There is a 4.5% (or 0.045) probability that the maximum safe weight will be surpassed.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.
Probability and odds are two distinct ideas.
Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
So, we know that;
Average u = 1.8 tons
r = 0.5 for the standard deviation
n = 35 data points
68 tons or more would be the combined weight of the 35 automobiles. Each car's average weight should be greater than:
X = 68/35 = 1.943
After that, we can utilize that to calculate the z value.
Z = (X - u)/(r/√n)
Z = (1.943 - 1.8)/(0.5/√35)
Z = 1.692
We must determine the p-value at Z > 1.692 in order to evaluate the likelihood:
P(Z > 1.692) = 0.0453
Therefore, there is a 4.5% (or 0.045) probability that the maximum safe weight will be surpassed.
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P varies inversely with x. If p = 14 when x = 16, find the value of p when x = 21.
The value of p when x = 21 is p = 32/3 .
Given :
we know that ,
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form p * x = k or p = k / x
we know that
For p = 14, x = 16
Find the value of k
k = p * x
substitute the values
k = 14 * 16
= 224
so
The equation is equal to
p = 224 / x
if x = 21
substitute the value of x in the equation
p = 224 / 21
Divide by 7 both numerator and denominator
p = 32 / 3
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Is the number 16 a square?
Yes, the number 16 is a square.
It is the square of the number 4, since 4 x 4 = 16.
A square root is a factor in mathematics that, when multiplied by itself, equals the initial number. For instance, 3 and -3 are both square roots of 9.
The square of a number's root is the value under the root. For instance, (3 + 2) = 3. Any even number's square unit will only include even numbers.
Each and every nonnegative real number x has a distinct nonnegative square root, known as the primary square root, which is represented by the symbol x, also known as the radical sign or radix. As an illustration, we write 9=3 to denote that 3 is the number 9's fundamental square root. The word (or integer) whose square root is being examined is known as the radicand. The word or number that appears beneath the radical symbol, in this case, 9, is referred to as the radicand. The principal square root can alternatively be expressed in exponent notation for nonnegative x as x1/2.
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What are the 3 consecutive odd numbers whose sum will be 45?
The 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.
Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.
Let the 3 numbers be x ,x+2 , x+4
The sum of numbers is 45
⟹x+x+2+x+4=45
3x+6=45
3x=39
x=13
Hence , the 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .
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What's the inverse of 2?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the inverse of a number a is [tex]\frac{1}{a}[/tex]
then
the inverse of 2 is [tex]\frac{1}{2}[/tex]
For a normal distribution, a negative value of z indicates O the z is to the right of the mean D a mistake has been made in computations, because z is always positive. o the area corresponding to the z is negative. O the z is to the left of the mean.
For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.
What is a normal distribution?A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.
The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.
Z is the number of standard deviations from the mean given by the formula:
z = ( X - μ ) ÷ ( σ )
where
x is the raw score,
μ is the population mean, and
σ is the population standard deviation
A negative value means that the number of standard deviations of an observation is to the left of the mean.
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How do you find the height of a triangle when you know the base and area?
We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is
A = 1/2 × b × h
A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.
The formula to determine area of a triangle of base b and height h is
A = 1/2 × b × h
Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.
h = 2×A/ b
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What does AA SSS and SAS mean in geometry?
SSS means side side side, SAS means side angle side and AAA means angle angle angle.
There are some postulates which can be used to prove that the two given triangles are similar. If two triangles are similar then we can find as a result that their respective sides and angles are also equal.
If three sides are given then we will use the SSS postulate
If two sides and one angle is given then we will use the SAS postulate
If three angles are given then we will use the AAA postulate.
Therefore SSS, SAS, and AAA are postulated that are used to prove two triangles are similar.
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Determine whether or not the equations represent a direct variation. Sort the equations into the appropriate category.
Direct Variation
Not Direct Variation
y=3x
x=-1
y=(2/7)x
-0.5x=y
y=22x+7
y=4
Answer:
Direct Variation
y = 3x
y = (2/7)x
y = -0.5x
NOT Direct Variation:
x = -1
y = 4
y = 22x + 7
Step-by-step explanation:
Direct Variations are in the form
y = kx
This is very similar to:
y = mx + b except the b MUST be zero.
Also, direct variations always go through (0,0) that's why b must be 0.
So easy to pick out:
y = 3x
y = (2/7)x and
y = -0.5x are all in the form y = kx and have a y-intercept of zero.
y = 22x + 7 has that extra +7 tacked on to the end of the equation. It does not go through (0,0). It has a b that is 7. So it starts at (0,7). It is not a direct variation.
The other two, x = -1 and y=4 are both not direct variations. Neither starts at (0,0).
x=anumber is a vertical line and y=anumber is a horizontal line. These are not direct variations.
(a.a+a.b+a.c) +b.a+b.b+b.c)
Answer:
this it's no a math problem
A label printer prints 5 pages of labels in 4.5 seconds. How long will it take to print 160 pages of labels?
Answer:
144 seconds
Step-by-step explanation:
4.5 seconds = 5 pages
x second = 160 pages
cross multiply
you get: 5x= 160 ×4.5
which equals 720 divide it by 5 you get 144
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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m
Step-by-step explanation:
Donovan made a snowman.The snowman weighed a total of 472 pounds . If the head was 202 pounds , and the base and torso weighted the same amount how much does the base and torso each weigh ? ASAP
Answer:
Base: 135 Pound
Torso: 135 Pound
Step-by-step explanation:
The snowman Weighed is 472 pounds
The head was 202 Pound
We have to find the total weight of the base and torso
472 - 202 = 270 pound
So, 270 pounds is the total weight of the base and torse
We know the base and torso weigh the same amount
So take 270 divided by 2 = 135 Pound
So, the Base weight is 135 Pound
the Torso weight is 135 Pound
Answer:
101 pounds
Step-by-step explanation:
if the torso and base weighs the same as the head
then each by itself should weigh 101 pounds
I hope this helps
and i hope i understood the question
The liu family buys 20 pounds of chicken at the local market for $50. Which equation can be used to represent the cost, c, of buying x pounds of chicken at the same price per pound?.
Answer:
[tex]c=2.50x[/tex]
Step-by-step explanation:
The cost per pound of chicken is [tex]50/20=\$2.50[/tex].
So, the equation is [tex]c=2.50x[/tex].
A rectangular sheet of paper 42 cm x 16 cm is rolled along its length and a cylinder is formed . Find the volume of the cylinder
Since a rectangle is rolled along length then circumference of circle is equal to length of rectangle and breadth equals to height.
=) 2*pi*r = 42cm
=) 2*22/7 * r = 42cm
=) r = 42*7 / 2*22
=) r = 147/22 cm
Since Volume of cylinder = pi* r^2*h
= 22/7 * 147/22 * 147/22 * 16 cm^3
= 2245.09 cm^3.
What is a domain of a function examples?
The domain of the function [tex]f(x)=\frac{1}{x}[/tex] is all real numbers except 0.
What is the Domain of function?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's domain is the collection of values it can take as input.
For example, let us take a function [tex]f(x)=\frac{1}{x}[/tex].
For this function, the domain is all the values x can take.
Here x cannot take 0 because 1/0 is not defined.
So, the domain of the function is all real values except 0 which can also be written as:
Domain= R-{0}
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Hiya, just need help with this. Thanks
Answer:
C, D
Step-by-step explanation:
Compare each choice with
x² + 5x - 8 = 0
A.
x² + 7x - 9 = 2x + 1
x² + 5x - 10 = 0
No
B.
x² + 4x - 5 = x - 3
x² + 3x - 2 = 0
No
C.
x² + 10x - 2 = 5x + 6
x² + 5x - 8 = 0
Yes
D.
12x + 4 = 7x + 12 - x²
x² + 5x - 8 = 0
Yes
Answer: C, D
What is Y =- 2x on a graph?
The equation Y=-2x is a linear equation, which can be plotted on a graph as a straight line.
The equation can be written in slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=-2 and the y-intercept is b=0. Therefore, the equation can be written as y=-2x+0.
The slope of the line is negative, meaning that as x increases, y decreases. The y-intercept is zero, which means that the line passes through the origin (0,0).
For example, if x = 2, then y = -2(2) + 0 = -4. Therefore, the point (2, -4) is on the line. Similarly, if x = 4, then y = -2(4) + 0 = -8, so the point (4, -8) is also on the line.
The graph of the equation y=-2x would thus be a line starting at the origin (0,0) with a negative slope. As x increases, y decreases, and the line never crosses the y-axis.
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pls help me this is hard
Answer:
in both questions the answer is option d.
What is the median of 4 9 6 3 4 2?
To find the median of a set of numbers, you need to arrange the numbers in order from smallest to largest, and then find the middle number. In this case, the numbers are already in order: 2, 3, 4, 4, 6, 9.
There are 6 numbers in the set, so the median is the middle number, which is 4.
What is the median in mathematics?the median value, which is arrived at by sorting all the data points and selecting the central one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are sorted, the number 4 is in the middle (1, 4, 7), making it the median of the numbers 4, 1 and 7.
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How many four-digit personal identification numbers (pin) are possible if the pin cannot begin with a 0 and the pin must be an odd number?.
If the four-digit personal identification number (PIN) cannot start with a 0 and must be an odd number, then 0 four-digit pins are conceivable.
There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used in a four-digit PIN. However, we are told that the PIN cannot begin with a 0, so there are only 9 possible digits that can be used for the first digit.
For the second, third, and fourth digits, any of the 10 digits can be used. Therefore, there are 9 x 10 x 10 x 10 = 9,000 four-digit PINs that can be created using any of the 10 digits.
We are also told that the PIN must be an odd number. This means that the last digit of the PIN must be odd. There are 5 odd digits (1, 3, 5, 7, and 9), so there are 5 possible digits that can be used for the last digit.
For the first three digits, any of the 9 digits that can be used for the first digit can be used. Therefore, there are 9 x 10 x 10 = 900 four-digit PINs that can be created using only odd digits.
However, we have double-counted the PINs that begin with 0. Since these PINs are not allowed, we need to subtract them from the total number of possible PINs. There are 9 x 10 x 10 = 900 four-digit PINs that begin with 0, so we need to subtract these from the total number of possible PINs.
The final number of possible four-digit PINs that cannot begin with 0 and must be odd is 900 - 900 = 0. Therefore, there are 0 four-digit PINs that meet these criteria.
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What is the factor of 42?
Answer:
Step-by-step explanation:
42 is an even number so it is divisible by 2
42 divided by 2=21
42 has digits that add up to give 6
If the sum of a number adds up to give 3, 6 or 9 that number is divisible by 3
42 divided by 3=14
Factors of 42 are 21 and 2 and 14 and 3 and 42 and 1
What is the median of 25 and 25?
Here, 25 and 25 are both middle numbers we can average them to get the median, which is 25.
The median of the data is given by the middle number which is obtained after arranging all the data in a certain order.
For example, we have numbers 1,2,3,4 and 5 which is a data of five data points.
Now, here if we see that two numbers are to the left of 3 and two numbers are to the right of 3, therefore the median of this data is 3.
In higher standards, the formulae of median are given by -
Divide the number of observations by two.
Now here arise two cases -
1. If there are an odd number of observations, round that number up, and the value in that position is the median.
2. If the number of observations is even, take the average of the values found above and below that position.
So, in a similar manner the median here is given by 25.
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Where is an expression in math?
We can identify an expression to see the numbers, variables and mathematical operator between them.
What is expression?An expression consists of at least two terms along with a sign. Terms can be a constant and variables or constant and variables accompanied by a number. In each case, there is one symbols in between. As example, 2+3z is a expression where 2 is a number called constant which is separated from variables z by a addition sign +, 3 is called coefficient of z.
How can we identify an expression?Mathematical expression is made up of combination of terms. We can find an expression with two or more numerical terms which are called numerical expression. Besides there are fractional expression with or without variables. We can identify an algebraic expression to observe that it has numbers, variables and operator. We can distinguish an equation from an expression by an equal sign. Whenever, an equal sign is present among the mathematical terms then the expression is called equation.
As example. the above expression is written as 2+3z=0
it is an equation, and we can determine the unknown value z.
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Which is an x-intercept of the continuous function in the table? Group of answer choices (–1, 0) (0, –6) (–6, 0) (0, –1)
In the given group of answer choices x-intercept, the only point that has a y-coordinate of 0 is (0, -1).
How do you find the x-intercept?An x-intercept is a point on the graph where the y-coordinate is 0. Therefore, the x-intercepts of the continuous function in the table are (0, 0) and (-6, 0). The other two points given in the group of answer choices, (-1, 0) and (0, -1), are not x-intercepts because they do not have a y-coordinate of 0.An x-intercept is a point where the function crosses the x-axis, meaning that the y-coordinate of the point is 0. In the given group of answer choices, the only point that has a y-coordinate of 0 is (0, -1),so (0, -1) is the x-intercept.To learn more about x-intercept refer :
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Brayden is ordering T-shirts for Student Government to
wear during the next volunteer event. He ordered 32 T-
shirts from Mascot Universe. However, Mascot Universe
reduced the price of each T-shirt by $6 for being a school
partner. The total came to $288. Write and solve an
equation to determine the cost per T-shirt.
What is the value of x in the equation
7
- =
9
2/3
x-7?
How many pattern block trapezoids would create 2 hexagons?
Which equation is the inverse of y x2?
The inverse of function y = x² is ±√x .
What is the inverse of a function?A function from a set X to a set Y assigns exactly one element of Y to each element of X.An inverse function is one that "undoes" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f⁻¹ .Given equation,
y = x²
We have to find the inverse.
By interchanging x and y variables,
y² = x
Solve this equation for y now. This is the inverse of this function.
Take the square root of both sides.
y = ±√x
Then the inverse of the function given is :
f⁻¹(x) = ±√x
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This year, Ken paid $1,611 for season tickets to his favorite baseball team, which is 10% cheaper than last year. What was the price of season tickets last year?
Answer:
$1772.10
Step-by-step explanation:
10% = 0.1
Take 1611 times 0.1 = $161.10
So, the 10% cheaper is $161.10
We add both numbers to find the price of last year's season ticket!
1611 + 161.10 = $1772.10
So, the price of last year season's ticket is $1772.10
Let's check to see if it is correct!
$1772.10 - $161.10 = $1611
So, my answer is correct!
Answer:
$1,790
Step-by-step explanation:
x -.1x = 1611 Combine like terms
.9x = 1611 Divide both sides by .9
x = 1790
Check:
1790 - .1(1790) = 1611
1790 - 179 = 1611
1611 = 1611
What are the roots of the quadratic equation x2 − 16 0?
The roots of a quadratic equation are the values of x that make the equation equal to 0.
The general form of a quadratic equation is [tex]ax^2[/tex] + bx + c = 0, where a, b, and c are constants.
To find the roots of the equation [tex]ax^2[/tex] - 16 = 0, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac))/(2a)
In this case, a = 1, b = 0, and c = -16. Plugging these values into the quadratic formula, we get:
x = (-0 +/- sqrt(0^2 - 41(-16)))/(2*1)
x = (-0 +/- sqrt(256))/(2)
x = (-0 +/- 16)/(2)
The roots of the equation are x = 8 and x = -8.
The complete question is:-
What are the roots of the quadratic equation x2 − 16 =0?
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How do you determine if two pairs of functions are inverses?
First make the graph of the functions, then if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Symmetric
A figure or shape that can be divided into two equal parts by a line is called symmetric figures.
Inverse Functions
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.
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These are the first 5 terms in a fibonacci sequence. 1, 4, 5, 9, 14. Write down the next 2 terms in the sequence
Answer:
The next two terms in the Fibonacci sequence would be 23 and 37.
Step-by-step explanation:
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So the next term in the sequence is found by adding the two previous terms, like this:
1 + 4 = 5
4 + 5 = 9
5 + 9 = 14
9 + 14 = 23
14 + 23 = 37