Answer:
[tex]0 < x < 60[/tex]
Step-by-step explanation:
By the Triangle Inequality Theorem:
30 + 30 > x, so 60 > x ----> x < 60
30 + x > 30, so x > 0
x + 30 > 30, so x > 0
Putting these inequalities together, we have 0 < x < 60. So the length of the third side can be greater than 0 inches but less than 60 inches.
Lamar will run at most 37 miles this week. So far, he has run 22 miles. What are the possible numbers of additional miles he will run?
The possible numbers of additional miles that Lamar can run are all the solutions of the inequality:
0 ≤ x ≤ 15
What are the possible numbers of additional miles?We know that Lamar will run at most 37 miles this week, and he already did run 22 miles, then the (maximum) distance left this week is:
D = 37mi - 22mi = 15mi
So he can run at most 15 miles, this means that he can run any distance between 0 miles and 15 miles by the end of the week.
So, if we define x as the distance that he will run on the week (in miles), then we can write the inequality:
0 ≤ x ≤ 15
so the possible numbers of additional miles he will run on this week are all the values of x that are a solution for the above inequality.
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In the Fig, O is the Center of the Circle
If ∠OPQ = 25° & ∠ORQ = 20°
Find: ∠PQR & ∠POR
The angles in the figure are:
∠PQR = 45°
∠POR = 90°
Given : O is the centre of circle, ∠OPQ = 25° and ∠ ORQ = 20°
To Find : values of ∠ POR and ∠ PQR.
OP = OQ = Radius
⇒ ∠OPQ = ∠OQP
⇒ ∠OQP = 25°
OR = OQ = Radius
⇒ ∠OQR = ∠ORQ
⇒ ∠OQR = 20°
∠PQR = ∠OQP + ∠OQR
⇒ ∠PQR = 25° + 20°
⇒ ∠PQR = 45°
∠POR = 2∠PQR
⇒ ∠POR = 2*45°
⇒ ∠POR = 90°
Hence we get the two angles as 45° and 90° respectively.
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There are 69 different species of flashing fireflies, also known as Lightning bugs, in the US a museum is designing a rectangular display of these 69 species with the same number of fireflies in each row. How many displays are possible
The number of displays are possible is 3
Total number of species Lightning bugs = 69
We have to arrange the same number of Lightning bugs in each row
First find the factors of the number 69
The factors of 69 = 1, 3, 23, 69
First combination is (1 × 69)
Arrange 1 Lightning bug in each row, then the number of rows will be 69
(3 × 23)
Arrange 3 Lightning bugs in each rows, then the number or rows will be 23
(23 × 3)
Arrange 23 Lightning bugs in each rows, then the number of rows will be 3
Hence, the number of displays are possible is 3
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in a small pond there are eleven lily pads in a row labeled 0 through 10. a frog is sitting on pad 1. when the frog is on pad , , it will jump to pad with probability and to pad with probability . each jump is independent of the previous jumps. if the frog reaches pad 0 it will be eaten by a patiently waiting snake. if the frog reaches pad 10 it will exit the pond, never to return. what is the probability that the frog will escape without being eaten by the snake? in a small pond there are eleven lily pads in a row labeled 0 through 10. a frog is sitting on pad 1. when the frog is on pad , , it will jump to pad with probability and to pad with probability . each jump is independent of the previous jumps. if the frog reaches pad 0 it will be eaten by a patiently waiting snake. if the frog reaches pad 10 it will exit the pond, never to return. what is the probability that the frog will escape without being eaten by the snake?
The probability that the frog will escape without being eaten by the snake is [tex]\frac{63}{146}[/tex]
What is Markov Process?
A Markov chain or Markov process is a stochastic model that depicts a series of potential occurrences where each event's likelihood is solely determined by the state it reached in the preceding event.
First, take notice that the frog has a probability of 1/2 of finally being eaten by the snake once it is on pad 5, and a probability of 1/2 of eventually emerging from the pond unharmed. Therefore, all that needs to be determined is the probability that the frog on pad 1 will make it to pad 5 without being eaten.
Consider the frog’s jumps in pairs. The frog on pad 1 will advance to pad 3 with probability [tex]\frac{9}{10} \frac{8}{10}[/tex][tex]=\frac{72}{100}[/tex] will be back at pad 1 with probability [tex]\frac{9}{10} \frac{2}{10}[/tex][tex]=\frac{18\\}{100}[/tex]
s
[tex]\frac{72}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{36}{41}[/tex] and the probability that it ultimately makes it to pad 0 is [tex]\frac{10}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{5}{41}[/tex].Similarly, in a pair of jumps the frog will advance from pad 3 to pad 5 with probability [tex]\frac{7}{10} \frac{6}{10} =\frac{42}{100}[/tex], will be back at pad 3 with probability [tex]\frac{7}{10} \frac{4}{10} +\frac{3}{10} \frac{8}{10} =\frac{52}{100}[/tex].
Because the frog will ultimately make it to pad 5 or pad 1 from pad 3, the probability that it ultimately makes it to pad 5 is [tex]\frac{42}{100}[/tex] ÷ [tex]( \frac{42}{100} +\frac{6}{100} )=\frac{7}{8}[/tex] and the probability that it ultimately makes it to pad 1 is [tex]\frac{6}{100}[/tex] ÷ [tex](\frac{42}{100} +\frac{6}{100} )=\frac{1}{8}[/tex]
The series of steps that must be made in pairs for the frog to get to pad 5 without being eaten is
1 → 3 → 5, 1 → 3 → 1 → 3 → 5, 1 → 3 → 1 → 3 → 1 → 3 → 5 and so on.
The sum of the respective probabilities of reaching pad 5 is then
[tex]\frac{36}{41} \frac{7}{8} +\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+.....[/tex]
[tex]= \frac{63}{82} (1+\frac{9}{82} +(\frac{9}{82})^{2} +....)[/tex]
[tex]=\frac{63}{82}[/tex]÷[tex](1-\frac{9}{82} )[/tex]
[tex]= \frac{63}{73}[/tex]
Therefore the requested probability is [tex]\frac{1}{2}\frac{63}{73} = \frac{63}{146}[/tex]
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LESSON 8 SESSION 2
Name
Practice Showing That the
Slope of a Line Is Constant
> Study the Example showing that the slope of a
line is constant. Then solve problems 1-5.
Example
Cece draws a graph representing her
family's car trip to the beach. She wants
to show her father that their gas
mileage in miles per gallon was the
same for the entire trip. Cece chose
three points on the line and drew
vertical line segments from the points to
the x-axis. How can she use these
segments to prove that the gas mileage
was constant for the trip?
Distance (mi)
250
150
100
30
0
(S. 155)
(1,31)
8 10
What was the gas mileage for the trip in the Example?
6
Gasoline Used (gal)
The vertical line segments create three
similar right triangles. Because the
triangles are similar, the quotient of the length of the vertical side to the length
of the horizontal side is the same for each triangle. These quotients are slopes
between (0, 0) and the points Cece chose. Because Cece could have chosen any
points on the line to make the similar triangles, the slope is constant for the
whole line. So, the gas mileage is constant for the whole trip
For the graph in the Example, find the slope between the origin and each of the
points Cece chose.
Vocabul
slope
for any two
a line, the
shange
change
of
The slope of origin (0, 0) with (1, 31); (5, 155), and (9, 279) is 31
The slope of a line:The slope of a line will indicate the direction and steepness. It is also defined as the change in the y-coordinate for a corresponding change in the x-coordinate.
Slope of a line with given points (x₁, y₁) and (x₂, y₂) is
Slope, m = (y₂ -y₁) /(x₂-x₁)Here we have
Points (1, 31) (5, 155) and (9, 279)
We need to find slopes between two points
As we know the formula for slope with given points is
Slope, m = (y₂ -y₁) /(x₂-x₁)
Here coordinates of the origin are (0, 0)
The slope between (0, 0) and (1, 31)
=> m = (31 - 0) /(1 - 0) = 31/1 = 31
The slope between (0, 0) and (5, 155)
=> m = (155 - 0) /(5- 0) = 155/5 = 31
The slope between (0, 0) and (9, 279)
=> m = (279 - 0) /(9 - 0) = 279/9 = 31
Therefore,
The slope of origin (0, 0) with (1, 31); (5, 155), and (9, 279) is 31
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a researcher was interested in the differences in the opinions about marriage between men and women. the researcher predicted that women would have different opinions about marriage from men. what would the null hypothesis suggest in this situation?
There is no null hypothesis in this situation there is no differences in the opinions about marriage between men and women
In the field of science, hypothesis testing is an effective method of determining whether or not there is a relationship between two or more variables. A null hypothesis is a default position or a general statement that no relationship or connection exists between the given variables.
The hypothesis is then tested, and based on the results of the tests, a conclusion is drawn either approving or rejecting the null hypothesis.
In the given situation, where the researcher predicted that women would have different opinions about marriage than men, the null hypothesis could be formulated because there is no difference in the opinions of men and women about marriage.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Simplify by expressing fractional exponents instead of radicals.
8√x²y⁴
The expression can be written without negative exponents as 64xy²
Simplification of ExponentsExponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.
Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a less complex form in a way that they cannot further be reduced. There are methods in algebra for simplifying exponents with different and same bases that we can use.
Steps to solving basic problems like this are;
Step 1
remove parentheses by multiplying factors.
Step 2
use exponent rules to remove parentheses in terms with exponents.
Step 3
combine like terms by adding coefficients.
Step 4
combine the constants.
In this case, we have an expression;
8√x²y⁴ which can be rewritten without using the square.
8√x²y⁴ = 64xy²
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a wire is to be cut into two pieces. one piece will be bent into a square, and the other piece will be bent into a circle. if the total area enclosed by the two pieces is to be 144 m2, what is the minimum length of wire that can be used?
A wire is cut into two pieces, one piece bent into square and other piece will be bent into circle. Therefore, the minimum length of wire that can be used is 43 m.
The relationships between the radius of a circle and its circumference and area are :
C = 2πr
A = πr²
The relationships between the side length of a square and its perimeter and area are :
P = 4s
A = s²
So, the length of wire will be
W= C + P
W = 2πr + 4s
Subject to the constraint that the sum of areas is 144 m²:
πr² + s² = 144
Using the method of Lagrange multipliers to find the extremes of wire length, we want to set the partial derivatives of the Lagrangian (L) to zero.
L = 2πr + 4s + λ(πr² +s² -144)
∂L/∂r = 0 = 2π +2πλr ------------------------------- (1)
∂L/∂s = 0 = 4 +2λs ------------------------------- (2)
∂L/∂λ = 0 = πr² +s² -144 -------------------------------- (3)
Solving for λ, we find,
1 +λr = 0 ---------------------------- (4)
⇒ λ = -1/r ----------------------------- (5)
Substituting into equation (2), we get,
4 + 2(-1/r)s = 4
⇒ s/r = 2 -------------------------------- (6)
This tells us the maximum wire length is that which makes the circle diameter equal to the side of the square.
Substituting the relation s=2r into the area constraint, we find,
πr² +(2r)² =144
⇒ r = √(144/(π+4))
⇒ r= 12/√(π+4) ≈ 2.068965 . . . m
∴ The minimum wire length will be required when the entire area is enclosed by the circle. In that case,
πr² = 144
⇒ r = √(144/π)
and, C = 2πr
= 2π√(144/π)
= 24√π ≈42.5388 . . m
rounding up the minimum value 42.5388... in 43.
∴ The minimum wire length will be required is 43 m
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QUESTION 4/10 HELP ASAPP
Answer:
Left bottom graph is the correct one.
Answer: The bottom left graph
Step-by-step explanation: The top two are decreasing, so you can rule those answers out. The bottom right one is increasing by more than 4, so that wouldn’t be the answer either. That leaves you with one option which fits the description of the graph.
The ratio of words missed to correct on Marcy’s test was 1:4 if she got 4 words wrong, how many were correct
Answer:
Marcy got 16 wrong.
Step-by-step explanation:
You simply multiply 1 ( from the missed side of the ratio ) by 4 ( how many Marcy got wrong ) which equals 4. Then you do the same to the other side. 4 ( from the "correct" side of the ratio ) by 4 ( how many Marcy got wrong ). 4 x 4 is 16. So, Marcy got 16 wrong.
Answer:
16
Step-by-step explanation:
The ratio is 1:4 means for 1 wrong word, she got 4 words correct. If she has 4 words wrong, multiply that with 4 and you got 16.
Vicky and John share some sweets in the ratio 2:7. If Vicky ends up with 12 sweets, how many will John have?
By using ratio, it is calculated that John have 42 sweets.
What is ratio?
Ratio between two quantity tells us how much bigger is one quantity as compared to the other quantity.
The first part of the ratio is called antecedent and the second part of the ratio is called consequent
Vicky and John share some sweets in the ratio 2:7
Let Vick shares 2x sweets and John shares 7x sweets
Vicky ends up with 12 sweets
By the problem,
[tex]2x = 12\\x = \frac{12}{2}\\x = 6[/tex]
Number of sweets John have = [tex]7 \times 6 = 42[/tex]
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help! ASAP!!!!!!! 4 points if you help!!!
Answer:
I believe it would be 300 dollars per week, I hope this was right :)
Step-by-step explanation:
.4x750=300
HELP DUE at 2:30 PM!!!!!
Solve.
−8/9 = −1/6 − 3/10x
Enter your answer as a mixed number in simplest form in the box.
Answer: hi
Step-by-step explanation:
If f(x) = x - 6 and g(x) = -2x + 4, what is f(x) times g(x)?
A.) -2x^2 - 24x + 16
B.) -2x^2 + 16x - 24
C.) -2x^2 + 16x + 16
D.) -2x^2 + 14x - 24
The product of f(x) and g(x) is -2x² +16x -24.
What is a function?A function is a relation such that there is only one unique output for every input.
Given that, the functions, f(x) = x-6 and g(x) = -2x + 4.
The value of f(x) × g(x) is,
f(x) × g(x)
= (x-6)(-2x+4)
= -2x²+4x + 12x -24
= -2x² +16x -24
Hence, the product of f(x) and g(x) is -2x² +16x -24.
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What is the remainder when the function, f(x)=x²-2x² -5x+16, is divided by (x+3)
O-32
O-14
O 10
022
Answer:
14/x+3
Step-by-step explanation:
Fractions and Decimals
Write each fraction as a decimal.
4. //
2/5
2/5 fraction as a decimal is 0.4.
Any number that is expressed as a fraction has two components, the numerator and the denominator. Typically, we divide the numerator by the denominator to convert a fractional number to decimal form. The formula p/q, where q=0, is used to denote fractions. While the decimal numbers, such as 7.575, are created by joining the entire number and fractional parts with a decimal point.
There are two methods to convert fraction to decimal which are given below:
Long division methodBy converting the denominator of the fraction into a power of 10For 2/5
We will divide them as mentioned above,
2/5 = 0.4
Hence, 2/5 is equal to 0.4 in decimal form.
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What is the sum of (3x + 4) + (9x – 10)?
Answer:
6(2x - 1)
Step-by-step explanation:
Just look up the answer on the calculator
The sum of 3 consecutive even numbers is 78.
What is the second number in this sequence?
Answer: 26
Step-by-step explanation:
1. Make an equation
n+n+2+n+4=78
(You have n+2 because to get to the next even number you'd have to add 2. For example, 2 is even, to get to the next even number, 4, you have you add 2.)
2. Combine like terms
3n+6=78
3. Solve for n
3n=72
n=24
4. Solve for the second number
(The second number would be n+2)\
n+2
24+2
26
ANSWER: 26
helpppppppppppppppppppppppppp asapppppppppppppppppppppppppppppppp
-2f-3.7 < 2.3 find inequality
The inequality results to f > -3.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
-2f-3.7 < 2.3
Now, solving the inequality
Add 3.7 both side
-2f-3.7 + 3.7 < 2.3 + 3.7
-2f< 6
Divide both side by 2.
-f< 3
f> -3
Hence, the inequality results to f > -3.
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when the british ship gaspee ran aground in rhode island, the local population: question 23 options: 1) burned it. 2) rescued its crew. 3) attacked it. 4) pillaged it. 5) claimed it.
Using theories of Rhode island ,we got that when the British ship Gaspee ran a ground in Rhode island, the local population 1) burned it.
On June 9, Gaspee gave chase to the packet ship Hannah, but the Gaspee ran aground in shallow water on the northwestern side of bay on what is now Gaspee Point. Her crew were unable to free her and the Dudingston decided to wait for the high tide, which would possibly set the vessel afloat. Before that could happen, however, the band of Providence men led by John Brown decided to act on a "opportunity offered of putting an end to the trouble and the vexation she daily caused." They rowed out to the ship and boarded at the break of dawn on June 10.
Hence, when the british ship gaspee ran aground in rhode island, the local population 1) burned it.
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how is random error different from systematic error? provide an example that illustrates this difference.
Systematic errors are consistently in the same direction
In contrast , random errors produce different values in random directions
Random error causes a slight difference of one measurement to from the next. It is quite unpredictable in it's variation during an experiment.
Systematic error always affects measurements by the same proportion, provided that a reading is taken the same way each time. It is predictable
An example that illustrates this difference are
Systematic errors are consistently in the same direction
for example they are always 50g , 1% or 99 mm too large or too small
In contrast , random errors produce different values in random directions
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a professor wants to estimate how many hours per week her students study. a simple random sample of 74 students had a mean of 20 hours of studying per week. construct a 99% confidence interval for the mean number of hours a student studies per week. assume that the population standard deviation is known to be 3.5 hours per week. round to two decimal places.
99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)
Given:
mean x = 20
standard deviation σ = 3.5
sample size n = 78
z score for 99% = 2.576
Interval = x±z*s/[tex]\sqrt{n}[/tex]
= 20±2.576*3.5/[tex]\sqrt{78}[/tex]
= 20±2.576*0.39629
= 20±1.0208
Interval = (21.0208,18.9792)
Therefore 99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).
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I need help with the properties of exponents. my work is past due and I'm failing my classes!
Answer:
answers found in pdf
Step-by-step explanation:
mathaway will help check your answers that what I did.
Caroline invested $900 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded continuously. Jaxon invested $900 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded daily. After 8 years, how much more money would Caroline have in her account than Jaxon, ?
Caroline would have $36 more money in her account than Jaxon.
From the question, we have
Caroline amount,
A = P* e^rt
= 900*e^(71*8)/800
= 900*e^(71/100)
=$1830.59
Jaxon amount,
A = P* e^rt
= 900*e^(69*8)/800
= 900*e^(69/100)
=$1794.34
Difference = $1830.59 - $1794.34
= $36.25
= $36 ( to the nearest dollar)
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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The equation d=3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.
What does 3 represent?
If t=1, then d=3: In 1 minute, the snail traveled 3 inches.
If t=2, then d=6: In 2 minutes, the snail traveled 6 inches.
If t=3, then d=9: In 3 minute, the snail traveled 9 inches.
The snails speed is 3 inches per minute. That's what the 3 represents. The change in distance (inches) for each minute that passes.
The tax that increases the price of an item or service is called
tax.
Answer:
also called a tariff.
Step-by-step explanation:
Please give the brainliest.
Alisa can work at most 30 hours next week, but she needs to earn at least $240. Her lawn mowing job pays $9 an hour, and her coaching job pays $15 an hour. Identify the variables, and then write a system of equations to represent the constraints on Alisa's work time and income.
The system of equation for the following conditions contains equation the equations: x + y ≤ 30 and 9x + 15y 240.
What is system of equation?
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."
Let the hours Alisa work for lawn mowing job is "x" hours and for coaching job is "y" hours.
As given in the question, Alisa can work at most 30 hours.
So the total working hours should be equal or less that 30 hours.
Therefore, the first equation can be written as:
x + y ≤ 30
And it is also given that, she needs to earn at least $240, while Her lawn mowing job pays $9 an hour, and her coaching job pays $15 for an hour.
So, Total earning = per hour earning x total hour
lawn mowing job earning = 9(x)
coaching job earning = 15(y)
Therefore, the second equation can be written as:
9x + 15y 240
Hence, the system of equation is: x + y ≤ 30 and 9x + 15y 240
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how to find the rate of change of a table
Answer:
To find the rate of change in a table, the same process applies:
Step-by-step explanation:
1. Find the coordinates of the given points. It's optional to label them.
2. Find the difference between the output values.
3. Find the difference between the input values.
4. Calculate the ratio between the change in y to the change in x: ΔyΔx.
On the first part of 550-kilometer trip a salesperson travels 4 hours and 15 minutes at an average speed of 100kilo meters per hour. The salesperson needs to arrive at the destination in another hour and 20 minutes. Find the average speed (in km/h) required for the remainder of the trip.
Answer:
you will need to go 80 km per hr
Step-by-step explanation: