We have a sample of size n=250. They are normally distributed with mean 88 and standard deviation of 15.
We have to find how many values from the sample are expected to be below 78.
We can calculate the z-score for 78 as:
[tex]z=\frac{X-\mu}{\sigma}=\frac{78-88}{15}=-\frac{10}{15}=-\frac{2}{3}\approx-0.67[/tex]Then, we can calculate the percentage of values below 78 as the probability P(z<-0.67):
[tex]P(X<78)=P(z<-0.67)=0.25249\approx25\%[/tex]This percentage is independent of the sample size: it is the same percentage for 100 numbers, 250 numbers or 1000 numbers.
For 250, 63 numbers are expected to be below 78, as 0.25*250=63 approximately.
Answer: 25%
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)
Please help i dont have as much time
Answer:
Step-by-step explanation
answer is f(x)=6x
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:
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
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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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]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)
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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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.
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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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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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]Graph JKL and its image after a reflection in the line x=-1
J(2,-1)
K (4,-5)
L (3,1)
The image after a reflection in the line x = -1 exists J(2, -1), K (4, -5) and L (3, 1) then of the reflection exists J' = (2, -1), K' = (4, -5) and L' = (3, 1).
What is meant by reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure exists said to reflect the other figure when they exists all equally spaced apart from one another.
When a shape exists reflected, it must be reflected across a line.
The coordinates are given as:
J(2,-1), K (4,-5) and L (3,1)
The rule of reflection across the y-axis exists:
(x, y) [tex]$\rightarrow[/tex](-x, y)
So, the image of the reflection exists:
J' = (2, -1)
K' = (4, -5)
L' = (3, 1)
Therefore, the reflection exists J' = (2, -1), K' = (4, -5) and L' = (3, 1).
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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.
Simplify (c3d2)4.
cd24
c12d8
c7d12
c7d6
By algebra properties, the simplified form of (c³ · d²)⁴ is equal to c¹² · d⁸. (Correct choice: B)
How to simplify an algebraic expression
In this problem we find the power of the product of two powers whose variables are c and d and which must be simplified by using algebra properties. The complete procedure is shown below:
(c³ · d²)⁴ Given(c³)⁴ · (d²)⁴ Power of a productc¹² · d⁸ Power of a power / Definition of multiplication / ResultThe simplified form of the algebraic expression is c¹² · d⁸.
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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:
Use the drawing tools to form the correct answer on the provided grid. For the sequence (1,4,7, 10, ...), the index starts at 1. Graph the function f(n) on the coordinate plane, where f is a function that describes the sequence. Graph as much of the sequence as will fit on the grid.
Given
The sequence (1,4,7,10,...).
To graph the function f(n) on the coordinate plane, where f is a function that describes the sequence.
Explanation:
It is given that,
The sequence is, (1,4,7,10,...).
Since, the given sequence is an arithmetic sequence.
Then,
The first term of the sequence is 1.
The common
Solve.
Separate your answers with a comma, and please write fractions in reduced form, no decimals.
8|6x−6|=24
The value of x in reduced fraction form is 3/2.
A fraction is a value written in the form of a quotient which has an upper number called numerator and lower called denominator. It represents a part of a whole.
8|6x−6|=24 (given equation)
|6x-6| = 24/8
|6x-6| = 3
6x = 3+6
6x = 9
x = 9/6 ( To reduce divide both the terms with 3 that is a common factor)
x = 3/2
Therefore, we can conclude that the value of x in reduced fraction is 3/2.
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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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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
out of 1,000 plants, some were given a new fertilizer and the rest were given no fertilizer. Some of the plants lived and some of them died, as shown in the table above
which of the following statements is supported by the data?
A.fertilized plants died at a higher rate than unfertilized rate than unfertilozed plants did
B.fertilized plants qnd unfertilized plants died at the same rate
C. fertilized plants died at a lower rate than unfertilized plants died
D.None of the above statements can be supported by the data
The correct statement that supports the given data is; B: fertilized plants and unfertilized plants died at the same rate
How to find the death rate?Death rate is defined as the total number of deaths during a given time interval.
Now, we are given the following;
Total Number of Plants = 1000 plants
Total number of fertilized plants that lived = 200
Total number of fertilized plants that Died = 50
Total number of unfertilized plants that lived = 600
Total number of unfertilized plants that died = 150
Now, from the above it means that;
Death rate of fertilized plants = 50/250 = 0.2
Death rate of unfertilized plants = 150/750 = 0.2
Survival rate of fertilized plants = 200/250 = 0.8
Survival rate of unfertilized plants = 600/750 = 0.8
The death rates in both cases are equal
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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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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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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]
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
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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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]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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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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