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The domain of a radical is the set of all values of the independent variable for which the radical is defined.
For example, consider the radical expression √x. This expression is defined for all nonnegative values of x, since the square root of a nonnegative number is always real. Therefore, the domain of the radical √x is the set of all nonnegative values of x:
{x | x ≥ 0}
This includes all real numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.
On the other hand, if we consider the radical expression √(x-2), this expression is defined for all values of x such that x-2 is nonnegative. This means that the domain of the radical √(x-2) is the set of all values of x such that x ≥ 2:
{x | x ≥ 2}
This includes all real numbers that are greater than or equal to 2, such as 2, 3, 4, 5, and so on.
In general, the domain of a radical is determined by the values of the independent variable that make the expression under the radical nonnegative. If the expression under the radical is always nonnegative, then the domain of the radical is the set of all real numbers. If the expression under the radical is not always nonnegative, then the domain of the radical is the set of all values of the independent variable that make the expression nonnegative.
Answer:
The domain of a radical is the set of all values that can be plugged into the radical without resulting in an undefined or imaginary value.For example, the domain of the square root function sqrt(x) is all non-negative real numbers, since the square root of a non-negative real number is always a real number. This means that the domain of sqrt(x) is the set of all real numbers x such that x >= 0.On the other hand, the domain of the square root function sqrt(x^2 - 4) is all real numbers except for the values x = 2 and x = -2, since the square root of a negative number is an imaginary number. This means that the domain of sqrt(x^2 - 4) is the set of all real numbers x such that x != 2 and x != -2.In general, the domain of a radical is the set of all values for which the expression inside the radical is greater than or equal to 0. This is because the radical of a negative number is an imaginary number, which is not included in the domain of the radical.
Step-by-step explanation:
answer for bottom one
Answer:
Step-by-step explanation:
good luck lol
Use the following table of 2010 exchange rates to solve the problem.
You wish to exchange 100 British pounds for Japanese yen. How many yen do you receive?
Answer:
aproximantly 131.1701yen
Step-by-step explanation:
Answer:
15430 Japanese yen
Step-by-step explanation:
To find out how many Japanese yen you receive for 100 British pounds, we need to find the exchange rate between British pounds and Japanese yen in the table. From the table, we can see that the exchange rate between British pounds and Japanese yen is 154.43. Therefore, if you exchange 100 British pounds, you will receive 100 * 154.43 = 15430 Japanese yen.
please help me with this
Answer:
Because when you divide 100 by 4 and 50 by 2, you will get the same value
Write 0.302 repeating as a fraction. show your work.
A triangle has points monkeys, giraffes, lions. The distance between lions and monkeys is 11 feet and monkey and giraffes is 16 feet. The distance between lions and giraffes is the hypotenuse of x feet. Which equations will find the distance between the lions and giraffes? Select all that apply. 11+16 = c 112+ 162 = c2 c2+ 162 = 112 121+ 256 = c2 11(2)+16(2) = 2
The equation to find the distance between the lions and giraffes is
x² = 121 + 256.
Option D is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Hypotenuse = Distance between lion and giraffes = x
Distance between lions and monkeys = 11 feet
Distance between monkeys and giraffes = 16 feet
Applying the Pythagorean theorem.
x² = 11² + 16²
x² = 121 + 256
x² = 377
x = √(377)
x = 19.42
Thus,
The distance between lions and giraffes is 19.42 feet.
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Answer:B and D
Step-by-step explanation:
a bicycle wheel has a diameter of 24 inches. there are 32 spokes evenly distributed around the wheel. how far apart is each spoke?
The diameter of a bicycle wheel is 24 inches. Around the wheel, there are 32 spokes that are spaced 48 meters away from one another.
The diameter of a circle is the distance measured through its center. The radius of a circle is the distance from the center to any point on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d . The simplest place to start would be to use a ruler to measure the distance between the circle's outside edges starting from its very center. The diameter would be that.
The diameter of the circle is the measurement at issue. The distance between the circle's center and its periphery can be measured.
far apart is each spoke (distance) = radius = diameter / 2
distance = 24/2
distance = 12
Since a wheel has 4 parts. so, 12*4 = 48 m
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Jack brought a lunch box for $8 and 7 forks. He spent a total of $105. How much did each fork cost?
Answer:
13.85$
Step-by-step explanation:
105$-8$=97$
97$/7$=13.85$
Answer: About $13.86
Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:
105 - 8 = 97
So, now since he bought 7 forks, we need to divide 7 by 97. So:
97 / 7 = 13.857142857142858
So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:
13.86(7) + 8
97.02 + 8
= 105.02
This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)
The length of a rectangle i meter longer than the width. If the area i quare meter, find the rectangle' dimenion. Round to the nearet tenth of a meter. The width i _____ meter
enter your repone here meter
The dimensions of the rectangle are, length = 5 inch and width = 6 inch.
What is rectangle?
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.
Let, the length of a rectangle is 7 inches less than twice the width, w, of the rectangle.
Suppose,
width = w = x, then,
length = l = 2x - 7
Since the area of the rectangle is 30 square inches.
We know that.
Area of rectangle = length x width
30 = (2x - 7) x (x)
30 = 2x^2 - 7x
2x^2 - 7x - 30 = 0
2x^2 - 12x + 5x - 30 = 0
2x(x - 6) + 5(x - 6) = 0
(2x + 5)(x - 6) = 0
⇒ 2x + 5 = 0, x - 6 = 0
⇒ x = -5/2, x = 6
Since length is not negative.
Therefore, w = 6.
So, l = 2(6) - 7 = 12 - 7 = 5
Hence, the length is 5 inches and the width is 6 inches.
complete question
The length of a rectangle i 7 inche le than twice the width, w, of the rectangle. Find the dimenion if the area i 30 quare meter
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a. What are the coordinates of points B and D?
B: Select Choice
D: Select Choice
Answer:
The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.
Frida orted polygon i group 1 wa only quare group 2 wa only rectangle not quare frida aid all the hape are parallelogram Sam aid they are all cuadriliterale who wa right
Both Frida and Sam are right.
In geometry, a quadrilateral is a type of close-shaped polygon that has four sides, four angles, and four vertices. In Latin, 'Quadri' means four, and 'latus' means side.
A parallelogram is a geometrical shape having both pairs of opposite sides parallel and equal.
Squares are a type of quadrilateral having two sets of parallel sides. Parallelograms may be called quadrilaterals which have two sets of parallel sides. As squares are quadrilaterals having two sets of parallel sides, all squares may be called parallelograms. As all rectangles are having two pairs of parallel sides and all angles of a rectangle are equal, it might be called parallelograms.
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The complete question is:
Frida sorted polygons so Group 1 only squared. Group 2 was only
rectangles, not squares. Frida said all the figures are parallelograms. Sam said they are all quadrilaterals. Who is right? Why?
Solve each equation by taking the square root.
7x2 +32 = -10
x= {___, ___}
Answer: x=(10-sqrt(128))/14=(5-4sqrt(2))/7=-0.094
Step-by-step explanation: (7x2 - 10x) - 1 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 7x2-10x-1
The first term is, 7x2 its coefficient is 7 .
The middle term is, -10x its coefficient is -10 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 7 • -1 = -7
Step-2 : Find two factors of -7 whose sum equals the coefficient of the middle term, which is -10 .
-7 + 1 = -6
-1 + 7 = 6
FIGURE EX 31.38 is a current-versus-potential-difference graph for a material. What is the material's resistance?
The value of material's resistance at 100 v voltage and at 2 A current is 50 Ω.
As per the data given in the question the value of Voltage is 100 v, Current is 2 A
Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
This law is one of the most basic laws of electricity.
Ohm’s Law Formula:
Voltage = Current× Resistance
V = I × R
V = Voltage, I = Current and R = Resistance.
Using Ohm's Law we have to determine the value of R.
R is Resistance and has units of ohms, with symbol Ω.
V = I × R
At Voltage = 100 v, Current = 2 A
100 = 2 × R
R = [tex]\frac{100}{2}[/tex]
R = 50 Ω
Therefore the value of Resistance of material, R = 50 Ω
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FIGURE EX 31.38 is a current-versus-potential-difference graph for a material. What is the material's resistance?
Diagram attaches at the end of solution.
the smaller triangle has a perimeter of 31 ft and an area of 40 ft2. if the larger triangle has a perimeter of 62 ft, what will it's area be?
If the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.
We know that the perimeter of the smaller triangle is 31 feet, which means that the sum of the lengths of its three sides is 31 feet. We also know that the area of the smaller triangle is 40 square feet. We can set up the following equation to calculate the length of each side of the smaller triangle:
Side 1 + Side 2 + Side 3 = 31
We can then use the formula for the area of a triangle, A = bh/2, to calculate the length of the base and height of the smaller triangle. Since we know the area is 40 square feet, we can set up the following equation:
40 = (b)(h)/2
We can then solve this equation for b and h. We know that b + h = 31, so we can set up the following equation and solve for h:
h = 31 - b
Now that we know b and h for the smaller triangle, we can use the same formula to calculate the area of the larger triangle. Since we know that the perimeter of the larger triangle is 62 feet, we can set up the following equation to calculate the length of each side of the larger triangle:
Side 1 + Side 2 + Side 3 = 62
We can then use the following formula to calculate the area of the larger triangle:
A = (b)(h)/2
We know that b + h = 62, so we can set up the following equation and solve for h:
h = 62 - b
Now that we know b and h for the larger triangle, we can plug those values into the area formula and calculate the area of the larger triangle. The area of the larger triangle is 120 square feet. Therefore, if the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.
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2√5 times √8 plus 2√5 times √2 divide by 2. Any surds in the answer in their simplest form.
Answer:
The area of the compound shape is 5√10 cm²
Step-by-step explanation:
In the given shape, there is a rectangle and a right angle triangle.
i.e.,
Compund shape = Rectangle + Triangle
So,
Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle
For Rectangle;Length (l) = 2√5 cmWidth (w) = √8cm = 2√2 cmFormula;
A = l × wA = 2√5 × 2√2 cm
A = 4√10 cm²
For Triangle;Base (b) = 2 cmHeight (h) = 2√5 cmFormula;
A = ½ × base × heightA = ½ × √2 × 2√5 cm
A = 1 × √2 × √5 cm
A = √10 cm²
Now,
Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle
A = 4√10 cm² + √10 cm²
A = 5√10 cm²
Thus, The area of the compound shape is 5√10 cm²
What are the domain and the range of this graph?
a) The domain is {x∈R|x≤0} and the range is {y∈R|y≤0}.
b) The domain is {x∈R|x≤0} and the range is {y∈R|y≥0}.
c) The domain is {x|x∈R} and the range is {y∈R|y≤0}.
d) The domain is {x|x∈R} and the range is {y∈R|y≥0}.
Answer:
d) The domain is {x|x∈R} and the range is {y∈R|y≥0}--------------------------------------
Given is the graph of an absolute value function.
It has no domain restrictions, so x can be any real number.
There is a restriction on its range, it has a minimum at y = 0 and the rest of the values are positive real numbers.
It is correctly described in option d).
brandon has two summer jobs. during the week he works in the grocery store, and on the weekend he works at a nursery. he gets paid $15 per hour to work at the grocery store and $20 per hour to work at the nursery. how many total hours does he work if he does 14 hours at the grocery store and 13 hours at the nursery? how many total hours does he work if he does gg hours at the grocery store and nn hours at the nursery?
If Brandon does 14 hours at the grocery store and 13 hours at the nursery the the total working hours = 96 hours
And if Brandon does g hours at the grocery store and n hours at the nursery then total working hours = (5g + 2n) hours
In this question we ahve been given Brandon has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery.
He gets paid $15 per hour to work at the grocery store and $20 per hour to work at the nursery.
We need to find the total working hours if he does 14 hours at the grocery store and 13 hours at the nursery.
Also, we need to find total working hours if he does g hours at the grocery store and n hours at the nursery.
We know that the number of week days = 5 and the number of weekend days = 2
if he does 14 hours at the grocery store during 5 days, then by unitary method he will work for 14 * 5 = 70 hours
Similarly, if he does13 hours at the nursery for 2 days, this means by unitary method he is working for 13 * 2 = 26 hours
So, the total number hours of working during a week,
70 + 26 = 96 hours
Let he does g hours at the grocery store
During week days total working hours would be,
= number of weekdays * number of working hours
= 5 * g
= 5g
and n hours at the nursery.
= number of weekend days * number of working hours
= 2n
so, the total hours would be 5g + 2n
Therefore, a) the total hours does he work if he does 14 hours at the grocery store and 13 hours at the nursery = 96 hours
b) the total hours does he work if he does gg hours at the grocery store and nn hours at the nursery = (5g + 2n) hours
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Please help me answer this question
Answer:
Divide 5 to both side.
Step-by-step explanation:
Original Equation:
[tex]5(x-3)=5[/tex]
2nd Equation:
[tex](x-3)=1[/tex]
Single Steps:
Divide 5 to both side on Original Equation to get 2nd Equation.
Provide the missing statement and reasons for the following proof: theorem: opposite sides of parallelograms are congruent.
Using the property of geometry and using a parallelogram , We can prove that the opposite sides of parallelograms are congruent.
What is a parallelogram?
In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The opposite sides and the opposite angles of a parallelogram are of equal length. A parallelogram is a special kind of quadrilateral with both pairs of its opposite sides parallel and equal.
What are the 4 types of parallelograms?
There are 4 types of parallelograms with 3 special types.
They are:
parallelograms
squares
rectangles
rhombuses.
According to the given question:
Let ABCD be a parallelogram where AB and CD are in opposition to each other, while BC and AD are.
According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.
The definition of a parallelogram is that segment AB is parallel to segment DC.
Segments BC and AD are transverse to line AC. As demonstrated below, this transversal generates alternate interior angles that are equal.
In the same way, segment AB and segment DC are transversals for line AC. This transversal generates equal alternate interior angles.
Segment AC is also divided into segments by its reflexive property.
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it takes 10 seconds to fill a one-quart jar with water from your kitchen faucet. what is the flow rate, in gallons per minute, from the faucet? group of answer choices 40 10 1.5 4
1.5 litres of water are released from the faucet per minute.
It is given to us that -
There is a one quart jar
Water from the kitchen faucet fills the 1-quart jar in 10 seconds.
We need to ascertain the faucet's flow rate in gallons per minute.
We know that -
1 quart = 0.25 gallon ---- (1)
We also know that -
1 minute = 60 seconds
=> 60 seconds = 1 minute
=> 10 seconds = 10/60 = 0.16 minutes ----- (2)
Now, the flow rate can be calculated as -
Flow rate = Amount of water filled/Time taken ----- (3)
Substituting the values from equation (1) and (2) in equation (3), we have -
Flow rate = Amount of water filled/Time taken
=> Flow rate = 1 quart water/10 seconds
=> Flow rate = 0.25 gallons/0.16 minutes
=> Flow rate = 1.5 gallons per minute
Therefore, the flow rate of water from the faucet is 1.5 gallons per minute.
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Logan bought a baeball bat on a trip. The baeball bat i 29 inche long. Logan think he can bring the baeball bat home in hi uitcae. I he correct? Ue your undertanding of
the Pythagorean Theorem to explain your anwer
Since the diagonal of the suitcase is 30 inches and the length of the bat is 29 inches means the bat can fit into the case diagonally.
The dimension of a suitcase is-
length = 24 in.
width = 18 in.
The length of the bat = 29 in.
Clearly, the bat cannot fit vertically or horizontally in the suitcase.
Now to see if it fits diagonally in the suitcase, we apply the Pythagoras theorem to determine the diagonal of the suitcase or say the hypotenuse of the rectangular suitcase.
Thus, by Pythagoras' theorem,
[tex](hyp)^2 = opp^2 + adj^2[/tex]
[tex](hyp)= \sqrt{opp^2 + adj^2}[/tex]
[tex](hyp)= \sqrt{18^2 + 24^2}[/tex]
[tex](hyp)= \sqrt{324+ 576}[/tex]
[tex](hyp)= \sqrt{900}[/tex]
hyp = 30 in.
Hence, the diagonal of the suitcase > the length of the bat.
Since the diagonal of the suitcase is 30 inches and the length of the bat is 29 inches means the bat can fit into the case diagonally.
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Eliot and William go running. Eliot ran for 8 mile, and William ran for 12 mile. Eliot finihed hi run in 40 fewer minute than William. If they run at the ame peed, for how long did William run?
William ran for 48 minutes since Eliot ran for 8 miles in 40 fewer minutes than William. They were running at the same speed.
Eliot and William both went running and ran for 8 miles and 12 miles respectively. Eliot finished his 8 mile run in 40 fewer minutes than William. This means that if the two of them were running at the same speed, it would take William 40 minutes longer than Eliot to finish his 12 mile run. To calculate how long William ran for, we can add 40 minutes to the time it took Eliot to run 8 miles. Since Eliot ran 8 miles in 40 fewer minutes than William, this means that Eliot ran 8 miles in the amount of time that William ran 12 miles. The total time William ran for is therefore 8 miles plus 40 minutes, which is 48 minutes.
Eliot: 8 miles ÷ 40 minutes fewer
= 0.2 miles/minute
William: 12 miles ÷ (0.2 miles/minute x 40 minutes)
= 48 minutes
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At the yum yum cafe the waiter combine their tip and divided the total by the number of waiter today' tip total i 132 and three waiter' are working how much money in tip doe waiter get
The amount of money each waiter get in tip is 44 dollars.
In this question we have been given at the yum yum cafe the waiters combine their tips and divide the total by the number of waiters.
Today's tip total is 132 and three waiters are working.
We need to find the amount of money each waiter get in tip.
Let x dollers be the amount each waiter get in tip.
Total tip amount = 132
number of waiters = 3
By unitary method,
x = 132/3
x = 44 dollars
Therefore, each waiter get 44 dollars in tip.
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The diagram below shows ano exterior wall of a house. The wall has a door opening that measures 3 feet by 7 feet and two windows opening that each measure 6 feet by 4 feet the wall,but not the openings will be covered with siding material that cost $1.50mper square foot. Find the total cost of the siding material.
The total cost of the siding material is given as follows:
B. $292.50.
How to obtain the cost of material?To obtain the cost of material, the first step is obtaining the area that will be covered, which is given as follows:
The rectangular area of 8 feet by 24 feet will be covered, with these following exceptions:
Two windows measuring 6 feet by 4 feet.One door measuring 3 feet by 7 feet.The triangular area with base 24 feet and height 6 feet will also be covered.
Then the total area to be covered is given as follows:
Area = 8 x 24 - (2 x 6 x 4) - (3 x 7) + 0.5 x 24 x 6
Area = 195 ft².
The total cost is of $1.5 per ft², hence it is calculated as follows:
Total cost = 195 x 1.5 = $292.50.
Meaning that option B is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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The trainer kept trying to teach her dolphins how to
play baseball, but after a year's worth of practice, only
4 out of 15 knew the difference between a "strike" and
a "ball." What percentage of the dolphins knew the
difference between a "strike" and a "ball"? Write your
answer as a fractional percent. Make sure your answer
is fully reduced.
Using the concept of percentage, the percentage of dolphins that knew the difference is 26%
PercentageA percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
The number of dolphins that knew the difference between strike and ball is given as 4 out of 15.
This can be represented in a fraction as 4 / 15
The percentage that knew the difference = (4 / 15) * 100
The percentage that knew the difference will be 0.26 * 100 = 26 %
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d) The sum of two consecutive integers is smaller than three times the smaller integer.
Answer:
The smaller integer is greater than 1
Step-by-step explanation:
The integers are x and x+1
[tex]x + x + 1 < 3x \\ 2x + 1 < 3x \\ 2x - 2x + 1< 3x - 2x \\ 1< x [/tex]
Cara earn a bae pay of $1,800 per month at a car dealerhip plu a commiion of 6% of her ale. What are Cara' total earning in a month in which he ale $40,000 worth of merchandie?
Using the concept of percentages the total earning of Cara can be found to be $4200.
What are percentages?Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.
How to solve percentages?Cara's earning = commission + basic salary
basic salary = $1800 (this is constant)
commission = 6% of $40000
= (6/100)*40000
= $2400
Cara's earning = 1800 + 2400
Hence, her earning is $4200
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a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 205.8-cm and a standard deviation of 0.5-cm. for shipment, 22 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is greater than 206.1-cm. p(m > 206.1-cm)
The required probability of the randomly selected steel rod with the average length greater than 206.1cm whose mean is 205.8cm and standard deviation is 0.5cm is equal to 0.0024012.
As given in the question,
Mean of the normally distributed steel rod ' μ '= 205.8cm
Standard deviation of the normally distributed steed rod 'σ ' = 0.5cm
Number of steel rod bundled together 'n' = 22
Randomly selected steel rods bundle the average length is greater than
'[tex]\bar {X}[/tex]' = 206.1cm
Required probability is given by :
P( [tex]\bar {X}[/tex] > 206.1 )
= P [([tex]\bar {X}[/tex] - μ )/ (σ/√n) > ( 206.1 - 205.8)/ (0.5/√22) ]
= P ( Z > (0.3/ 0.1064))
= P ( Z > 2.8195)
= P ( Z > 2.820)
= 0.0024012
Therefore, the probability of the randomly selected steel rod with the average length greater than 206.1cm is equal to 0.0024012.
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Hassan rings up an item that costs
$6,400. After sales tax, the total is
$6,848. What is the sales tax
percentage?
Answer: 7%
Step-by-step explanation:
Take 6848 divided by 6400, then times 100 = 107%
Then take 107% - 100% = 7%
The sales tax percentage is 7%
Shade 4 circles shade 3/3 more
2. Renting is a great option for many people.
Oue
False
Answer: True. Renting is a great option for many people because it offers flexibility and affordability. Renting allows individuals to live in a desired location without the financial burden and commitment of owning a home. It also provides flexibility, as renters can easily move to a different location if their needs or circumstances change. Additionally, renting can be a more affordable option compared to owning a home, as it typically involves lower upfront costs and maintenance expenses. For these reasons, renting is a viable and attractive option for many people.
Step-by-step explanation: