g the diameters of bolts produced by a certain machine are normally distributed with a population mean of 20.00 milimeters (mm) and a population standard deviation of 0.2 mm. what is the probability that a randomly selected bolt will have a diameter greater than 20.329 mm? use 4 decimal places in answering.
The probability that a randomly selected bolt will have a diameter greater than 19.705 mm is 0.9812.
Given that:
mean = 19.0
standard deviation = 0.3
P(18.295 < x < 19.705)
The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
= P[(18.295 - 19.0)/0.3) < (x-mean)/standard deviation < (19.705-19.0)/0.3)]
= P(-2.35 < z < 2.35)
= P(z<2.35)-P(z<-2.35)
= 0.9906 - 0.0094
= 0.9812
Probability = 0.9812
Hence we get the required probability.
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Let f(x) = e ^ (6x) and g(x) = 8in(x) Find and simplify g(f(- 2)) -96 -48 48 C B A
Answer: g(f(-2))=-96
Step-by-step explanation:
[tex]Given: \ f(x)=e^{6x}\ \ \ \ g(x)=8ln(x)\ \ \ \ g(f(-2))=?\\\\f(-2)=e^{6*(-2)}\\\\f(-2)=e^{-12}\\\\Hence,\\\\g(f(-2))=8ln(e^{-12})\\\\g(f(-2))=8*(-12)\\\\g(f(-2))=-96[/tex]
Answer:
-96
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=e^{6x}\\ g(x)=8 \ln (x) \end{cases}[/tex]
To find g[f(-2)], substitute x = -2 into the function f(x):
[tex]\implies f(-2)=e^{6 \times -2}=e^{-12}[/tex]
Then substitute the function f(-2) in place of the x in function g(x):
[tex]\implies g[f(-2)]=8 \ln \left(e^{-12}\right)[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\begin{aligned}\implies g[f(-2)]&=-12\cdot 8 \ln \left(e\right)\\&=-96 \ln \left(e\right)\end{aligned}[/tex]
Apply the log law: ln(e) = 1
[tex]\begin{aligned}\implies g[f(-2)]&=-96 \ln \left(e\right)\\&=-96(1)\\&=-96\end{aligned}[/tex]
---------------------------------------------------------------------
As one calculation:
[tex]\begin{aligned}g[f(-2)]&=8 \ln \left(e^{6 \times -2}\right)\\& = 8 \ln \left(e^{-12}\right)\\& = -12 \cdot 8 \ln \left(e\right)\\& = -96(1)\\& = -96\end{aligned}[/tex]
If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of
getting exactly o ones?
Answer:
0.402
Step-by-step explanation:
The probability of not rolling a one on any given roll is [tex]5/6[/tex].
Since the die is rolled 5 times, the probability is [tex](5/6)^5 \approx 0.402[/tex].
Imagine that you could increase the gravitational
force on Earth to 200% its current force. What would life be like?
Compose a written response below in complete sentences.
Your joints and bones would first have to work harder to support your heavier weight.
What would happen if there was a 200% increase in gravity?If you were subjected to double gravity for an extended length of time, it may be deadly since it would put your body under a lot of strain. Your joints and bones would first have to work harder to support your heavier weight. Even minor motions would be difficult for your muscles.Our blood will be drawn down into our legs if the gravity is too powerful, and we risk having our bones break or perhaps being helplessly stuck to the earth. It is preferable to determine the gravitational limit of the human body before we set foot on a sizable new planet.To learn more about gravitational limit refer to:
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1. Determine whether the following tables represent a direct variation.
a.
X
-4
-2
6
у
-8
-4
18
The table does not represent a direct variation as there is mismatch of k in three expressions.
We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.
What is direct variation?
A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.
For the first value of x and y, x=-4 and y=-8
Thus, it can be expressed as -8 = 2*-4, hence k=2
For the second value of x and y, x=-2 and y=-4
Thus, it can be expressed as -4 = 2*-2, hence again k=2
For the third value of x and y, x=6 and y=18
Thus, it can be expressed as 18 = 3*6, thus k here is 3 and not 2
Hence, this table does not represent a direct variation as there is mismatch of k in three expressions.
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the interior angles of a regular polygon each measures 165 degrees. how many sides does the polygon have
Trent and his family are heading to Perfect Putt Mini-Golf. They plan to purchase the group package. With the package, the cost per person is $3 less than the normal cost for an individual. There are 6 people in Trent's family. His mom called ahead and found that the total cost for the family will be $30.
Which equation can you use to find the normal cost, x, for an individual?
3x-6=30
6(x-3)=30
6x-3=30
3(x-6)=30
PLEASE EXPLAIN WHY YOU GOT YOUR ANSWER PLEASEE!!!!
When Skip was a puppy, he weighed 5.6 lbs. When he visited the vet, he weighed 13.3 lbs. How much weight did Skip gain between the time he was a puppy and his vet visit?
Answer:
7.7
Step-by-step explanation:
I got this by subtracting 13.3 - 5.6
Estimate the values to the nearest hundredth to complete the table.
angleadjacent leg ++ hypotenuse
A= 0.31
C= (blank)
opposite leg ++ hypotenuse
A= 0.95
C= (blank)
opposite leg ++ adjacent leg
A= 3.06
C= (blank)
The required trigonometric ratios of angle C in the given table are
(a) adjacent leg ÷ hypotenuse (cos C) = 0.95
(b) opposite leg ÷ hypotenuse (sin C) = 0.31
(c) opposite leg ÷ adjacent leg (tan C) = 0.33
What are required trigonometric ratios?The three important trigonometric ratios are:
sin θ = opposite leg ÷ hypotenuse
cos θ = adjacent leg ÷ hypotenuse
tan θ = opposite leg ÷ adjacent leg
Calculation:In the given right-angle triangle, the ratios are given as
cos A = adjacent leg ÷ hypotenuse = 0.31
sin A = opposite leg ÷ hypotenuse = 0.95
tan A = opposite leg ÷ adjacent leg = 3.06
These ratios are w.r.t the angle A.
Since we know that, in the right angle triangle,
∠A + ∠B + ∠C = 180°
⇒ ∠A + 90° + ∠C = 180°
⇒ ∠A = 180° - 90° - ∠C
∴ ∠A = 90° - ∠C
So, the trigonometric ratios w.r.t the angle C are:
(a) cos A = cos (90° - ∠C) = sin C
But we have cos A = 0.31
∴ sin C = 0.31
(b) sin A = sin (90° - ∠C) = cos C
But we have sin A = 0.95
∴ cos C = 0.95
(c) Then, tan C = sin C/cos C
Here we got sin C = 0.31 and cos C = 0.95
So, tan C = 0.31/0.95 = 0.33
Thus, the table is as follows:
angle adj ÷ hyp opp ÷ hyp opp ÷ adj
A 0.31 0.95 3.06
B 0.95 0.31 0.33
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Which of the following expressions are equivalent to 16/24? Select all that apply.
After evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expresion 16/24.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
So, we have the expression:
16/24
We need to find the equivalent expression from the options as follows:
So, let's take option (E) as it seems the answer and evaluation is:
8/2 * 2/12 (Be LHS)
Now, multiply:
8/2 * 2/12 = 16/24
16/24 = 16/24
Therefore, after evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expression 16/24.
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This graph shows all the key characteristics of a particular polynomial function. Drag tiles to complete the function rule that could be represented by the graph
The function rule that could be represented by the graph is given as follows:
y = 2x³ + x - 3.
How to define the function?The first step in defining the function is looking at it's y-intercept, which is the value of y when the graph of the function crosses the y-axis.
This value is of -3, hence the function can be defined as follows:
f(x) = ax^n + x - 3.
Then we look at the behavior of the function. It has an inflection point, as it is concave down and then it becomes concave up, hence:
It's second derivative is of the first degree.It's first derivative is of the second degree.The function is of the third degree, hence n = 3.Thus:
f(x) = ax³ + x - 3.
Then we look at the x-intercept, meaning that when x = 1, y = 0, this the leading coefficient is obtained as follows:
0 = a + 1 - 3
a = 2.
Thus the function is defined as follows:
y = 2x³ + x - 3.
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The graph showsf(x)and its transformationg(x).
What is the function equation for g(x)?
The function equation for g(x) is given as follows:
g(x) = 2^(x - 3).
How to define the equation for g(x)?The equation for g(x) is defined as a translation of function f(x), as the graph has the same format and orientation, just has a different position.
The definitions of each type of translation are given as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function f(x) is defined as follows:
f(x) = 2^x.
The graph of g(x) was moved three units right, meaning that:
g(x) = f(x - 3) = 2^(x - 3).
This means that the third option is the correct option for the equation of function g(x).
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Determine whether the relation is a function. (0,-3) (1,0) (2,3) (2,2) (3,1)
Answer:
function
Step-by-step explanation:
I did this math before
Answer:
this relation is a function
Name the property of real numbers illustrated by the equation. -2(x 4)=-2x-8
Distributive property of real numbers illustrated by the equation. -2(x 4)=-2x-8
The equation -2(x 4)=-2x-8 is an example of the distributive property of real numbers. This property states that when a number is multiplied by a group of numbers that are being added together, the number can be distributed to each of the terms in the group. To rewrite this equation as -2x + (-2)(-4) = -2x - 8, the number -2 is allocated to each of the terms in the group (x and -4) in this equation.Simplifying further, we get -2x - 8 = -2x - 8.
-2(x 4) = -2x - 8
Distribute -2 to each term in the group
-2x + (-2)(-4) = -2x - 8
Simplify
-2x - 8 = -2x – 8
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The expression 102+24x represents the total amount, in dollars, a painter spends at a store to purchase paintbrushes and x gallons of paint. What does the 24 represent?
Responses
the cost per gallon of paint
the cost per paintbrush
the number of gallons of paint the painter purchases
the number of paintbrushes the painter purchases
24 represents the cost per gallon of paint.
What is slope?The process of finding the rate of change of the value dependent variable of the function changes with respect to that of the variable independent variable.
Given that, The expression 102+24x represents the total amount, in dollars, a painter spends at a store to purchase paintbrushes and x gallons of paint.
The equation is 102+24x
Here, the slope of the equation is 24, which tells the rate of change.
Hence, 24 is the cost per gallon of paint
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Solve the system of equations using the substitution method. y = -5x -2x - y = 0 (x, y) = ( ¯\____|
Answer:
x= -2y/7
Step-by-step explanation:
y=-5x-2x-yif you switch sides you get
-5x-2x-y=y
add similar elements -5x-2x-y=-7x
-7x-y=y
move y to the right side
-7x=2y
decide both sides by -7
-7x/-7 = 2y/-7y
simplify
x = -2y/7
y = -2x + 1
4x + y = 9
Solve the system of equations without graphing. Show all the math steps needed to find the solution to this system.
Answer:
x =4 & y = -7
Step-by-step explanation:
this is the right answer
A manager of a self-service car wash charges a flat fee in addition to a fee per minute, x, for use of the services. The expression 5+0.75x models the scenario.
Which statement is true?
Responses
The coefficient 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The coefficient 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 5+0.75x.
In the given expression, 5 is constant term and 0.75x is another term.
In the term 0.75x, 0.75 is the coefficient of x
In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.
Therefore, option D is the correct answer.
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cory has $3$ apples, $2$ oranges and $2$ bananas. if cory eats one piece of his fruit per day for a week and the pieces of fruit within each category are indistinguishable, in how many orders can cory eat the fruit? one such order is $aaaoobb.$
Then the orders can Cory eat the fruit is = 25
Given that,
If Cory has eat apples = 3$
If Cory has eat oranges = 2$
If Cory has eat bananas = 2$
Total eat fruits = 3 + 2 + 2
Total eat fruits = 7$
We have to express the amount of total fruits as an equation.
The amount of apples will be x,
The amount of oranges will be y,
The amount of bananas will be z
The amount of apples multiplied by 7 because they ate each day of the week.
7*(x) + y + z = now we have to replace the values of x, y and z with the ones that gave us the problem
Then,
x = 3
y = 2
z = 2
So,
We can write,
7*(x) + y + z = 7 *(3) + 2 + 2
= 21 + 2 + 2
= 25
Therefore,
Then the orders can Cory eat the fruit is = 25
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The library sponsors a chess club for members of all ages and skill levels. Currently, the ages of the members are 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, and 22. The librarian uses a histogram to track the number of members in different age groups. For this situation, which is the appropriate way to label the age intervals on the x-axis?
Answer:
B. 7−10; 11−14; 15−18; 19−22
Step-by-step explanation:
Select the correct answer. Solve the following inequality. 21 ≤ -3(x − 4) < 30 A. -3 ≤ x < 6 B. -10 < x ≤ -3 C. 28 ≤ x < 37 D. -6 < x ≤ -3
Answer:
D. -6 < x ≤ -3
Step-by-step explanation:
21 ≤ -3(x − 4) < 30
21/3 ≤ -3(x − 4)/3 < 30/3
7 ≤ -(x − 4) < 10
7 ≤ -x - (-4) < 10
7 ≤ -x + 4 < 10
7 - 4 ≤ -x + 4 - 4 < 10 - 4
3 ≤ -x < 6
(3 ≤ -x < 6)/(-1)
-3 >= x > -6 ==> when dividing by a negative number, switch the inequality
sign
-6 < x ≤ -3 ==> D
what is the product of each equation?
[tex]\left(3a^{2}b^{4}\right)\left(-8ab^{3}\right)[/tex]
[tex]\left(3a^{2}b^{7}\right)\left(5a^{3}b^{8}\right)[/tex]
[tex]\left(-2d^{2}+s\right)\left(5d^{2}-6s\right)[/tex]
[tex]\left(3x-6\right)\left(2x^{2}-7x+1\right)[/tex])
[tex]\left(7x^{2}y^{3}\right)\left(3x^{5}y^{8}\right)[/tex]
[tex]\left(y^{2}+3y+7\right)\left(8y^{2}+y+1\right)[/tex]
[tex]\left(4s+2\right)\left(5s^{2}+10s+3\right)[/tex]
The solution to the products of exponents is as follows;
1) -24a³b⁷
2) 15a⁵b¹⁵
3) -10d⁴ + 17sd² - 6s²
4) 6x³ - 33x² + 45x - 6
5) 21x⁷y¹¹
6) 8y⁴ + 25y³ + 60y² + 10y + 7
7) 20s³ + 50s² + 32s + 6
How to find product of exponents?The Product of Powers Property of exponents states that when we multiply two powers with the same base, we add the exponents.
1) (3a²b⁴) * (-8ab³)
= -24a³b⁷
2) (3a²b⁷) * (5a³b⁸)
= 15a⁵b¹⁵
3) (-2d² + s)(5d² - 6s)
Expanding the bracket to get;
(-10d⁴ + 5sd² + 12sd² - 6s²)
= -10d⁴ + 17sd² - 6s²
4) (3x - 6) * (2x² - 7x + 1)
= 6x³ - 33x² + 45x - 6
5) (7x²y³) * (3x⁵y⁸)
= 21x⁷y¹¹
6) (y² + 3y + 7) * (8y² + y + 1)
= 8y⁴ + 25y³ + 60y² + 10y + 7
7) (4s + 2) * (5s² + 10s + 3)
= 20s³ + 50s² + 32s + 6
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browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins, what net payout will you be promised in a fair betting game in case your bet works out?
Net payout will you be promised in a fair betting game in case your bet works out is $0 .
Given :
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .
P ( browns ) = 60 / 100 = 0.60
P ( steelers ) = 40 / 100 = 0.40
Net payout = Number of wins * 10 - Number of loses * 10
= 1 * 10 - 1 * 10
= 10 - 10
= $0.
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1. Given a mean of 165 and a standard deviation of 4, use the empirical rule to answer the following questions: a. What percent is less than 161? b. What percent is more than 173? c. What percent is between 157 and 169? d. What is the 84 th percentile?
Using a mean and standard deviation as inputs, the following formula can be used to get the percentile of a normal distribution:
Percentile Value is equal to z +.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.
The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation.
Standard deviation may be written as SD.
A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.
Though in algebra, it is simpler
According to our question-
a. 157 is less then 161
b. n>173, n be a real number.
Hence, Using a mean and standard deviation as inputs, the following formula can be used to get the percentile of a normal distribution: Percentile Value is equal to z +.
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The area of a triangle with base b and height h is 1/2bh. Larry painted a mural of different foods on the wall of the school lunchroom. He painted a triangular tortilla chip with a 15-inch base and a 10-inch height.
What is the area of Larry's tortilla chip?
Larry's tortilla chip has a surface area of 75 square inches.
Describe area.Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
A triangle with base b and height h has a surface area of 1/2bh. You need to calculate the area of a triangle with a 15-inch base and a 10-inch height.
For b=15 and h=10,
Evaluate the expression
1/2bh for b=15 and h=10
1/2bh=1/2(15)(10)
=1/2(150)
=75inch
Larry's tortilla chip has a surface area of 75 square inches.
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Yujin Pon has a principal of $900 in her savings Iccount on October 1. The money earns interest at a rate of 6.5% compounded quarterly until July 1 of the following year. What is the amount in the account on July 1?
а.$914.63
b. $943.75
c.$943.87
d. $944.59
Answer: The correct answer is c. $943.87.
Step-by-step explanation: To solve this problem, we need to first determine the length of time between October 1 and July 1 of the following year. This is a period of 9 months, or 3 quarters. We can then use this information to calculate the amount of interest earned over this time period.
The principal in Yujin Pon's account is $900, and the interest rate is 6.5% compounded quarterly. This means that for each quarter, the account will earn 6.5/4 = 1.625% in interest. Over the 3 quarters between October 1 and July 1 of the following year, the account will earn a total of 1.625% * 3 = 4.875% in interest.
To calculate the amount of interest earned, we can multiply the principal by the interest rate:
Interest = Principal * Interest Rate
= $900 * 0.04875
= $43.87
The total amount in the account on July 1 will be the original principal plus the amount of interest earned over the 3 quarters:
Total = Principal + Interest
= $900 + $43.87
= $943.87
Therefore, the correct answer is c. $943.87.
Solve for y. Find m∠ C and m∠ D. Show all work.
The value of y is 10. The measure m∠ C and m∠ D are 40° and 76° respectively.
What is external angle?
The angle created when a transversal cuts one of two lines and is located outside of the line. It describes the angle between a side of a polygon and an expanded adjacent side.
The measure of an external angle of a triangle is equal to the sum of opposite interior angles.
∠DEF is an exterior angle. The opposite interior angles of ∠DEF are m∠ C and m∠ D
Therefore,
m∠ C + m∠ D = ∠DEF
4y° + (7y + 6)° = 116°
Add like terms
11y + 6 = 116
Subtract 6 from both sides:
11y = 110
Divide both sides by 11:
y = 10
Putting y = 10 in m∠ C = 4y° and m∠ D = (7y + 6)°
m∠ C = 40°
m∠ D = 76°
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does anyone have the answer
Angle BAC is an inscribed angle, which means that its size is equal to the size of the arc it attempts to represent, arc BC, and that arc BC is the arc that it attempts to represent. Taking that portion of 360° will allow us to calculate the angle 45°.
What is the measure of ∠ BAC?One degree is represented by each of these tiny notches on a scale. Therefore, eleven degrees are equal to 10 plus one. And that is how we responded: the BAC angle is eleven degrees in length.Percentages are all that are involved here. The proportion of the surface area that is represented by 4.5 must first be calculated. Calculating the overall surface area is necessary to accomplish that. Radius equals six if the diameter is twelve.A = π * 6 * 6 = 36π
The current value
Taking that portion of 360° will allow us to calculate the angle:
0.125 * 360 = 45°.
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-8x - 5(-5x - 1) - 7 = 3(x − 3)
Answer:
-8x+25x+5-7=3x-9
or ,17x -2=-9+2
or, -14x=-7
or, x=-7/-14
x=1/2
Answer:
-8x +25x +5-7=3x-9
17x-2 = 3x-9
17x-3x=9+2
14x =11
x= 14/11
If using the method of completing the square to solve the quadratic equation x 2 + 2 x + 16 = 0
Answer:
Step-by-step explanation:
[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]
The solution does not exist because all numbers squared are greater than zero.
