Answer: -1.73 ft
Step-by-step explanation:
(-2.54 - 3.16 - 2.82 + 1.6) / 4 = -1.73
the average starting salary of graduates of a large university (lu) is $20,000 with a standard deviation of $8,000. furthermore, it is known that the starting salaries are normally distributed. if 189 of the graduates have salaries of at least $32,240, how many students graduated from this university?
Total students who graduated this year from this university is 3000.
This is a normal distribution problem with
Mean , μ = $20,000
Standard deviation, σ = $8,000
If 189 of the recent graduates have salaries of at least $32240.
Then, We first find the percentage of LU graduates with salaries more than $32240.
Required probability = P(x ≥ 32240)
We first normalize or standardize $32,240, then as we know,
z = (x - μ)/σ
= (32240 - 20000)/8000 = 1.53
The required probability:
P(x ≥ 32240) = P(z ≥ 1.53)
We'll use data from the normal probability table for these probabilities
P(x ≥ 32240) = P(z ≥ 1.53) = 1 - P(z < 1.53)
= 1 - 0.93699
= 0.06301
= 6.301%
So, 6.301% of the graduates this year = 189
Total Number of graduates this year = (189/0.06301) = 2999.5 = 3000 graduates this year.
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which of the following is not true of a chi squared test?(a) a chi-squared test can be used if one of the sample cells has a value of less than five
(b) the Chi-square test can be used to test how likely it is that an observed distribution is due to chance.
(c) a chi-square test can be used to analyze nominal data
(d) a chi-squared test can be used to test the probability of independence of a distribution of data
A) Chi-square test can be used if one of the samples has a value of less than five is the correct option.
Chi-square distribution and Chi-square test for independence:
A Chi-square distribution is the sum of squares of the standard normal deviates. The Chi-square test can be used for checking the association between categorical variables.The test can be used to decide whether the effect of one categorical data is dependent on the other variable or not on the basis of the critical value and p-value. The expected frequency of each categorical variable is calculated to compute the test statistic.The assumptions for the chi-square test are:
The frequency of each cell should be at least or more than 5.The variables should be categorical in nature and the observations should be independent of each other.Chi-square test can be used to analyze the nominal or categorical data. It can be used to test whether the observed data fits well with the expected frequency or not. It is used to test the independence of the data distribution by calculating probability.Hence, options (b), (c), and (d) are the assumptions that are true for chi-square test. Therefore, the options (b), (c), and (d) are considered incorrect.
The Chi-square test of independence can be used only if none of the frequencies of the sample cell is less than five.Hence, option (a), that is, “a Chi-square test can be used if one of the samples has a value of less than five” is the correct option.
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If f (x) = 2x2 + 4x − 3, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
The difference quotient for the given quadratic equation is:
d = (2h + 4x + 4)
How to get the difference quotient for f(x)?Here we have the quadratic function:
f(x)= 2x² + 4x - 3
And we want to get the difference quotient that is defined as:
d = ( f(x + h) - f(x))/(h)
Replacing our function there, we get:
d = ( 2(x + h)² + 4*(x + h) - 3 - (2x² + 4x - 3)/h
d = (2x² + 2h² + 4xh + 4x + 4h - 3 - 2x² - 4x + 3)/h
d = (2h² + 4xh + 4h)/h
d = (2h + 4x + 4)
That is the difference quotient.
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Please help me!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-24
Step-by-step explanation:
-3[-4(3-10)-12]/-2(-1)
-3[-4(-7)-12]/2
-3[28-12]/2
-3[16]/2
-48/2
-24
Hopes this helps
teacher: how can we change the base of a logarithm? student:
We can change the base formula by:
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
The change of base formula is used to change the base of a logarithm. We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.
The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.
Base Formula: -
The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.
Change of base formula
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
Change of Base Formula
Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:
logₐ b = [logₐ x] / [logₐ y]
In this formula,
The argument of the logarithm in the numerator is the same as the argument of the original logarithm.The argument of the logarithm in the denominator is the same as the base of the original logarithm.The bases of both logarithms of numerator and denominator should be the same and this base can be any positive number other than 1.Change of Base Formula Derivation
Change of base formula derivation can be understood from the following steps. Let us assume that
log ₐ b = p, logₙ a = q, and logₙ b = r.
By converting each of these into exponential form, we get,
a = [tex]b^{p}[/tex], a = [tex]x^{q}[/tex], and b = [tex]n^{r}[/tex]
From the first two equations,
[tex]x^{q}[/tex] = [tex]n^{r}[/tex]
Substituting b = [tex]n^{r}[/tex] (which is from third equation) here,
([tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex]
[tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex](Using a property of exponents)
p r = q
p = q / r
Substituting the values, we get,
logₐ b = [logₐ x] / [logₐ y]
For Example:
Evaluate the value of log₆₄ 8 using the change of base formula.
Solution:
We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.
log₆₄ 8 = [log 8] / [log 64]
= [log 8] / [log 82]
= [log 8] / [2 log 8] [∵ log am = m log a]
= 1 / 2
Answer: log₆₄ 8 = 1 / 2
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Select the correct answer.
Which graph represents this equation?
y − 4 = -3(x + 5)
A. The first graph
B. The second graph
C. The third graph
D. The last graph
( I know it is not the third graph)
Solve each equation.
9^(x+2)=2^(5x-4)
Value of x is 1.411
Given Eq.
[tex]9^{x+2} = 2^{5x-4} \\\\[/tex]
Applying exponent rules
[tex](x+2)ln(9) = (5x-4)ln(2)\\[/tex]
Solving for x
[tex]x = \frac{4ln(6)}{5ln(2)-2ln(3)}[/tex]
[tex]x = \frac{1.791}{5(0.693)-2(1.098)}[/tex]
[tex]x = \frac{1.791}{3.465-2.196} \\[/tex]
[tex]x = \frac{1.791}{1.269}[/tex]
[tex]x = 1.411[/tex]
Value of x is 1.411
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What is the measure of ZD in the parallelogram below?
Check the picture below.
what’s the question mark?
Answer:
? ≈ 5.01
Step-by-step explanation:
using the sine ratio in the right triangle
sin24.3° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2.06}{?}[/tex] ( multiply both sides by ? )
? × sin24.3° = 2.06 ( divide both sides by 24.3° )
? = [tex]\frac{2.06}{sin24.3}[/tex] ≈ 5.01 ( to 3 significant figures )
x varies inversely as the square of y. If x= 6 when y = 2, then the value of x when y = 8 will be
Answer: 24
Step-by-step explanation:
You can use proportions to calculate this:
[tex]\frac{6}{2} =\frac{x}{8} \\\\2x=6*8\\\\2x=48\\\\x=\frac{48}{2} =24[/tex]
Drag the numbers below to put them in order from least to greatest:
6.426.42 6.536.53 6.4976.497 6.66.6 6.4536.453 6.486.48
The numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.
What is number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that the numbers are,6.42,6.53,6.497,6.66,6.453,6.486.
Ascending order refers to a list of numbers that are arranged from least to greatest. The numbers are arranged in ascending order in this form. The first figure must be less than the second figure. It is referred to in descending order when the numbers are listed from greatest to least.
Thus, the numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.
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I need help ASAP!!!!!!!
Step-by-step explanation:
in that setup they will both explode after traveling the same distance.
A is just going faster and has to launch therefore a little bit later.
so, we need to make an equation based on distance traveled and find in that process the number of seconds needed to travel that distance.
speed is distance/time, so we need to multiply speed by time to get distance.
x = seconds for B
x - 0.25 = seconds for A
A is launched after B but explodes at the same time.
so, A's trip is of shorter time than B's trip.
(x - 0.25)×360 = x×320
360x - 90 = 320x
40x - 90 = 0
40x = 90
4x = 9
x = 9/4 = 2.25 seconds
both fireworks will explode 2.25 seconds after B launches (and 2.25 - 0.25 = 2 seconds after A launches).
the explosion will be at
320×2.25 = 360×2 = 720 feet height.
Every complex number can be written in the form a+bi. For the complex numbers 8-4i, identify the values of a and b
Answer:
C
Step-by-step explanation:
What is one over four to the fifth power?
one over one thousand twenty-four
one over six hundred twenty-five
five over twenty
six over nine
a baseball diamond is a square with side 90 feet. if a batter hits the ball and runs towards first base with a speed of 25 ft/sec, at what speed is his distance from second base decreasing when he is two thirds of the way to first base?
The rate when his distance from second base changes and it is two third of the way to first base is - 13.86 feet/s.
let us consider the following values
distance between batter to Second base = d feet
distance between batter to First base
= x feet
distance between first to second base
= 90 feet
Using the Pythagorean theorem:
d² = x² + 90²
Knowing that the velocity of the bat to first base is 25 ft/s,
the distance x can be written as: x
= 90 - 25t
The equation for is,d² = 90²+(90 -25t)²--(1)
we want to find the rate of change of d.
let it be d' and from implicit differentiation:
2d.d' = 2(90-24t) × (-25)
d' = -50(90 - 25t) / (2d)
d' = -25 (90 - 24t) / d ---(*)
We can determine t and d from the fact that the batter is two third to his first base: d = √90^2 + 60^2 = √1 = 108.2 feet
putting the values of d in (1) we get,
=> 90 - 25t = 60 => 25t = 30 => t = 6/5.
Substitute d' in the formula equation (*)
d' = -25 (90 - 24t) / d = -25(90-30)/108.2
d'= - 13.86
d' = - 13.86 feet/s
negative sign means decreasing distance from second base (as it approaches the first
bases, it approaches the second base).
Hence,The required speed is 13.86 feet/s
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Describe the transformations that map the
function y = 8* onto each function.
b) y = 84x
d) y = 8-2x
a) y = ( 1⁄2 8×18x
c) y = -8x
In the first function have vertical compression by 1/2, in second function have horizontal compresion by 1/4, in third compression have Vertical reflection and in fourth function have Horizontal reflection and horizontal compression by 1/2.
In the given question we have to find the transformations that map the function y = [tex]8^x[/tex] onto each function.
Since we have to find the transformation, so we know that in a transformation;
The transformation from the first equation to the second one can be found by finding a, h and k for each equation.
[tex]y=ab^{x-h}+k[/tex]
The horizontal is define by the value of h. The horizontal shift is defined as:
g(x)=f(x+h) - The graph is shifted to the left h units.
g(x)=f(x−h) - The graph is shifted to the right h units.
Horizontal Shift: None
The vertical shift define on the value of k. The vertical shift is defined as:
g(x)=f(x)+k - The graph is shifted up k units.
g(x)=f(x)−k - The graph is shifted down k units.
Vertical Shift: None
The value of a describes the vertical stretch or compression of the graph.
a>1 is a vertical stretch
0<a<1 is a vertical compression.
(a) The given first function is [tex](\frac{1}{2})8^{x}[/tex].
y = [tex]8^x[/tex]
Combine [tex]8^x[/tex] and 1/2.
y = [tex]8^x[/tex]/2
Assume that
y = [tex]8^x[/tex] is f(x)=[tex]8^x[/tex] and y= [tex](\frac{1}{2})8^{x}[/tex] is g(x)= [tex](\frac{1}{2})8^{x}[/tex].
On comparing the equation [tex]y=ab^{x-h}+k[/tex]
The value of a, h, and k for f(x)=[tex]8^x[/tex].
a=1, h=0, k=0
The value of a, h and k for g(x)=[tex](\frac{1}{2})8^{x}[/tex].
a=1/2, h=0, k=0
Since the value of h and k so tnere is no horizontal and vertical shift.
SInce the value of a changes from 1 to 1/2 and 1/2 is greater that 0 but less than 1 so there is vertical compression by 1/2.
(b) The given second function is [tex]8^{4x}[/tex].
y= [tex]8^{4x}[/tex] is g(x)= [tex]8^{4x}[/tex].
On comparing the equation [tex]y=ab^{x-h}+k[/tex]
The value of a, h and k for g(x)=[tex]8^{4x}[/tex].
a=1/4, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: None, Vertical Compression or Stretch: None, horizontal compresion by 1/4.
(c) The given third function is [tex]-8^{x}[/tex].
y= [tex]-8^{x}[/tex] is g(x)= [tex]-8^{x}[/tex].
The value of a, h and k for g(x)=[tex]-8^{x}[/tex].
a=-1, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.
Vertical reflection
(d) The given fourth function is [tex]8^{-2x}[/tex].
y= [tex]8^{-2x}[/tex] is g(x)= [tex]8^{-2x}[/tex].
The value of a, h and k for g(x)=[tex]8^{-2x}[/tex].
a=-1/2, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.
Horizontal reflection and horizontal compression by 1/2.
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aaliyah went into a grocery store and bought 5 peaches and 6 mangos, costing a total of $17.75. tristan went into the same grocery store and bought 2 peaches and 3 mangos, costing a total of $8. write a system of equations that could be used to determine the price of each peach and the price of each mango. define the variables that you use to write the system.
Answer:
Step-by-step explanation:
Define Variables:
Let p= the price of each peach
Let m=the price of each mango
One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:
5p+6m=17.75
Likewise, if 2 peaches and 3 mangos cost $8, then:
2p+3m=8
Write System of Equations:
5p+6m=17.75
2p+3m=8
System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.
Let p= the price of each peach
Let m=the price of each mango
One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:
5p+6m=17.75
Likewise, if 2 peaches and 3 mangoes cost $8, then:
2p+3m=8
System of Equations:
5p+6m=17.75
2p+3m=8
Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.
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PLEASE HELP I DONR UNDERSTAND DENSITY CURVES AT ALL
As per the given graph, the correct statement is option (A) The median of the density curve is 3.
Median:
Basically, median refers the middle value in a set of data.
And it can be obtained by organize and order the data from smallest to largest. And to find the midpoint value, divide the number of observations by two. And then if there are an odd number of observations, round that number up, and the value in that position is the median.
Given,
Here we have the graph.
Now, we have to identify in with of the option is correct according to the given graph.
While we looking into the given graph,
We have identified that it form the triangle and as the middle point as 3.
So, based on this fact me have identified that the median density of the curve is 3.
Therefore, the option (A) The median of the density curve is 3.
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-3/10 + 1 = 10 plsss
can anyone please help me? (pic attached)
Answer:
No, Eduardo made a mistake from Step 1 to Step 2. Eduardo should have subtracted 4 from 6 instead of evaluating the exponent. The order of operations says to perform all operations inside parentheses first.
a pole that is 3m tall casts a shadow that is 1.4m long. at the same time, a nearby tower casts a shadow that is 39.5m long. how tall is the tower? round your answer to the nearest meter.
The nearby tower that casts a shadow that is 39.5 m long is 85 m tall.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
The ratio of the shadow of a pole to its length is 1.4 m : 3 m.
At the same time, the ratio of the shadow of a tower to its length should also be equal to the ratio of the shadow of a pole to its length, which is 1.4 : 3.
Let x = length of the tower
Using proportion, determine the length of the tower by solving for x.
1.4 : 3 = 39.5 m : x
x = 39.5(3)/1.4
x = 84.64
Round off to the nearest meter.
length of the tower = 85 meters
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What is the value of (−13)4?
52
−52
28,561
−28,561
Yesterday was the first playoff game for the Culver City Cyclones baseball team. The
stadium's manager predicted attendance at the game would be 5,600 fans. Unfortunately, the
threat of a storm caused many to stay home, and his prediction wound up being 28% higher
than the actual attendance. What was the actual attendance at the baseball game?
The actual attendance at the baseball game is 7168 fans
What is meant by percentage?A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviations "pct," "pct," and occasionally "pc" are also used to represent percentage in addition to the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.
Given,
The actual attendance at the game=5600 fans
Also given that, the threat of a storm caused many to stay home, and his prediction wound up being 28% higher than the actual attendance.
Then,
28% of 5600
=5600×(28/100)
=1568
Total=5600+1568
Total=7168
Therefore, the actual attendance at the baseball game is 7168 fans.
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Answer:
4,375 fans
Step-by-step explanation:
percent error= amount of error/correct amount
1.28x=5600
1.28x/1.28= 5000/1.28
x=4375
PLEASE HELP ME I FEEL LIKE THIS SHOULD BE SUPER EASY BUT MY BRAIN CAN NOT RN
Answer:
x = 62
y = 41
Step-by-step explanation:
y + 21 = x
x + y + 77 = 180
2y+77 = 180
2y = 82
y = 41
x = 62
1) How long will it take for the population of a certain country to double if its annual growth rate is 2%? Round to the nearest year.
Answer:
For example, a population with a 2% annual growth would have a doubling time of 35 years.Mar 24, 2015
Step-by-step explanation:
pls check and see if i'm wrong
Answer:
I think you are right.Because im sure
What is the rectangular form of Θ = 3π/4?
x − y = 0
x − y = 1
x + y = 0
x + y = 1
The rectangular form of Θ = 3π/4 will be; y + x = 0.
What are Complex value?Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the Θ = 3π/4
Therefore, θ = tan⁻¹y/x = 3π/4
y/x = tan (3π/4)
Now multiply both side by x
yx/x = tan (3π/4) x
y = tan (3π/4) x
Thus, y = -x
in rectangular form y + x = 0
Hence, the rectangular form of Θ = 3π/4 will be; y + x = 0.
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On a straight road, Jorge is 7 kilometers east of Peter, Jason is
10 kilometers west of Juan, and Juan is 13 east of Peter. how
many miles is Jorge from Jason?
Answer:
7x10x13=910=910 kilograms
Step-by-step explanation:
Can anybody solve this for me?
Answer:
y = x + 6
Step-by-step explanation:
y = mx + c
2 = -4m + c
-2 = -8m + c
2 + 4m = c
-2 = -8m + 2 + 4m
-2 - 2 = -4m
-4 = -4m
-4/-4 = m
m = 1
2 + 4(1) = c
c = 6
y = x + 6
i need help with b helpppppppppppppppp plssssssssssssssssssssssssssssssss
The order of in which the operation in the expression 9 + 3·2² - 1·4, indicates;
3. (a) The value of the expression, 9 + 3·2² - 1·4 is 17
(b) The left and right side of the grouping symbol (the left side) should be placed between the number 3 and 2 and then (the right side should be placed between 1 and 4, so that we get;
9 + 3 × (2² - 1) × 4 = 45
What is the order of operations in mathematics?The order of operations is a rule or guide, that states the sequence in which the operations in an expression are to be performed.
3. The specified expression is; 9 + 3·2² - 1·4
(a) The value of the expression 9 + 3·2² - 1·4 can be found using the order of operation of PEMDAS, which stands for; operations from left to right, items in Parenthesis, then Exponents, followed by Multiplication, and Division first then Addition and Subtraction of the terms from left to right as follows;
Therefore;
9 + 3·2² - 1·4 = 9 + 3 × 4 - 1 × 4 = 9 + 12 - 4 = 17
The value of the expression, 9 + 3·2² - 1·4, is 17(b) A grouping symbol is the parenthesis.
The location of the parenthesis in the specified expression so that the value is 45 can be found as follows;
Placing the grouping symbol between 3 and 2 and the right parenthesis between 1 and 4, we get;
9 + 3·2² - 1·4 = 9 + 3·(2² - 1)·4 = 9 + 3 × (2² - 1) × 4
9 + 3 × (2² - 1) × 4 = 9 + 3 × (3) × 4 = 9 + 36 = 45
The location to place the grouping symbol so that the value of the expression is 45 is between 3 and 2 and between 1 and 4.
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