The die has 6 faces
[tex]\begin{gathered} \text{ In n number of throws, the number outcomes is given by 6}^n \\ ^{} \end{gathered}[/tex][tex]\begin{gathered} \text{ In 8 throws, the possible outcomes will be 6}^8 \\ =1679616 \end{gathered}[/tex]In an effort to cut costs and improve profits, many US companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted. What is the probability (as a decimal) that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years? Round to 4 decimal places
0.23% probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.
What is Central Limit Theorem ?
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean μ and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s.
The central limit theorem will be used to find the probability (as a decimal) that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.
Now we use the sampling distribution of the sample proportions, which have:
μ = p = 0.54
s = √{(p(1-p)/n)}
s = √{(0.54x0.46)/555)}
s = 0.0212
The probability is the p-value of Z when X = 0.48. So
Z = (X- μ)/σ
By the Central Limit Theorem
Z = (X- μ)/s
Z = (0.48-0.54)/ 0.0212
Z = -2.84, has a p-value of 0.0023.
0.0023 x 100% = 0.23%
This, 0.23% probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.
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The function g(c)=75-3.5c represents the amount of money remaining on a gift card after purchasing c number of ice cream cones how much does an ice cream cone cost
The price of an ice cream, as calculated with the help of given function is 3.5
What is function in mathematics?
A function is a relationship between a set of inputs and a set of permitted outputs, and it has the property that every input is connected with exactly one output. If every element in set A has one end and only one image in set B, then the mapping from set A to set B is merely a function. Choose any two non-empty sets for A & B.
In order to get price of 1 ice cream, we will first calculate the amount left after purchasing 2 ice creams and the amount left after purchasing 1 ice cream with the help of given function. then we will do subtraction to get the answer.
The amount left after purchasing 2 ice creams:
given function is: g(c)=75-3.5c
putting c = 2
g(2) = 75 - 3.5(2)
g(2) = 68
So, the amount left after purchasing 2 ice creams.
The amount left after purchasing 1 ice cream1:
given function is: g(c)=75-3.5c
putting c = 1
g(2) = 75 - 3.5(1)
g(2) = 71.5
So, the amount left after purchasing 1 ice cream.
Subtracting the amount left after purchasing 2 ice cream from the amount left after purchasing 1 ice cream.
71.5 - 68
= 3.5
Hence, the price of an ice cream is 3.5.
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PM Fri Feb 26oneAA47%b.socrative.comIdentify the coordinates for AABC after a 90 °rotation counter-clockwise about the origin.A) A'(6,-5), B'(4,-2), C'(4, -7)B) A'(-5, -6), B'(-2,-4), C'(-7,-4)C) A'(-6,5), B'(-4, 2), C (-4, 7)D) A'(5,0), B’(2,4), C'(7,4)
EXPLANATION
Given the triangle ABC,
We can see that after a rotation 90 degrees counter-clockwise about the origin, the new coordinates are:
A'=(-4,2) B= (-6,5) C=(-4,7)
07ess inWhich statement concerning the equation x2 + 2 = x is true?0 Its discriminant is 0, so it has one real solution.O Its discriminant is – 7, so it has two complex solutions.Its discriminant is -7, so its solutions are negative.-Its discriminant is 0, so it has no solution.
The given quadratic equation is;
[tex]x^2+2=x[/tex]This can be written properly as;
[tex]x^2-x+2=0[/tex]The discriminant is used to test for nature of roots of a quadratic equation and it is given by the equation;
[tex]D=b^2-4ac[/tex]From the given quadratic equation;
[tex]\begin{gathered} x^2-x+2=0 \\ a=1;b=-1,c=2 \end{gathered}[/tex]Thus, the discriminant will be;
[tex]\begin{gathered} D=b^2-4ac \\ D=(-1)^2-4(1)(2) \\ D=1-8 \\ D=-7 \end{gathered}[/tex]Since the discrimiant has a value(-7) less than zero(0), thus it has two(2) complex roots.
Hence, the correct option is option B
Simplify each exponential expression. (Do not add extra spaces in your response.)
9.) [tex]9^{2}[/tex] =
10.) 2power4 =
11.) (13)power2 =
12.) (−7)power2 =
13.) 4power3 =
14.) (−1)power5 =
15.) 4.52 =
16.) 10power5 =
Answer:A
Step-by-step explanation:
if 5 lb of oranges cost $11.55 how many would it cost for 12 lb of oranges
To solve this problem we can apply the rule of three, in our case
[tex]\begin{gathered} 5\rightarrow11.55 \\ 12\rightarrow x \end{gathered}[/tex]Then, 12 lb of oranges will cost
[tex]\frac{(12)(11.55)}{5}=\frac{138.6}{5}=27.72.[/tex]Therefore, 12 lb of orange will cost $27.72.
Please help i dont have as much time
Answer:
Step-by-step explanation
answer is f(x)=6x
how would solve for 2x – 17y = 13 for y
SOLUTIONS
To solve for y in 2x – 17y = 13
[tex]2x-17y=13[/tex]Make y the subject of formular
[tex]\begin{gathered} 2x-17y=13 \\ 2x-13=17y \end{gathered}[/tex]divide both side by 17
[tex]\begin{gathered} \frac{2x-13}{17}=\frac{17y}{17} \\ y=\frac{2x-13}{17} \end{gathered}[/tex]Therefore the value of y is
[tex]y=\frac{2x-13}{17}[/tex]A line passes through (1, 7) and (2, 10).
Which answer is the equation of the line?
The equation of the line is y - 10 = 3(x - 2)
What are linear equations?Linear equations are equations that have constant average rates of change.
How to determine the equation of the line?The given parameters are
Points (x, y) = (1, 7) and (2, 10)
Start by calculating the slope of the line using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (1, 7) and (2, 10)
So, we have
Slope = (10 - 7)/(2 - 1)
Evaluate
Slope = 3
A linear equation is represented as
y - y₁= slope * (x - x₁)
Where
(x₁, y₁) = (2, 10)
Substitute (x₁, y₁) = (2, 10) and Slope, m = 3 in the equation
So, we have
y - 10 = 3* (x - 2)
Evaluate
y - 10 = 3(x - 2)
Hence. the linear equation is y - 10 = 3* (x - 2)
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Consider the function f(x) =−5x−8 how do you find the following? B) The average rate of change between the points (a,f(a)) and (b,f(b)) . c) The average rate of change between the points (x,f(x)) and (x+h, f(x+h)).
The rate of change between a and b is -5, and between x and x + h is also -5.
How to find the rates of change?
For a function f(x) the formula for the rate of change on an interval [a, b] is:
( f(b) - f(a))/(b - a)
so if the function is f(x) = -5x - 8, the average rate of change will be:
( -5b - 8 + 5b + 8)/(b - a) = 5*(a - b)/(b - a) = -5
c) Now we want to use the interval [x, x + h], we will get:
( -5*(x + h) - 8 + 5*x + 8)/(x + h - x)
= (-5h)/h = -5
Again, the rate is -5
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Given -86=4+5(3x-3), what is the value of 3/5x ? Help meeee
To solve for the value of 3/5x, we can start by distributing.
-86 = 4 + 5(3x - 3) → -86 = 4 + 15x - 15
-86 = 15x - 11
Add 11 to both sides-86 = 15x - 11 → -75 = 15x
Divide both sides by the coefficient
-75 = 15x → -5 = x
Therefore, x = -5.
Plugging in -5 for x
To find the value of 3/5x, we can plug in -5 for x.
3/5(-5) = -3
Hence, the value of 3/5x is -3.
What are the 2 right angle measures? * 40 and 120 120 and 60 180 and 120 140 and 40
The two right angle measure is 120° and 60° and 140° and 40° .
In mathematics and trigonometry, a right angle is a quarter-turn or an angle that is exactly 90 degrees or π/2 radians . If a ray is positioned so that its terminal is in a line and they are equal, the adjacent angles represent right angles.
Orthogonality, which refers to the property of producing right angles, and perpendicular lines, which are defined as lines that intersect at right angles, are important and closely related geometrical concepts.
The existence of a feature resembling a right angle, which distinguishes right triangles, makes all right angles a fundamental notion in trigonometry.
We know that a right angle is equal to 90° .
Hence 2 right angles = 90° × 2 = 180°
Now we will use the options to check if they add up to 2 right angles or 180°
120° + 60° = 180°
140° + 40° = 180°
Therefore they are he required options that satisfy the given condition.
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Marcus needs a grade higher than 88 on his quiz for an A. Which inequality represents this?
this is:
grade = g, so
[tex]g>88[/tex]A process for which its result is well defined is called a/an _____________.experimentprocesssample spaceevent
In any experiment, all the possible out comes are well defined. So,
A process for which its result is well defined is called a/an experiment.
Answer: Experiment
8-1.2.41 Graph the equation and find the y-intercept AY 10- y = 5x - 2 - o Use the graphing tool to graph the equation 6- Click to enlarge graph 2- -10 8 -5 4 2 2 4 6 10 -2- -6- -8-
From the equation of the line, the y-intercept is the point (0, -2) and its slope is m = 5
To graph this line, first, we need to find the point (0, -2), and then we need to find another point of the line, we can do that with the help of the slope, as follows:
(0+1, -2+5) = (1, 3)
Next, we have to connect these two points
3. What should be done first to simplify: 16 - 8 • 4 8.2
In that case we must perform the division (16÷8) before multiplication as the rules says that we must work from left to right in case of only having multiplications and divisions.
So the answer is the first option.
D. AABC AD EF by AAS B E What makes this true? F A с ABS DE ZCE ZF AC = DF
You need to know what makes that
triangle ABC being similar to triangle DEF by A (angle) A (Angle) S (side)
It means that triangle DEF needs to have two similar angles with ABC and one similar angle with ABC that side has to be the non-included side:
Then:
The non-include side in:
ABC are BC and AC
DEF are DF adn EF
To make
[tex]\Delta ABC\cong\Delta DEF\text{ by AAS}[/tex]You need:
[tex]AC\cong DF[/tex]I need help with this practice problem with that is from trigonometry prep book
Answer:
[tex]cos(\alpha-\beta)=-0.9691[/tex]Explanation: The diagram of the alpha and the beta angles is as follows:
the angles are as follows:
[tex]\begin{gathered} \arctan (-\frac{12}{5})=-67.38^{\circ}\Rightarrow\alpha=180+(-67.38^{\circ})=112.62^{\circ} \\ \alpha=112.62^{\circ} \\ \arccos (\frac{3}{5})\Rightarrow arc\cos (0.6)=53.1^{\circ} \\ \beta=360^{\circ}-53.1^{\circ}=306.9^{\circ} \\ \beta=306.9^{\circ} \\ \therefore\Rightarrow \\ cos(\alpha-\beta)=\cos (112.62^{\circ}-306.9^{\circ}) \\ \cos (-194.28^{\circ})=-0.9691 \end{gathered}[/tex]Therefore the answer is:
[tex]cos(\alpha-\beta)=-0.9691[/tex]Enter the degree of the polynomial below.5x^5 + 8x^2 + 2x - 3x^9 - 8x^4 - 4x^5A. 8B. 9C. 6D. 5
By definition, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients.
In this case, the monomial with the highest degree is
[tex]-3x^9[/tex]Then, the degree of the polynomial is 9 and the correct answer is B. 9.
solve the simultaneous equation:
y=1/2x
3y=x-2
If y=1/2x and 3y=x-2 then value of x is -4 and y is -2.
What is Equation?Two or more expressions with an equal sign is called as Equation.
y=1/2 x...(1)
3y=x-2 ...(2)
Multiply equation (1) with 3
3y=3/2x
Now subtract the above equation from 2
3y-3y=x-2-3x/2
Take 2 as LCM on right hand side.
0=2x-4-3x
Add common terms
0=-x-4
Add x on both sides
x=-4
Now substitute value of x in 1 to get value of y
y=1/2(-4)
y=-2
Hence value of x is -4 and value of y is -2.
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A gardener plants three different sapling at East Green Central Park. The number of magnolia saplings he planted was 3 less than crab apples saplings. The Kwanzan cherry sapling planted amounted to twice the number of magnolia. Is 35 saplings were planned in all, how many Kwanzan cherry sapling he planted?
16 number of Kwanzan cherry saplings he planted.
Let the gardener plant the no of Crab apple saplings was x
Since the no of magnolia in saplings he planted was 3 less than crab apple saplings.
Therefore, the no. of magnolia Saplings planted was x-3
Also, the Kwanzan Cherry sapling planted amounted to twice the number of magnolia.
Therefore, the Kwanzan Cherry sapling was. planted by him 2(x-3)
Conditionally,
x+(x-3)+2(x-3) = 35
= x+x-3 +2x-6 = 35
4x = 44
x = 11
Hence the no. of kwanzan Cherry sapling. he planted was
=2(11-3).
2x8 = 16
What is sampling?Sampling means choosing a group from which you will collect data in your research. For example, if you are researching the opinions of students at your university, you can study a sample of 100 students. In statistics, sampling allows testing a hypothesis about the characteristics of a population. There are two types of sampling methods: Probability sampling involves random selection that allows strong statistical inferences to be made about the entire group.Non-probability sampling involves non-random selection based on convenience or other criteria that allow you to easily collect data.To learn more about sampling, refer;
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Mr Smith wants to put fence around his yard. the dimensions of the yard are 65ft by 32ft . the fencing is sold in whole meters. how much should he buy? round to the nearest meter
To determine how much fence is needed to fence the yard, you have to calculate the perimeter of the yard.
The yard is rectangular with dimensions 65ft by 32ft. To calculate the perimeter you have to add twice the length and twice the width:
[tex]\begin{gathered} P=2l+2w \\ P=2\cdot65+2\cdot32 \\ P=130+64 \\ P=194ft \end{gathered}[/tex]The perimeter of the yard is 194ft.
Next, you have to express the perimeter in meters to determine how much fence he must buy.
1foot = 0.3048meters
To express the result in meters you have to multiply it by 0.3048:
[tex]194\cdot0.3048=59.1312m[/tex]The perimeter of the yard is 59.13 meters, round it to the next whole number, so he needs to buy 60 meters of fence.
Answer:
The perimeter of the yard is 59.13 meters, round it to the next whole number, so he needs to buy 60 meters of fence.
Step-by-step explanation:
The 7 students in Mr. Campbell's class were asked how many minutes it takes them to get to school in the morning. Here is what they answered:11, 8, 11, 8, 7, 9, 4Find the median and mean travel times for these students.If necessary, round your answers to the nearest tenth. median:mean:
Given:
The data set = 11, 8, 11, 8, 7, 9, 4.
The number of the data =7.
Aim:
We need to find the mean and median of the given data set.
To find:
We know that
[tex]\text{Mean}=\frac{The\text{ sum of the data}}{the\text{ number of the data in the set}}[/tex]Substitute known values.
[tex]\text{Mean}=\frac{11+8+11+8+7+9+4}{7}[/tex][tex]\text{Mean}=8.3[/tex]Rewrite the given data in terms from least to greatest.
4, 7, 8, 8, 9, 11, 11
We know that the median is the middle term of the data set.
The median = 4th term
[tex]\text{Median =8}[/tex]Final answer:
[tex]\text{Median =8}[/tex]
[tex]\text{Mean}=8.3[/tex]
Drag numbers to the line to complete the solution to the equation.
HELP PLEASEE
When solving the quadratic equation x² + 4x + 3 = 0 we get:
x = -1 and x = -3 .
What is completing the squares?In mathematics, completing the square is a method for converting a quadratic expression of the form ax² + bx + c to the vertex form ,a(x + m)² + n.
The most common application of this method is to solve a quadratic equation by rearranging the expression obtained after completing the square: a(x + m)² + n, so that the left side is a perfect square trinomial.Here given an equation,
x² + 4x + 3 = 0
(x² + 4x +4) + (-4 + 3) =0
(x² + 4x + 4 ) = 1
(x + 2)² = 1
x + 2 = ±√1
x + 2 = ± 1
x + 1 = 0
x + 3 = 0
x = -1
x = -3
The answers are underlined.
By solving the equation x² + 4x + 3 = 0 we get x = -1 and x = -3.
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PLEASSEEE HELPP
Find the coordinates of the image of point A(3, –9) after a rotation of 90 degrees clockwise about the origin.
(–3, 9)
(9, 3)
(–9, –3)
(3, 9)
Answer:
B
explanation
I just did it on a paper
Answer:
See below
Step-by-step explanation:
(x,y) which is (3, -9) will change to ( y, -x ) = ( -9,-3)
which is an equivalent ratii to 6/7
Let:
[tex]\begin{gathered} k=constant_{\text{ }}of_{\text{ }}proportionality \\ k\in\N \end{gathered}[/tex][tex]\begin{gathered} 6\colon7=\frac{6}{7} \\ let \\ k=2 \\ \frac{6}{7}\equiv\frac{k}{k}\times\frac{6}{7}=\frac{2}{2}\times\frac{6}{7}=\frac{12}{14} \\ so\colon \\ \frac{6}{7}\equiv\frac{12}{14} \end{gathered}[/tex][tex]\begin{gathered} 9\colon5=\frac{9}{5} \\ let \\ k=3 \\ \frac{9}{5}\equiv\frac{k}{k}\times\frac{9}{5}=\frac{3}{3}\times\frac{9}{5}=\frac{27}{15} \\ so\colon \\ \frac{9}{5}\equiv\frac{27}{15} \end{gathered}[/tex]Rectangular prism has a length of 8½ inches, a
width of 4.25 inches and a height of 3 %. What is the volume in cubic
inches? Round to the nearest hundreths. (V = Bh or V = lwh
Volume of rectangular prism with length 8.5 inch , width 4.25 and
height 3 inch is :
108.38 cubic inches
What is the volume of rectangular prism?A rectangular prism is a 3-dimensional solid shape with six faces, all of which are rectangles. Right rectangular prisms and non-right (oblique) rectangular prisms are the two types of rectangular prisms.To calculate the volume of a rectangular prism, multiply its three dimensions: length, width, and height. Volume is measured in cubic units.
Volume = l x w x h
Here given,
l = 8 .5 inch
w = 4.25 inch
h = 3 inch
To find volume ,
Volume = l x w x h
= 8.5 x 4.25 x 3
= 108.375 cubic inches
= 108 .38 cubic inches
So the volume of rectangular prism is 108 .38 cubic inches .
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find the slipe of 3,9 and 1,12
The slope of the line that passes through 3, 9 and 1, 12 is -3/2
How to calculate the slope of the line?From the question, the points are given as
3, 9 and 1, 12
Rewrite the above points properly
So, we have the following ordered pairs
(3, 9) and (1, 12)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (3, 9) and (1, 12)
Substitute the known values in the above equation
So, we have the following equation
Slope = (12 - 9)/(1 - 3)
Evaluate
Slope = -3/2
Hence, the slope of the line is -3/2
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Approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. (Enter your answers as a comma-separated list.)
A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).
An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.
Our function starts increasing, and approximately at x = 2, it starts decreasing, which means this is a relative maximum point, and this is also the greatest possible value for our function, therefore, this is also an absolute maximum. There are no further critical points.
Q = p^2 - r / t for p
The equation solved for the variable p is p = √Qt + r
What is subject of formula?A subject of formula can simply be defined as the variable in an equation or given expression that is being worked out.
The subject is mostly made to stand on its own on one end of the equality sign.
It is also described as the variable mathematical written in terms of other variables found in an equation or expression.
Given the expression;
Q = p^2 - r / t
To solve for , we take the following steps
cross multiply
p^2 - r = Qt
Now, collect the variable 'r' over the equality sign, we have;
p² = Qt + r
Now, to make 'p' stand alone, find the square root of both sides
√p² = √Qt + r
p = √Qt + r
Hence, the expression is p = √Qt + r
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