The inverse of the functions g(x), p(x), and t(x) are expressed as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3. respectively.
What is Inverse of a functionA function is said to have an inverse if it is both one-to-one and onto
we replace the functions g(x), p(x), and t(x) with y and make x the subject to arrive at the inverse g⁻¹(x), p⁻¹(x), and t⁻¹(x) as follows;
For g(x)= x³ - 5:
y = x³ - 5
y + 5 = x³ {add 5 both sides}
x = 3√(y + 5) {take cube root}
g⁻¹(x) = 3√(x + 5).
For p(x) = 2(x+3)³:
y = 2(x+3)³
y/2 = (x+3)³ {divide through by 2}
3√(y/2) = x + 3 {take cube root}
x = 3√(y/2) - 3 {subtract 3 from both sides}
p⁻¹(x) = 3√(x/2) - 3.
For t(x) = 10(x-4)/3:
y = 10(x-4)/3
3y = 10(x-4) {cross multiplication}
3y/10 = x + 3 {divide through by 10}
(3y/10) - 3 = x {subtract 3 from both sides}
t⁻¹(x) = (3x/10) - 3.
Therefore, the inverse of the functions g(x), p(x), and t(x) are derived by interchanging the value of x for y and expressed respectively as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3.
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which type of graph would best display the following data? the number of hours a student spent studying for several tests and the student's grade on each test.
A scatter plot would best display the relationship between the number of hours a student spent studying for several tests and the student's grade on each test.
A scatter plot is a graph that displays the relationship between two continuous variables. In this case, the number of hours a student spent studying is the independent variable, which would be plotted on the x-axis. The student's grade on each test is the dependent variable, which would be plotted on the y-axis. Each data point would represent a single test, with the x-coordinate indicating the number of hours studied for that test and the y-coordinate indicating the grade received.
By using a scatter plot, you can easily identify any patterns or relationships between the number of hours studied and the student's grades on each test. It can also help to identify any outliers or anomalies in the data.
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Please help me:
Find the measure of a in parallelogram ABCD 
Answer:
angle a = 122°
Step-by-step explanation:
since the opposite angles in a parallelogram are equal, therefore,
Angle a = angle c
therefore,
14x -4 = 15x - 13
-4 +13 = 15x - 14x
x = 9
therefore angle a = 14 x 9 - 4 = 122°
F(x)=3x+5
G(x)=4x^2-2
H(x)=x^2-3x+1
Find f(x) + g(x)-h(x)
A.-5x^2+4
B.5x^2+4
C.5x^2+6x+4
D.-5x^2+6x+6
The value of the function expression evaluation; f (x) + g (x) - h (x) as required is; 3x² + 6x + 2.
What is the expression which represents f (x) + g (x) - h (x)?It follows from the task content that the expression which represents f (x) + g (x) - h (x) be determined.
Since;
F(x) = 3x + 5
G(x) = 4x² - 2
H(x) = x² - 3x + 1
Therefore,
f (x) + g (x) - h (x) = 3x + 5 + 4x² - 2 - (x² -3x + 1)
= 3x² + 6x + 2
Ultimately, the value of f (x) + g (x) - h (x) is; 3x² + 6x + 2.
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Arjun's piggy bank contains two kinds of coins and two kind of bills. There are twice as many $1 bills as $5 bills. The number of quarters is 1 more than three times the number of $5 bills. And the number of dimes is 7 less than the number of quarters. How many of each type of bill and coin if the total is $39.90
The total number of each type of bill and coin are
$5 bills x 5,
$1 bills x 10,
quarters x 16,
dimes x 9.
What is Equation ?Equations are mathematical expressions with two algebraic expressions flanking the equals (=) sign on either side. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.
Now in the given question,
$5 bills = x, total = 5x
$1 bills = 2x, total = x
Quarters = 3x + 1, total = 0.25(3x + 1)
Dimes = 3x + 1 - 7= 3x - 6, total = 0.1(3x - 6)
Equation below as the sum, solve for x:
5x + 2x + 0.25(3x + 1) + 0.1(3x - 6) = 39.9
7x + 0.75x + 0.25 + 0.3x - 0.6 = 39.9
8.05x - 0.35 = 39.9
8.05x = 40.25
x = 40.25/8.05
x = 5
Number of each bill and coin:
$5 bills = 5
$1 bills = 2*5 = 10
Quarters = 3*5 + 1 = 16
Dimes = 3*5 - 6 = 9
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a researcher randomly selects 2 fish from among 8 fish in a tank and puts each of the 2 selected fish into different containers. how many ways can this be done? a) 112 b) 28 c) 56 d) 168 e) 32
There are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers. Hence, the accurate answer is option (b) 28.
To determine the number of ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers, we will use the formula for combinations, which is given by -
nCk = n! / (k!(n-k)!)
where n is the total number of items, k is the number of items to be selected, and ! denotes the factorial function (the product of all positive integers up to a given number).
Here, we are given n = 8 fish and k = 2 fish.
Thus, the number of ways to select and place 2 fish from 8 fish will be -
8C2 = 8! / (2!(8-2)!) = (8 x 7) / (2 x 1) = 28
Therefore, there are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers.
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What is the source of this graph?
Answer:
to help navigate the answer
Which of the following is equivalent to the fraction above?
OA. 13
-7
OB. 7
13
OC. -13
-7
OD. 3
-13
-(13)
The Equivalent Fraction of -117 / 63 is -13/7.
What is Equivalent Fraction?The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½.
A rule that says the outcome of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.
Given:
We have the Fraction -117 / 63
As, Equivalent fraction can have different numerators but the denominators should be necessarily same.
Now, simplifying the fraction
= -117/ 63
= - (13 x 9) / (7 x 9)
= -13 / 7
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Help please I need this answer
Step-by-step explanation:
We know all angles on a traingle equal 180
We also know one angle is a right angle which is 90
180 - 90 = 90, indicating the other two angles equal 90
[tex](2x - 1) + (3x + 6) = 90[/tex]
Now we will combine the X's and constants
[tex]5x +5 = 90[/tex]
Now to subtract 7
[tex]5x = 85[/tex]
Lastly, divide by 5
[tex]x = 17[/tex]
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function C(x)=0.9x²-180x+20,985. How many machines must be made to
minimize the unit cost?
Do not round your answer.
Number of X-ray machines:
The company must make 100 X-ray machines to minimize the unit cost.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
To minimize the unit cost, we need to find the value of x that minimizes the function C(x) = 0.9x² - 180x + 20985.
We can start by taking the derivative of C(x) with respect to x and setting it equal to zero:
C'(x) = 1.8x - 180 = 0
Solving for x, we get:
x = 100
Therefore, the company must make 100 X-ray machines to minimize the unit cost.
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A family wants to rent a car to go on a vacation. Company A charges $45.50 and 11¢ per mile. Company B charges $65.50 and 17¢ per mile. How much more does Company B charge for x milkes than Company A?
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answer:
SOLVE IT!
Step-by-step explanation:
A. 45.50+0.11= answer
B. 65.50+0.17= answer
Minus A plus B to get answer!
Select the correct answer.
Consider the equation below.
-2x
|-3 + 1| =
-2√x - 1
Use the graph to find the approximate solutions to the equation.
The approximate solutions to the equation is (0.655, -2.618)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
-2x
|-3 + 1| =
-2√x - 1
Express the equation properly
So, we have the following representation
-2x|-3 + 1| = -2√x - 1
This gives
-4x = -2√x - 1
Next, we split the equation
y = -4x
y = -2√x - 1
To solve graphically, we plot the equation and write out the point of intersection
Hence, the solution is (0.655, -2.618)
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Evaluate 6(2x + 5y) if x = 3 and y = 4
Answer:
156
Step-by-step explanation:
6(2×3+5×4)
6(6+20)
6×26
156
another way
6(2x+5y)
12x+30y
12×3+30×4
36+120
156
is this true or false? 1 half n (n space plus log space n )space element of space omicron (n squared )true false
The statement is false.
O(nlogn), commonly known as loglinear complexity, denotes that n times will be required to perform logn operations.
The term "1 half n (n space plus log space n )space" is equivalent to O(n log n) which is a class of functions that grow asymptotically no faster than n log n.
On the other hand, the term "omicron (n squared)" is equivalent to o(n^2), which is a class of functions that grow asymptotically slower than n^2.
As a result, it is untrue to say that there is a single half-n (n space plus log n)space element in the omicron (n squared) space.
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Jade decided to rent movies for a movie marathon over the weekend. The
function g(x) represents the amount of money spent in dollars where x is the
number of movies. Does a possible solution of (6.5, $17.50) make sense for this
function? Explain your answer.
A solution (6.5, 17.50) does not make sense in the context of the problem, as the number of movies watched must be a non-negative integer.
How to interpret the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The variables for this problem are given as follows:
x: number of movies watched.g(x): amount of money spent.You can watch 1, 2, 3, ... and so on movies, a countable amount, hence 6.5 movies watched does not make sense in the context of this problem as decimal numbers are outside the function's domain.
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What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14. cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.8 feet and a height labeled 4.2 feet
10.39 cubic feet
25.85 cubic feet
36.93 cubic feet
73.85 cubic feet
Answer:
25.85 cubic feet
Step-by-step explanation:
Volume of a cylinder is
Base Area • height
The Base Area of a cylinder is a circle. The area of a circle is pi•r^2.
Vol = pi•r^2•h
They gave the diameter of the circle as 2.8, so the radius is half of that.
r = 1.4
The height was given
h = 4.2
Fill in radius and height and 3.14 for pi. Square the radius and then multiply everything.
see image.
Round to two decimal places.
hi i just did the test and the answer is 25.85 cubic feet
and it was correct btw other person deserves brainly have a nice day!
What is the measure of each angle in a regular 18-gon? If necessary, round your answer to the nearest tenth.
A regular polygon with 18 sides has a central angle that is 20 degrees in size.
What is meant by angle?An angle is a figure created by two rays or lines that have the same termination in plane geometry. The common terminal of the two rays—known as the vertex—is referred to as an angle's sides. Two lines converge at a common point to form an angle. They are expressed by the sign ° and are measured in degrees. Acute, right, obtuse, and reflex angles are four crucial types. There are 360° in a circle. It has completed two full rotations if you observe an angle of 720°.A polygon's total number of central angles equals 360 degrees.
As a result, the regular polygon's centre angle has a ratio of 360 to its number of sides. It may be expressed as,
[tex]$C_a=\frac{360}{n}[/tex]
Here, (n) denotes the regular polygon's number of sides.
The polygon in the provided issue has an overall total of 18 sides. Using the method above, it is possible to determine the polygon's centre angle, which has 18 sides. Thus,
[tex]$& C_a=\frac{360}{18} \\[/tex]
[tex]$& C_a=20^{\circ}[/tex]
Therefore, a regular polygon with 18 sides has a central angle that is 20 degrees in size.
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Which answer choice below is equivalent to 50(1+0.15)" ?
A (50.15)*
B 50 (1.15)
c) None of the above
D (57.5)
E (50+ 50.15)*
F) All of the above
The answer choices 50(1.15) and 57.5 below are equivalent to 50(1+0.15)
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).
50(1+0.15)
Add the numbers
= 50(1.15)
Multiply the numbers
= 57.5
The answer choices 50(1.15) and 57.5 below are equivalent to 50(1+0.15)
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Subtract and simplify. Show work to earn full credit. (9^2 − 4 − 4) − (−2^3 − + 12)
The simplified form of the numerical expression (9² - 4 - 4) - (- 2³ - + 12) is 93.
What is a numerical expression?Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.
Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
By mixing numbers with different mathematical operators, we can create a numerical expression. There is no restriction on how many operators can be used in a numerical expression. Between two numbers, some mathematical expressions utilize just one operator, whereas others may use multiple operators.
Given, An expression (9² - 4 - 4) - (- 2³ - + 12).
= (9×9 - 8) - (- 2×2×2 - 12).
= (81 - 8) - (- 8 - 12).
= (73) - (- 20).
= 73 + 20.
= 93.
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the superstone patio company designed these patios.Calculate the area of each. Determine the total cost of each at 23 dollars / m
1.
2.
1. The area of the marble is 6.6m² and the cost is
$3491.4
2. The area of the marble is 42.84m² and the cost is $22662.36
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
1. The area of the marble is
A=( 3.7 × 1.2 ) + 0.9 × 2.4
A= 4.44 + 2.16
A= 6.6m²
if the cost is 23 dollars /meter
per meter square = 23² = $ 529 / meter square
1 meter square = 529
6.6 meter square = 529 × 6.6 = $3491.4
2. The area of the marble is obtained by cutting it into rectangle and trapezium
A= ½(8.8+4.8) 3.9 + 4.8 × 3.4
A= ½(13.6× 3.9) + 16.32
A= 26.52+ 16.32
A= 42.84 m²
The cost will be 529 × 42.84
= $22662.36
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Which inequality correctly orders the numbers:
-5/4 -2 1/2 and -0.1
Choose 1 answer:
A: -2 1/2 > -5/4 > -0.1
B: -0.1 > -2 1/2> -5/4
C: -0.1 > - 5/4 > 2 1/2
D: -5/4 > -2 1/2 >-0.1
For the digits -5/4, -2 1/2, and -0.1, the correct inequality is -
Option D: -0.1 > -5/4 > -2 1/2
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The values for the inequality are -
A fractional number = -5/4
A mixed fractional number = -2 1/2
A decimal number -0.1
Convert the fraction number into decimal value using arithmetic operation of division -
-5/4 = -1.25
Convert the mixed fraction number into decimal value using arithmetic operation of multiplication and division -
-2 1/2 = -5/2 = -2.5
Here the greatest value is -0.1.
Then the second greatest value is -1.25 or -5/4.
The lowest value is -2.5 or -2 1/2.
So, the inequality obtained is = -0.1 > -5/4 > -2 1/2
Therefore, the inequality is -0.1 > -5/4 > -2 1/2.
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3. Two numbers are in the ratio 2:3. If 3 is added to the numbers, the ratio changes to 3:4. Find the numbers. use linear equation
Using the ratio formula the unknown numbers are found to be 6 and 9.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
The original ratio value is 2 : 3.
Three is added to the ratio.
The new ratio value is 3 : 4.
Let the unknown numbers be 2x and 3x.
The equation will be -
2x + 3 / 3x + 3 = 3/4
Solve the equation -
4(2x + 3) = 3(3x + 3)
8x + 12 = 9x + 9
8x - 9x = 9 - 12
-x = -3
x = 3
Substitute the value of x in the unknown numbers -
2x = 2(3) = 6
3x = 3(3) = 9
Therefore, the numbers are 6 and 9.
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0.8 divided by 3.49 =?
Solve for X
This was on a Geometry Honors quiz
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]
A =
1 2 1
1 1 1
For the given matrix A, a 3x2 matrix B such that AB=I, where I is the 2x2 matrix B = [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex] when AB=I
Given matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₂ₓ₃
B = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₃ₓ₂
In such a way we know that, that AB = I ₂ₓ₂
therefore = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
we can say that [tex]\left[\begin{array}{ccc}a+2c+e&b+2d+f\\a+c+e&b+d+f\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
then, a+2c+e=1
then, when elaborated we get, a+2(-a-e)+e=1
a-2a-2e+e=1
-a-e=1
a+e = -1
2c-c = 1, c = 1 hence we get the value for c
similarly we can do the same steps for the other values
b+2d+f=0
1-d+2d=0
1+d = 0
d = -1
we get the value of d as well now for the value of a and e we can proceed as shown below:
a+c+e=0
c= -a-e
a+e= -c
a+e= -1
a= -2, e=1
similarly we can proceed as shownfor the values of b and f
b+d+f=1
b+f=1-d
b+f=2
b=1, f=1
when we put these values in the correct order and place we get the value for matrix b such as shown below,
therefore, matrix B = [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex]
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the smaller the p-value, the . a. greater the evidence against h0 b. greater the chance of committing a type i error c. greater the chance of committing a type ii error d. less likely one will reject h0
The p-value is a measure of the evidence against the null hypothesis (H0)
The correct answer is (a) greater the evidence against H0.
It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming that the null hypothesis is true.
The smaller the p-value, the less likely it is that the observed result is due to chance alone, and the stronger the evidence against the null hypothesis. This means that if the p-value is very small (e.g., less than 0.05), we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis.
In contrast, a large p-value indicates weak evidence against the null hypothesis, and we may not have enough evidence to reject H0. Therefore, the smaller the p-value, the greater the evidence against H0.
Option (b) is incorrect because the chance of committing a Type I error (rejecting the null hypothesis when it is actually true) is related to the level of significance (alpha) and not the p-value. Option (c) is also incorrect because the chance of committing a Type II error (failing to reject the null hypothesis when it is actually false) is related to the power of the test and not the p-value. Option (d) is incorrect because a smaller p-value actually makes it more likely that one will reject H0, assuming that the level of significance is held constant.
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If you double the down payment what happens to the total cost and payment of the vehicle? What two ways can you lower your monthly payment?
Doubling the down payment reduces the total cost of the vehicle, and increasing the down payment or extending the loan term are two ways to lower the monthly payment.
Let's assume that you're planning to buy a car worth $20,000. The down payment is the initial amount you pay towards the purchase of the car, and it is usually expressed as a percentage of the total cost of the car. Let's assume that the down payment is 10% of the total cost, which means you have to pay $2,000 initially.
If you double the down payment from 10% to 20%, you will have to pay $4,000 initially. This means that the amount you borrow from the bank to buy the car will be reduced. As a result, the total cost of the vehicle will decrease because the interest on the loan will also decrease.
Now, let's move on to ways to lower your monthly payment.
Increase the down payment: As we discussed earlier, making a higher down payment reduces the loan amount, which, in turn, reduces the monthly payment. So, if you can increase the down payment, you can lower the monthly payment.
Increase the loan term: The loan term is the length of time you have to repay the loan. If you extend the loan term, the monthly payment will be lower. However, keep in mind that a longer loan term means you'll end up paying more interest over the life of the loan, which will increase the total cost of the vehicle.
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Two sides of a triangle have lengths 3 cm and 8 cm respectively. The third side has a length of x cm, where x is an integer. Write down an inequality that must be satisfied by x
======================================================
Explanation:
Let's label the sides of the triangle a, b, and c.
Furthermore, let's have 'a' & b represent known sides and [tex]b \ge a[/tex] be the case. For a triangle to be possible, the missing side c must have these restrictions placed on it:
b-a < c < b+a
This inequality is valid because of a modification to the Triangle Inequality Theorem. I'll leave the proof to the reader.
-------
In this case we have a = 3 and b = 8 which lead to...
b-a < c < b+a
8-3 < x < 8+3
5 < x < 11
The third side is between 5 and 11, excluding both endpoints. We cannot have x = 5. Furthermore, we cannot have x = 11 either. If x were either of those endpoints, then we'd form a straight line rather than a triangle.
Having x be an integer leads to the roster set notation {6,7,8,9,10} to represent all possible values of x. For instance, we could have a triangle with side lengths 3, 8, and 6. I recommend getting slips of paper of these lengths to try it out yourself. Or you can use software such as GeoGebra to see why this works.
5. Function G takes a student's first name for its input and gives the number of letters in the first name for its
output.
a. Describe the meaning of G(Jada) = 4
b. Find the value of G(Diego) …………..I need helpppp!!
a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.
b. G(Diego) =5
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that a Function G takes a student's first name for its input and gives the number of letters in the first name for its output.
a.
Given that G(Jada) = 4
In the above function Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.
b. We need to find the value of G(Diego)
In the above function Diego is the input and 5 will be output, the output is 5 because there are 5 letters in Diego word.
G(Diego) =5
Hence, a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.
b. G(Diego) =5
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You must show all work and explain your strategy (with the reason for each step) to receive full credit!
Using the diagram in the problem angle TQU is solved to be
53.14 degreesHow to find angle TQU
The angle at U is 90 degrees, Using the concept of adjacent angles the three angles at U is solved
Using the trigonometry relations of right triangle we solve for angle PQT'
tan (angle PQT) = 1 / 3
angle PQT = arc tan (1 / 3)
angle PQT = 18.43
angle PQT = angle UQS and
angle PQT + angle UQS + angle TQU = 90 degrees adjacent angles
2 * 18.43 * angle TQU = 90
angle TQU = 90 - 2 * 18.43
angle TQU = 53.14 degrees
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the weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. what is the probability that the next report will weigh less than 45g?
The probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%. We can use the standard normal distribution to find the probability that the next report will weigh less than 45g.
z = (x - mu) / sigma
where z is the standard score, x is the value we want to standardize (45g), mu is the mean (60g), and sigma is the standard deviation (12g).
Substituting the given values, we get:
z = (45 - 60) / 12
z = -1.25
Next, we use a standard normal distribution table (or a calculator) to find the cumulative probability of z being less than -1.25. This gives us:
P(z < -1.25) = 0.1056
Therefore, the probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%.
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