When using a standard normal table or calculator, it becomes clear that the area under the standard normal curve to the right of z=1.0 is approximately 0.1587.
Hi we to explain the data givenSimilarly, with the aid of this table or calculator, one can further deduce that the region under the standard normal curve to the left of z=-1.25 is roughly equal to 0.1056, while the section to the right of z=1.25 shares the same probability of 0.1056. Therefore, their combined value equates to 0.2112.
Through utilizing a standard normal table or calculator:
a. The possibility of z being lower than 1.96 is approximately 0.9750.
b. The likelihood of z being greater than 1.28 is about 0.1003. (It's crucial to note that this differs from the area to the right of z=1.28, which includes the region all the way up to z=1.28.)
Suppose one wishes to determine the z-score that corresponds to an IQ score of 90. In that case, we employ the following formula:
z = (x - μ) / σ
Indicating that x is the IQ score, μ denotes the mean (100), and σ is the standard deviation (15). By entering in these variables, one derives:
z = (90 - 100) / 15 = -0.67
Thus, the corresponding z-score to an IQ score of 90 is -0.67.
If finding out what IQ score corresponds to a z-score of -1.45 while considering the previously mentioned formula, one would alter it as follows to solve for x:
x = μ + z * σ
After substitution, this produces:
x = 100 + (-1.45) * 15 = 78.25
Consequently, the IQ score corresponding to a z-score of -1.45 is 78.25.
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The smallest number that is a product of both numbers being compared (can be one of the numbers, can't be smaller than both numbers) is called the ______.
The smallest number that is a product of both numbers being compared (can be one of the numbers, can't be smaller than both numbers) is called the "least common multiple" (LCM).
The LCM is the smallest positive integer that is a multiple of both numbers without leaving a remainder. It is also known as the lowest common multiple or smallest common multiple. For example, the LCM of 6 and 8 is 24 because 24 is the smallest integer that is a multiple of both 6 and 8 without leaving a remainder. Similarly, the LCM of 10 and 15 is 30 because 30 is the smallest integer that is a multiple of both 10 and 15 without leaving a remainder. The LCM is an important concept in mathematics and is used in various applications, such as finding common denominators, solving equations involving fractions, and analyzing periodic phenomena. There are different methods to find the LCM of two or more integers, such as prime factorization, the division method, and the use of the GCD (greatest common divisor) or GCF (greatest common factor).
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How to find a number based on a fraction for example 5/8 of a number is 175. What is the number?
The solution is, The number is 280.
We have,
The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
Let the number be x.
According to the given question.
5/8 of number is 175.
The linear equation in one variable of the above statement is given by
5/8 * (x) = 175
Solve the above linear equation in one variable for x.
⇒5/8 * (x) = 175 ( multiplying both the sides by 8)
⇒ 5x = 175 * 8
⇒ 5x = 1400 ( dividing both the sides by 5)
⇒ x = 280
Hence, the number is 280.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
The best measure of variability for the data, and its value is: D. The range is the best measure of variability, and it equals 9.
What is a line plot?In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
From the data set for the number of roses purchased per day, we have:
10, 1, 1, 4, 4, 2, 2, 2, 5, 5, 5, 3, 3, 3, 3
For the IQR, we have:
IQR = Third quartile (Q₃) - First quartile (Q₁)
IQR = 5 - 2
IQR = 3
For the range, we have;
Range = maximum - minimum
Range = 10 - 1
Range = 9.
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a = 5, b = ? , c = 8
The value of the side is 6. 2
How to determine valueTo determine the value of the missing side, we need to know the Pythagorean theorem.
The Pythagorean theorem of triangles states that the square of the longest side of a triangle which is called the hypotenuse side is equal to the sum of the squares of the other two sides of the triangle.
This is represented as;
c² = b² + a²
Such that the parameters are;
c is the hypotenuseb is the oppositea is the adjacentSubstitute the values
8² = 5² + b²
find the square value, we have;
64 = 25 +b²
subtract the values
b² = 64 - 25
b² = 39
Find the square root of both sides
b = 6. 2
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Exploring Denominators
Which of these statements about plotting fractions on a number line are true? Check all that apply.
The denominator is the top number of the fraction.
The denominator is always equivalent to the number of segments to the left of the point.
The denominator is equivalent to the number of segments that the whole is divided into.
The denominator is the bottom number of a fraction.
The denominator is same as the numerator when the point is plotted at 1.
Answer:
The denominator is equivalent to the number of segments that the whole is divided into.
The denominator is the bottom number of a fraction.
Answer:
C d e
Step-by-step explanation:
Find the slope of a line perpendicular to the line whose equation is 5x+ 6y = 48.
Fully simplify your answer.
Answer:
-5/6
Step-by-step explanation:
y=mx+6
so,
6y=-5x+48
y=-5/6x+48
m=-5/6
the test scores for a class of 207 students are computed. what is the location of the test score associated with the third quartile?
The third quartile of the test scores for a class of 207 students is located at the 156th term, which is obtained by multiplying the sample size by 0.75. The correct answer is A).
To find the location of the test score associated with the third quartile, we need to first calculate the position of the third quartile in the ordered data set
Third quartile = 75th percentile = 0.75
Sample size n = 207
Position of the third quartile = 0.75 * 207 = 155.25
Since the position is a whole number, we round up to the next integer to get the location of the test score associated with the third quartile
Location of the test score associated with the third quartile = 156
Therefore, the answer is "156". The correct option is A).
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--The given question is incomplete, the complete question is given
" The test scores for a class of 207 students are computed when 3rd quartile =75percentile. What is the location of the test score associated with the third quartile? Multiple Choice O 156 52 104 105%"--
in a large population, 66 % of the people have been vaccinated. if 3 people are randomly selected, what is the probability that at least one of them has been vaccinated? give your answer as a decimal (to at least 3 places) or fraction.
The probability that at least one of the three randomly selected people has been vaccinated is approximately 961/1000 as a fraction.
Percent of vaccinated people = 66%
Number of people randomly selected = 3
The probability that a person has been vaccinated is
= 66%
= 0.66 as a decimal.
The probability that at least one of three people has been vaccinated
= Total probability - Probability that none of them have been vaccinated
Total probability = 1
The probability that the first person selected has not been vaccinated is
1 - 0.66 = 0.34.
The probability that the second person selected has not been vaccinated is also 0.34.
And the same goes for the third person.
So, the probability that none of the three people have been vaccinated is,
= 0.34 x 0.34 x 0.34
= 0.039304
The probability that at least one of the three people has been vaccinated is ,
= 1 - 0.039304
= 0.960696
= 0.961
= 961/1000 as a fraction.
Therefore, the probability that at least one of the three people has been vaccinated is approximately 961/1000 as a fraction.
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6(x-8)
Simplify the expression
Answer:
6x-48
Step-by-step explanation:
Multiply using the distributive property.
Step 1:
Multiply 6 and x:
6xStep 2:
Multiply 6 and -8:
-48Step 3:
Put them together:
6x-48Step 4:
have a good day :)
What is the solution to l x + 2 | <1?
OA. 1
OB. -3
OC. x>3 or x< 1
OD. x>-1 or x < -3
Answer:
Answer:
x > - 3 or x < -1
I cannot see this answer choice; perhaps you typed it wrong and it is option C. Please check again
Step-by-step explanation:
The absolute value rule says for a given variableu,
if |u| < a where a is a constant,
then -a < u < a
Here we can represent x + 2 as u giving
|u| < 1
=> - 1 < u < 1
Substituting for u = x + 2 gives
-1 < x + 2 < 1
Subtract 2 from all sides
-1 - 2 < x + 2 - 2 < 1 - 2
-3 < x < -1
This can be represented as
x > -3 or x < -1
I do not see this choice anywhere but that is the correct answer. Check your answer choices
20.
A garden has a lawn with the dimensions 2x - 5m by xm, as shown in
the diagram below.
2x - 5
(a) Find an expression, in terms of x, for the perimeter of the lawn.
Give your expression in its simplest form.
A lawn has a perimeter of 110m.
(b) Work out the value of x.
X
[2 marks]
[2 marks]
Answer:
Below in bold.
Step-by-step explanation:
Perimeter P = sum of all the sides
P = 2(2x - 5) + 2x
P = 4x - 10 + 2x
P = 6x - 10.
If the perimeter = 110m then:
110 = 6x - 10
6x = 110 + 10 = 120
x = 120/6
x = 20m.
how do i answer this?
The answer of the number simplified in scientific notation is 1 × 10¹.
What is scientific notation of numbersScientific notation is a way of expressing very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to an exponent.
(2 × 10⁻³)/(2 × 10⁻⁴) = 2¹⁻¹ × 10⁻³⁻⁽⁻⁴⁾
(2 × 10⁻³)/(2 × 10⁻⁴) = 2¹⁻¹ × 10⁻³⁺⁴
(2 × 10⁻³)/(2 × 10⁻⁴) = 2⁰ × 10¹
(2 × 10⁻³)/(2 × 10⁻⁴) = 1 × 10¹ {numbers to the power of zero is equal to 1}
Therefore, the answer of the number simplified in scientific notation is 1 × 10¹.
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A publishing company wanted to test whether typing speed differs when using word processor a or word processor b. a random sample of 25 typists was selected and the typing speeds (in words per minute) were recorded for each typist when using word processor a and then when using word processor b. (which word processor is used first is determined for each secretary by a coin flip). In this case, what is the appropriate set of hypotheses?
These hypotheses can be tested using the data collected from the random sample of 25 typists.
The appropriate set of hypotheses in this scenario would be:
Null hypothesis (H0): There is no significant difference in typing speed between word processor a and word processor b.
Alternative hypothesis (Ha): There is a significant difference in typing speed between word processor a and word processor b.
In this case, the publishing company wants to test if there is a difference in typing speeds between word processor A and word processor B. The appropriate set of hypotheses can be defined as follows:
Null hypothesis (H0): The mean typing speed difference between word processor A and word processor B is equal to 0. In other words, there is no significant difference in typing speeds between the two processors.
H0: μA - μB = 0
Alternative hypothesis (H1): The mean typing speed difference between word processor A and word processor B is not equal to 0. In other words, there is a significant difference in typing speeds between the two processors.
H1: μA - μB ≠ 0
These hypotheses can be tested using the data collected from the random sample of 25 typists.
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Write an equation of the line that passes through the point (0,-3) and is parallel to the line y=-2x-5
Answer:
y=-2x-3
Step-by-step explanation:
The point you first stated (0, -3) is the y-intercept of the line given that the x is zero. Parallel lines share a slope. Soooooooooo the equation would be y=-2x-3
Answer: y=-2x-3
hope this helps
Oliver bought a hat and a cardigan for a total of £18. The cardigan cost
£8 more than the hat.
How much did the hat cost?
Give your answer in pounds.
The cost of the hat is £5.
Let's say that the hat costs x pounds.
The cardigan's price might be represented as follows as it is £8 more expensive than the hat according to the problem:
x + £8
The cap and cardigan combined are listed as costing £18. Thus, we may represent an equation as:
x + (x + £8) = £18
Simplifying this equation, we get:
2x + £8 = £18
Subtracting £8 from both sides, we get:
2x = £10
Dividing both sides by 2, we get:
x = £5
Therefore, the hat costs £5.
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A school dance club is selling bottled water at a football game to raise funds. The club has raised $26 so far and has the goal of raising $100. If each bottle of water earns the club an additional $2, which equation can be used to find the number of bottles of water w that the club needs to sell to reach their goal?
Answer choices:
A: 26+w=100
B: 26+2w=100
C: 100+w=26
D: 100+2w=26
The correct equation that can be used to find the number of bottles of water w that the club needs to sell to reach their goal is: 26+2w=100. Option B
How to find the number of bottles of water w that the club needs to sell to reach their goalLet w be the number of bottles of water that the club needs to sell to reach their goal of raising $100.
Total amount = $26 + $2w
To find the number of bottles of water w that the club needs to sell to reach their goal of raising $100 will be:
Total amount = Goal amount
$26 + $2w = $100
Simplifying the equation, we get:
$2w = $100 - $26
$2w = $74
Dividing both sides by 2, we get:
w = 37
Therefore, the club needs to sell 37 bottles of water to reach their goal of raising $100.
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Amy raises ducks, and she takes their eggs to the farmers' market to sell. Today she collected 19 dozen green eggs and 32 dozen white ones. She sells the eggs for $5 a dozen. Amy estimates she will make about $2,500 if she sells all the eggs. Is that a good estimate?
Answer:
To determine if Amy's estimate of $2,500 is a good estimate, we need to calculate the actual total revenue she would earn from selling the eggs.
First, we need to convert the number of dozens of eggs to the total number of eggs. One dozen is equal to 12 eggs, so:
- 19 dozen green eggs = 19 x 12 = 228 green eggs
- 32 dozen white eggs = 32 x 12 = 384 white eggs
The total number of eggs is:
- 228 green eggs + 384 white eggs = 612 eggs
Next, we can calculate the total revenue Amy would earn if she sells all the eggs:
- 612 eggs ÷ 12 eggs/dozen = 51 dozen eggs
- 51 dozen eggs x $5/dozen = $255
Therefore, the actual total revenue Amy would earn from selling all the eggs is $255, which is significantly less than her estimate of $2,500. Amy's estimate is not a good estimate and is over 9 times the actual revenue she would earn.
mark me brilliant
Answer: No this is not a good estimate.
Step-by-step explanation:
19 dozen + 32 dozen= 51 dozen
so she has 51 dozen eggs for $5 per dozen
So you multiply 51 by 5 and you get 255.
So No her estimate was over the amount she will make.
Hope this helps :)
Sam's basketball game team won 70% of the 30 games they played. How many games did they win
Answer:21
Step-by-step explanation:
Meghann uses cruise control to drive at a constant speed She travels the first 183 miles in 3 hours . At this rate, how long will it take meghann to drive a total of 366 miles
Since she travels 183 miles in 3 hours, her speed is:
183 miles / 3 hours = 61 miles per hour
To calculate how long it will take her to drive a total of 366 miles, we can use the formula:
time = distance / speed
Plugging in the values, we get:
time = 366 miles / 61 miles per hour
time = 6 hours
Therefore, it will take Meghann 6 hours to drive a total of 366 miles at a constant speed using cruise control.
Help pls with an explanation
The number of scooters sold in year 4 is 2240
What is word problem?A word problem is a math problem written out as a short story or scenario. This statement is actually interpreted into mathematical equation or expression.
The total scooter sold in the previous 3 years is ;
725+579+696 = 2000.
Therefore the store sold a total of 2000 scooters for 3 years.
In the 4th year they sold 112% of the total of the 3 years.
therefore the number of scooters sold in the 4th year can be calculated as;
112/100 × 2000
= 112 × 20
= 2,240
therefore 2240 scooters were sold in the 4th year.
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A park in a subdivision is triangular shaped. Two adjacent sides of the park are 487 feet and 465 feet. The angle between the sides is 49°. To the nearest unit, what is the area of the park in square yards? 9,495 square yards 16,508 square yards 18,990 square yards 28,485 square yards
The area of the park to the nearest unit is 85454 ft²
What is area of triangle?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
A triangle is a 3 sided polygon. The types of triangle are,; equilateral, scalene , isosceles triangle e.t.c
The area of a triangle is expressed as;
A = 1/2 absinC
here, a = 487ft, b= 465ft and C = 49°
therefore;
A = 1/2 × 487 × 465 × sin49°
A = 1/2 × 226455 × 0.755
A = 113227.5 × 0.755
A = 85454 ft² ( nearest unit)
Therefore the area of the park to the nearest unit is 85454ft²
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due now!!!!!!!!!!!!!!!!!
Answer:
d. the points seem to be clustered around a line
Step-by-step explanation:
:)
the annual snowfall in a town has a mean of 39 inches and a standard deviation of 10 inches. last year there were 64 inches of snow. how many standard deviations from the mean is that?
The number of standard deviations from the mean for the 64 inches of snow last year is 2.5 standard deviations.
First, we need to find the difference between the actual snowfall (64 inches) and the mean snowfall (39 inches). To do this, subtract the mean from the actual snowfall:
64 - 39 = 25 inches.
Next, we need to divide this difference by the standard deviation (10 inches) to find how many standard deviations away from the mean the actual snowfall is:
25 / 10 = 2.5.
Hence, Last year's snowfall of 64 inches is 2.5 standard deviations away from the mean annual snowfall of 39 inches.
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a ray of sunlight forms a 24°-angle with the ground. what is the length of the shadow cast by a person 1.82 m tall?
The length of the shadow cast by a person 1.82 m tall will be 4.09m
A ray of sunlight forms a angle of Elevation to the sub is 24°.
The angle from horizontal to the point where we stopped our head is called angle of elevation.
On this note, the shadow cast on the floor shows the adjacent of the angle of Elevation.
Hence, the length of the shadow cast can be calculated from Tangent identify as;
Tan 24° = 1.82/l
l = 1.82/Tan 24
l = 1.82/0.445
Thus, Length of shadow = 4.09m
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How does one do 25? I dont know how to do it
Check the picture below.
so the prism is really two triangles, with a base of 9.8 and a height of 5.33, and then three rectangles
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{two triangles} }{2\left[ \cfrac{1}{2}(\underset{b}{9.8})(\underset{h}{5.33}) \right]}~~ + ~~\stackrel{\textit{front rectangle}}{(9.8)(3.8)}~~ + ~~\stackrel{\textit{left rectangle}}{(6.2)(3.8)}~~ + ~~\stackrel{\textit{right rectangle}}{(8.5)(3.8)}} \\\\\\ 52.234~~ + ~~37.25~~ + ~~23.56~~ + ~~32.3 ~~ \approx ~~ \text{\LARGE 145.3}~ft^2[/tex]
Answer:
145.3 ft²
Step-by-step explanation:
You want the surface area of the triangular prism shown.
AreaThe surface of the prism consists of 5 faces:
3 rectangles2 triangleThe dimensions required to find the areas of these are given in the diagram.
Rectangle areaThe area of a rectangle is the product of its length and width. All of the rectangles shown have a height of 3.8 ft, so their total area is ...
lateral area = (3.8 ft)(9.8 ft) +(3.8 ft)(8.5 ft) +(3.8 ft)(6.2 ft)
= (3.8 ft)(9.8 +8.5 +6.2 ft) . . . . . . . factoring out 3.8 ft
You will recognize this as the product of the height of the prism and the perimeter of the triangular base.
Triangle areaThe area of one triangle base is ...
A = (1/2)bh
The base is given as 9.8 ft, and the height is given as 5.33 ft, so the area is ...
A = (1/2)(9.8 ft)(5.33 ft)
There are two such triangular faces, so their total area is ...
base area = 2(1/2)(9.8 ft)(5.33 ft)
base area = (9.8 ft)(5.33 ft)
TotalThe total surface area is the sum of the areas of the 5 faces:
surface area = rectangle area + base area
= (3.8 ft)(9.8 +8.5 +6.2 ft) +(9.8 ft)(5.33 ft) = 145.334 ft²
The surface area of the prism is about 145.3 ft².
__
Additional comment
The surface area of any figure is the sum of the areas of the various surfaces that make it up. For polygonal prisms, the lateral area is made of rectangles. The total base area is the sum of the areas of the two polygonal bases. Here the bases are triangular, so the triangle area formula is used.
For figures such as cylinders, or cylinders with conical or hemispherical ends, you use the appropriate formulas for lateral area and spherical area, as needed.
It is usually helpful to memorize or keep handy the formulas for areas of various plane and curved figures.
The circular mirror hanging on Julie's wall has a diameter of 22 centimeters. What is the mirror's area? Use 3.14 for . If necessary, round your answer to the nearest hundredth.
The area of the circular mirror hanging on Julie's wall is approximately 379.94 square centimeters.
What is the area of the circular mirror hanging on Julie's wall?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given that, the diameter of the mirror is given as 22 cm, the radius is half of that:
r = diameter/2
r = 22/2
r = 11 cm
Substituting this into the formula, we get:
A = π × r²
A = 3.14 × ( 11 cm )²
A = 3.14 × 121 cm²
A = 379.94 cm²
Therefore, the area of the mirror is 379.94 cm².
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AB and PQ are lines of length 6 cm a) AX: AB = 1:3 Mark where point X would be on the line, with a cross. A b) PX: XQ= 1:3 Mark where point X would be on the line, with a cross. mark where to put the x's in a colour for me
The X would be on the line at 1.5cm in first case while in second case it would be at 4.5cm.
Define line?A line is a geometric figure that is defined as a straight, continuous arrangement of infinitely many points extending infinitely in both directions. In mathematics, a line is often represented by a straight line with arrows on both ends, indicating its infinite nature.
What is point?In mathematics, a point is a precise location in space that has no size or dimension. It is often represented as a dot or a small circle. Points are used as basic elements in geometry and other branches of mathematics to define and describe shapes, lines, curves, and other objects. They are typically named using a single capital letter or a combination of letters and numbers.
a) Since AX:AB = 1:3, we can find the length of AX by dividing the length of AB by 4 (1+3). Thus, AX = (1/4)×AB = (1/4)×6 cm = 1.5 cm. To mark point X on the line, we can start at point A and measure 1.5 cm towards point B and mark that point with a cross.
b) Similarly, since PX:XQ = 1:3, we can find the length of XQ by dividing the length of PX by 4 (1+3). Thus, XQ = (3/4)×PX = (3/4)×6 cm = 4.5 cm. To mark point X on the line, we can start at point P and measure 4.5 cm towards point Q and mark that point with a cross. We can mark the points with red x's for clarity.
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If it is known that a and b are positive integers and that a-b=2 evaluate the following.
The given system of equations can be written as a vector equation (7x1 + x2 - 3x3) = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.
Vector equation:
(7x1 + x2 - 3x3) = 7
Part 2
Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.
Matrix equation:
=
A =
[7 1 -3
3 2 2]
B =
[7
0]
Conclusion:
The given system of equations can be written as a vector equation (7x1 + x2 - 3x3) = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].
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The value of the expression [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} }[/tex] is 1/9.
Exponent rules :Exponent rules are a set of mathematical properties that help simplify expressions with exponents and make it easier to manipulate them in algebraic operations.
The fractional exponent or power rule:
The rule states that for any real numbers a and b, and any positive integer n, the expression [tex]a^{\frac{1}{n} }[/tex] is equal to the nth root of the fraction a/b. That is: [tex]a^{\frac{1}{n} }[/tex] = [tex]\sqrt[n]{a}[/tex]
Here we have
=> [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} }[/tex]
Using the fomrula, [tex]a^{\frac{1}{n} }[/tex] = [tex]\sqrt[n]{a}[/tex]
=> [tex]27^{ \frac{1}{3} b} = (\sqrt[3]{27})^{b}[/tex]
As we know 27 = 3³
=> [tex](\sqrt[3]{27})^{b} = (\sqrt[3]{3^{3} })^{b} = 3^{b}[/tex]
=> [tex]9^{ \frac{1}{2} a} = (\sqrt {9})^{a}[/tex]
As we know 9 = 3²
=> [tex](\sqrt {9})^{a} = [\sqrt{3^{2} } ]^{a} = 3^{a}[/tex]
Hence the expression will be
=> [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} } = \frac{3^{b} }{3^{a} }[/tex]
=> [tex]\frac{3^{b} }{3^{a} } = \frac{1}{3^{a-b} }[/tex]
=> [tex]\frac{1}{3^{a-b} } = \frac{1}{3^{2} }[/tex]
=> [tex]\frac{1}{3^{2} } = \frac{1}{9}[/tex]
Therefore,
The value of the expression [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} }[/tex] is 1/9.
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I need help with this question
Answer:
c
Step-by-step explanation:
Is 3^5 the same as 3x5 ? Please explain
Answer:
No
Step-by-step explanation:
3^5 or using a superscript, 3⁵ means 3 × 3 × 3 × 3 × 3 which is 243
The 5 is an exponent. This format is a shortcut for multiplying. But it means to multiply 3 times itself, over and over again (5 times)
3 × 5 is of course regular multiplication as your learned in elementary school. 3 × 5 is just 15. (regular multiplication like this is a shortcut for adding-- it means to add 3 groups of 5 or 5 groups of 3)
