to a poisson process with a rate of 5 accidents per hour. between 9 a.m. and 11 a.m., they occur as an independent poisson process with a rate of 3 accidents per hour. what is the pmf of the total number of accidents between 8 a.m. and 11 a.m.?
Traffic accidents occur according to a poisson distribution.
The probability mass function of the total number of accidents between 8 a.m. and 11 a.m is
P(Z = z) = (e⁻⁸× 8ᶻ) /z! ; z = 0, 1, 2, ...........
= 0 ; otherwise
Let X be the random variable that denotes the number of traffic accidents occurring between 8 am and 9 am.
X ~ P(5) and P(X) = 5
Let Y be random variable that denotes the number of traffic accidents occurring between 9am and 11 am.
Possion process with rate 3 accidents per hour
Y~ P(3)
Let Z be random variable that denotes the number of traffic accidents occurring between 8a.m. and 11 am.
For 8 a.m. to 11 a.m. ,P(Z = X+Y) = P(Z = 3+5 = 8)
Possion probability mass function for it is
P(x, λ ) =(e⁻λ λˣ)/x!
The p.m. f of the total number of accidents between 8 am and 11 am is
P(Z = z) = (e⁻⁸× 8ᶻ) /z! ; z = 0, 1, 2, ...........
= 0 ; otherwise
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PLEASE HELP ASAP THANK YOU
in triangle LMN, m∠L = (6c + 35)°. If the exterior angle to ∠L measures 79°, determine the value of c.
c = 24
c = 7
c = 44
c = 11
The value of c for the angle of the triangle will be 7.34.
What are sides and angles?Congruence and likeness tests in geometry require comparing matching sides and angles of polygons. Each side and angle in one polygon is paired with a side or angle in the second polygon in these tests.
Given that in triangle LMN, m∠L = (6c + 35)°. If the exterior angle to ∠L measures 79°,
The value of angle c will be calculated as,
(6c + 35)° = 79°
Apply the mathematical operations and solve further,
6c = 79 - 35
6c = 44
c = 7.34
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QR has endpoints at Q(9, 3) and R(1, 1). Find the midpoint M of QR.
Answer = (5), (2)
The midpoint of points Q(9.3) and R(1,1) will be M(5,2).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the two endpoints of QR are Q(9.3) and R(1,1). The midpoint will be calculated as,
Midpoint = [x₁ + x₂]/2 , [y₁ + y₂] / 2
Midpoint = [(9 + 1 ) /2 , ( 3 + 1 ) / 2
Midpoint = 5, 2
M is the midpoint of points Q(9.3) and R(1,1) (5,2).
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Does anyone know what -7x > -35 is?
The given expression is showing an inequality.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given that, -7x > -35
The given expression is showing inequality where -7x is greater than -35
On simplifying, we get,
-7x > -35
7x < 35
x < 5
Therefore, x is less than 5
Hence, The given expression is showing an inequality.
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a boat travels 42 miles upstream in 3 hours looking for a lost diver. it then travels downstream 70 miles in 2 hours. write a system to represent the situation. then find the speed of the boat and the speed of the current. use b for boat and c for current.
The system of equations for the given situation are 14=b-c ; 35=b+c and the speed of boat is 24.5 miles/hr and speed of current is 10.5 miles/hr.
Given,
Distance covered by boat in upstream in 3 hours = 42 miles
Distance covered by boat in downstream in 2 hours = 70 miles.
Let
speed of boat in still water be 'b'
speed of current of stream be 'c'
we know that distance=speed x time
If the boat is moving upstream, the current (which is 'c' miles per hour) will push against it, reducing the boat's speed by 'c' miles per hour. The boat's resulting speed (as it travels upstream) is 'b-c' miles per hour. If, on the other hand, the boat is travelling downstream, the current will push it faster, increasing the boat's speed by 'c' miles per hour. The boat's downstream speed is 'b+c' miles per hour as a result.
Then the system of equations will be
distance while going upstream ,
distance=speed x time
42=(b-c)(3)
14=b-c....i
distance while going downstream,
70=(b+c)(2)
35=b+c....ii
solving eq. i and eq. ii
14=b-c
35=b+c
------------
49=2b
b=24.5
Substitute in eq. i,
14=24.5-c
c=24.5-14
c=10.5
Thus, the boat's speed is 24.5 miles per hour and the current's speed is 10.5 miles per hour.
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how many even integers are there bewteen 200 and 700 whose digits are all diferetn and come from the set (1,2
There are 12 even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.
What is number of permutation?
Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to determine the number of permutations.
For instance, four-digit PINs have 10 possible combinations because each digit can range from 0 to 9.
We see that the last digit of the 3 -digit number must be even to have an even number. Therefore, the last digit must either be 2 or 8.
Case 1 - the last digit is 2. We must have the hundreds digit to be 5 and the tens digit to be any 1 of {1,7,8,9}, thus obtaining 4 numbers total.
Case 2 - the last digit is 8. We now can have 2 or 5 to be the hundreds digit, and any choice still gives us 4 choices for the tens digit. Therefore, we have 2 x 4 = 8 numbers.
Adding up our cases, we have 4 + 8 = 12 numbers.
Hence, there are 12 even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.
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Complete question:
how many even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.
Serena claims that (x+3) is a factor of p(x)=x4+6x3+12x2+10x+3. Which equation must Serena show to be true in order to prove her claim?
A
p(0)=3
B
p(3)=0
C
p(0)=−3
D
p(−3)=0
Answer:
In order to prove that (x+3) is a factor of p(x), Serena must show that p(-3) = 0. This means that if we plug -3 into the polynomial p(x), the resulting value must be 0. Therefore, the correct answer is option D, p(-3)=0.
Step-by-step explanation:
each square of the three by three grid is painted so that the whole picture has at least the two lines of symmetry indicated. each grid square is painted one solid color. what is the maximum number of colors that could have been used?
3 colors are the maximum that can be used.
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
each square of the three-by-three grid is painted so that the whole picture has at least the two lines of symmetry indicated.
each grid square is painted one solid color
Based on the symmetry lines the groups that must be the same color are
{1,3,7,9}
{2,4,6,8}
and {5}
Hence, 3 colors are the maximum that can be used.
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