Answer:
Step-by-step explanation:
a. What test is appropriate for this analysis?
A Chi-square test of independence is appropriate for this analysis because it is used to compare two variables or testing relationship on categorical variables.
b. State the null hypothesis:
The null hypothesis is the default hypothesis
[tex]\mathtt{H_o:}[/tex] There is no particular preference for any brand of toothpaste among students.
c. State the alternative hypothesis:
The alternative hypothesis is the research hypothesis which comes in place to challenge the validity of the null hypothesis.
[tex]\mathtt{H_a:}[/tex] There is particular preference for brands of toothpaste among students.
d. Find the critical value:
degree of freedom = n-1
degree of freedom = 3 - 1
degree of freedom = 2
At the level of significance ∝ = 0.05
The confidence interval = 0.95 and degree of freedom = 2, the critical value from the chi-square distribution table = 5.991
e. Calculate the test statistic:
Using the chi square test statistics; we have the following:
Crest Colgate Aquafresh Total
24 13 8 45
Since we have three brands. Then, for each brand, the expected value
= Total /3
= 45/3
=15
Thus:
Chi -square [tex]\mathtt{X^2 = \dfrac{(observed \ value - expected \ value)^2}{expected \ value}}[/tex]
[tex]\mathtt{X^2 = \dfrac{(24 - 15)^2}{15} + \dfrac{(13 - 15)^2}{15} + \dfrac{(8 - 15)^2}{15} }[/tex]
[tex]\mathtt{X^2 = \dfrac{81}{15} + \dfrac{4}{15} + \dfrac{49}{15} }[/tex]
[tex]\mathtt{X^2 = \dfrac{81+4+49}{15}}[/tex]
[tex]\mathtt{X^2 = \dfrac{134}{15}}[/tex]
[tex]\mathtt{X^2 =8.93 }[/tex]
f. Make a decision:
Since the chi-square value is greater than the critical value , we reject the null hypothesis and conclude that the students have particular preference for brands of toothpaste.
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?
Answer:
federal loans = $29,000
private loans = $14,000
Step-by-step explanation:
x + y = 43000
.045x + .02y = 1585
x = 29,000
y = 14,000
Answer:
Amount of loan from federal : $ 29,000
Amount of loan from private bank : $ 14,000
Step-by-step explanation:
We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.
If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -
x + y = 43,000
At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -
0.045x + 0.02y = 1585
Let's solve the following system for x and y, the amount of each loan,
[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )
[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )
[tex]1935-0.025y=1585[/tex],
[tex]1935000-25y=1585000[/tex],
[tex]-25y=-350000[/tex],
[tex]y=14000[/tex],
[tex]x=29000[/tex]
Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.
The manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2. The manufacturer also has fixed costs each month of $8,000.
Answer:
C(x)=1.2x+8,000.
Step-by-step explanation:
C(x)=cost per unit⋅x+fixed costs.
The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by
In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.
Suppose that you have to sell [x] number of bars to make profits. So, we can write -
{2x} - {1.20x} > {8000}
0.8x > 8000
8x > 80000
x > 10000
Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
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5.39 jings =15.4 hings
4.9 hings = 2.8 gings
According to the conversion rates above, how
many jings equal 1 ging?
E. 7/40
F. 5/8
G. 49/80
H. 20/7
Step-by-step explanation:
It is given that,
5.39 jings =15.4 hings ....(1)
4.9 hings = 2.8 gings ...(2)
From equation (2), the value of 1 ging is :
[tex]1\ \text{ging} = \dfrac{4.9}{2.8}\ \text{hing}\ .....(3)[/tex]
From equation (1), the value of 1 jing is :
[tex]1\ \text{jing} = \dfrac{15.4}{5.39}\ \text{hing}\ .....(4)[/tex]
From equation (3) and (4), we get :
[tex]\dfrac{\text{1 ging}}{\text{1 jing}}=\dfrac{4.9}{2.8}\times \dfrac{5.39}{15.4}\\\\\dfrac{\text{1 ging}}{\text{1 jing}}=\dfrac{49}{80} \\\\1\ \text{ging}=\dfrac{49}{80}\ \text{ jings}[/tex]
Hence, the correct option is (g) "49/80"
If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
14. Twice the sum of a number and eight
Answer: 2(x + 8) is the expression.
Use distributive property to simplify,
2x+16
I didn't know which answer you wanted so....
Answer:
2(x + 8)
Step-by-step explanation:
Hello!
Twice the sum means we multiply by 2
2
the sum of a number and eight is x + 8
2 * x + 8
Since we have to twice the sum we put x + 8 in parenthesis to show to do that first
2(x + 8)
Hope this Helps!
how many pounds are in 2 tons 1,760 ounces
Answer:
4110
Step-by-step explanation:
One ton is equal to 2000 pounds and one ounce is equal to 0.0625 pounds.
2 tons*2000 lbs per ton = 4000 lbs
1760 ounces*0.0625 lebs per ounce = 110 lbs
4000+110=4110 lbs
A study collects samples of water from the tap in Vacaville and from bottled water available from the Nugget stores and samples their pH levels. The results are in the table below. I find a bottle marked #13 but cannot read the label for the type of water. He measures the pH and gets 6.32. What type of water do you think it is?
Answer:
see below
Step-by-step explanation:
the observed ph is 6.32
the mean pH of Tap water is shown below
sum of observations
Mean (Tap) = -----------------------------------
number of observations
(7.24 +7.05 +7.07 +6.6 +7.28 +7.29 +7.05 +6.7 +7.16 +7.07 +7.12 +6.56
= ---------------------------------------------------------------------------------------------------------
12
= 7.016
then mean pH of bottle water is shown below
sum of observations
Mean (Bottles) = -----------------------------------
number of observations
(5.35 + 5.29 + 5.46 + 5.4 + 5.95 + 6.22 + 5.43 +5.48 +6.06 +5.33 +5.46 +5.41)
= --------------------------------------------------------------------------------------------------------------
12
= 5.57
theoretically.. the higher the pH values should be between 0 to 14.
based from the above results, the mean tap water has an average of 7.016 and by looking at the pH chart... its a neutral or pure water.
while the average pH Bottles has 5.57, this means its more acidic water, or by looking at the pH chart its an acid rain water.
a 6.32pH is below pure water, based on the chart looks like a urine/saliva.
What is the volume of a cube with a side length of
of a unit?
Solve for y.
-1 = 8+3y
Simplify you answer as much as possible.
Answer:
-3
Step-by-step explanation:
[tex]8+3y = -1\\3y = -9\\y = -3[/tex]
Answer:
y = -3
Step-by-step explanation:
-1=3y+8
3y+8=-1
3y=-9
y=-3
What is 5 feet and 11 inches in inches
Answer:
60
Step-by-step explanation:
5 is 60 inch
h(x) = x2 + 1 k(x) = x – 2
Evaluate 3h(2) + 2k(3) =
Answer:
17
Step-by-step explanation:
[tex]h(x) =x^2 +1\\k(x)=x-2\\\\3h(2)+2k(3)\\\\h(2)= ?\\k(3)=?\\\\h(2) = (2)^2 +1\\= 4+1\\h(2)=5\\\\\\k(3)= 3-2\\k(3) = 1\\\\3h(2) +2k(3)\\\\= 3(5)+2(1)\\=15+2\\3h(2)+2k(3) = 17[/tex]
5, 9, and 17
Step-by-step explanation:
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
write a thirdthird-degree polynomial expression that has only two terms with a leading term that has a coefficient of five and a constant of negative two
Answer:
5x^3-2
[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]
Explanation:
The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.
We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.
The coefficient is the number to the left of the variable.
The degree is the largest exponent, which helps form the leading term.
The third degree polynomial written above is considered a cubic binomial. "Cubic" refers to the third degree, while "binomial" means there are 2 terms.
We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.
Jilk Inc.'s contribution margin ratio is 62% and its fixed monthly expenses are $45,000. Assuming that the fixed monthly expenses do not change, what is the best estimate of the company's net operating income in a month when sales are $132,000?
Answer: $ 36,840.
Step-by-step explanation:
contribution margin=62% =0.62
fixed monthly expenses = $45,000
Sales = $132,000
We assume that the fixed monthly expenses do not change.
Then, company's net operating income = (contribution margin×Sales )-fixed monthly expenses
=$( (0.62×132000)-45000 )
= $ (81840-45000)
= $ 36,840
Hence, the best estimate of the company's net operating income in a month when sales are $132,000 is $ 36,840.
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
Step-by-step explanation:
formula of area for square:
A=s^2
s=6
A=6^2
A=36
Answer:
36
Step-by-step explanation:
I got it right
what are the steps required to determine the equation of a quadratic function given its zeros and a point?
Answer:
Below
Step-by-step explanation:
The quadratic equations form is:
● ax^2+bx+c
Using the zeroes, we can write a factored form.
● a (x-x') (x-x")
x and x' are the zeroes
■■■■■■■■■■■■■■■■■■■■■■■■■■
●y = a (x-x') (x-x")
x' and x" are khown but a is not.
We are given a point so replace x and y with its coordinates to find a.
So the steps are:
● 1) Write the factored form of the quadratic equation
● 2) replace x' and x" with their values.
● 3) replace x and y with the coordinates of a khwon point.
● 4) solve the equation for a.
The steps are write the factored form of the quadratic equation then, replace x' and x" with their values. To replace x and y with the coordinates of a known point. To solve the equation for a.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Using the zeroes, we can write a factored form;
a (x-x') (x-x")
x and x' are the zeroes
y = a (x-x') (x-x")
x' and x" are known but a is not.
We are given a point so replace x and y with their coordinates to find a.
So the steps are:
1) Write the factored form of the quadratic equation
2) To replace x' and x" with their values.
3) To replace x and y with the coordinates of a known point.
4) To solve the equation for a.
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A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation 1 lb and 0.5 lb, respectively. What percent of filled boxes weighing between 104 lb and 106 lb are to be expected?
a. 67%
b. None
c. 37%
d. 57%
Answer:
Option b. None is the correct option.
The Answer is 63%
Step-by-step explanation:
To solve for this question, we would be using the z score formula
The formula for calculating a z-score is given as:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We have boxes X and Y. So we will be combining both boxes
Mean of X = 100 lb
Mean of Y = 5 lb
Total mean = 100 + 5 = 105lb
Standard deviation for X = 1 lb
Standard deviation for Y = 0.5 lb
Remember Variance = Standard deviation ²
Variance for X = 1lb² = 1
Variance for Y = 0.5² = 0.25
Total variance = 1 + 0.25 = 1.25
Total standard deviation = √Total variance
= √1.25
Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,
For 104lb
z = (x-μ)/σ,
z = 104 - 105 / √25
z = -0.89443
Using z score table ,
P( x = z)
P ( x = 104) = P( z = -0.89443) = 0.18555
For 1061b
z = (x-μ)/σ,
z = 106 - 105 / √25
z = 0.89443
Using z score table ,
P( x = z)
P ( x = 106) = P( z = 0.89443) = 0.81445
P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555
= 0.6289
Converting to percentage, we have :
0.6289 × 100 = 62.89%
Approximately = 63 %
Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%
Since there is no 63% in the option, the correct answer is Option b. None.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be
Then the Variance will be
[tex]Var = \sigma ^2[/tex]
Then for X, we have
[tex]Var (X) = 1^2 = 1[/tex]
Then for Y, we have
[tex]Var (Y) = 0.5^2 = 0.25[/tex]
Then the total variance will be
[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]
The total standard deviation will be
[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]
For 104 lb, then
[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]
For 106 lb, then
[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]
Then
[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]
Approximately, 63%.
More about the normal distribution link is given below.
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A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t
The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
(a^8)3/2 in simplest form
Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
a company should stop making a part internally and buy externally when
Answer:
Make-or-Buy Decision
Step-by-step explanation:
What is the error in this problem
Answer:
12). LM = 37.1 units
13). c = 4.6 mi
Step-by-step explanation:
12). LM² = 23² + 20² - 2(23)(20)cos(119)°
LM² = 529 + 400 - 920cos(119)°
LM² = 929 - 920cos(119)°
LM = [tex]\sqrt{929+446.03}[/tex]
= [tex]\sqrt{1375.03}[/tex]
= 37.08
≈ 37.1 units
13). c² = 5.4² + 3.6² - 2(5.4)(3.6)cos(58)°
c² = 29.16 + 12.96 - 38.88cos(58)°
c² = 42.12 - 38.88cos(58)°
c = [tex]\sqrt{42.12-20.603}[/tex]
c = [tex]\sqrt{21.517}[/tex]
c = 4.6386
c ≈ 4.6 mi
If f(x) = 2x2 – 3x – 1, then f(-1)=
The value of function at x= -1 is f(-1) = 4.
We have the function as
f(x) = 2x² - 3x -1
To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:
f(-1) = 2(-1)² - 3(-1) - 1
= 2(1) + 3 - 1
= 2 + 3 - 1
= 4.
Therefore, the value of function at x= -1 is f(-1) = 4.
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Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Answer:
(5x³+3x²-5x+4) + (8x³-5x²+8x+9)
= 5x³+3x²-5x+4 +8x³-5x²+8x+9
= 5x³+8x³+3x²-5x²-5x+8x+4+9
= 13x³-2x²+3x+13
Hope this helps
if u have question let me know in comments ^_^
F
19) The points (6,5), (7,2), (9,6), and (10,3) are vertices of an inscribed square.
A)(x - 8)2-(y - 4)2 = 5
B) (x – 8)2 + (y - 4)2 = 15
C) (X + 8)2 + (y + 4)2 = 5
D) (x - 8)2 + (y - 4)2 = 5
Find an equation for the circle
Answer:
The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]
(D) is correct option.
Step-by-step explanation:
Given that,
Points (6,5), (7,2), (9,6) and (10,3) are vertices of an inscribed square.
We need to calculate the distance between (7,2) and (9,6)
Using formula of distance
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Put the value into the formula
[tex]d^2=(9-7)^2+(6-2)^2[/tex]
[tex]d^2=20\ m[/tex]
The radius will be
[tex]r^2=\dfrac{20}{4}[/tex]
[tex]r^2=5[/tex]
We need to calculate the center of the point (7,2) and (9,6)
Using formula of center point
For x axis,
[tex]h=\dfrac{x_{2}+x_{1}}{2}[/tex]
Put the value into the formula
[tex]h=\dfrac{9+7}{2}[/tex]
[tex]h=\dfrac{16}{2}[/tex]
[tex]h=8[/tex]
For y axis,
[tex]k=\dfrac{y_{2}+y_{1}}{2}[/tex]
Put the value into the formula
[tex]k=\dfrac{6+2}{2}[/tex]
[tex]k=\dfrac{8}{2}[/tex]
[tex]k=4[/tex]
We need to find the equation for the circle
Using formula of equation of circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Put the value into the formula
[tex](x-8)^2+(y-4)^2=5[/tex]
Hence, The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]
(D) is correct option.
Which of the following is NOT a property of a paralleogram? * The opposite sides are equal. The opposite angles are equal. Each diagonal bisects the parallogram. The diagonals of all parallograms bisect each other at 90 degree angles. I will give brainliest
Answer:
The diagonals of all parallelograms do not bisect each other at 90 degree angles.
Step-by-step explanation:
Which of the following is the solution to the inequality below? -5x — 10 -6 B. x > -2 C. x <-6 D. x < -2
Answer:
x > -6
Step-by-step explanation:
-5x — 10 < 20
Add 10 to each side
-5x — 10+10 < 20+10
-5x < 30
Divide each side by -5, remembering to flip the inequality
-5x/-5 > 30/-5
x > -6
Answer:
x>-6Step-by-step explanation:
[tex]-5x - 10 < 20\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\\\-5x-10+10<20+10\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-5x\right)\left(-1\right)>30\left(-1\right)\\\\\mathrm{Simplify}\\\\5x>-30\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x}{5}>\frac{-30}{5}\\\\x>-6[/tex]
Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide
Answer:
150,000
Step-by-step explanation:
1 m = 100 cm
260 m = 260 * 100 cm = 26000 cm
15 m = 15 * 100 cm = 1500 cm
area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2
area of 1 tile = 26 cm + 10 cm = 260 cm^2
number of tiles needed = 39,000,000/260 = 150,000
Answer: 150,000 tiles
According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?
Answer:
The probability is [tex]P(X > x ) = 0.19215[/tex]
Step-by-step explanation:
From the question we are told that
Th The population mean [tex]\mu = \$ 1,999[/tex]
The standard deviation is [tex]\sigma = \$ 574[/tex]
The values considered is [tex]x = \$ 2,500[/tex]
Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as
[tex]P(X > x ) = P(\frac{ X - \mu}{\sigma } > \frac{ x - \mu}{\sigma } )[/tex]
Generally
[tex]X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > x ) = P(Z > \frac{ x - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X > 2500 ) = P(Z > \frac{ 2500 - 1999}{574 } )[/tex]
[tex]P(X > 2500 ) = P(Z >0.87 )[/tex]
From the normal distribution table the value of [tex]P(Z >0.87 )[/tex] is
[tex]P(Z >0.87 ) = 0.19215[/tex]
Thus
[tex]P(X > x ) = 0.19215[/tex]
A train is running at the speed of 90 mph. The length of the train is 300 ft. How long would it take to cross a railway platform 492 ft long?
Answer:
Time = 1.45152 seconds
Step-by-step explanation:
1 foot = 0.000189 mile
300 ft = 300*0.000189
300 ft = 0.0567 miles
492 ft = 492*0.000189
492 ft = 0.092988 miles
Distance left to be covered by the train
= 0.092988-0.0567
= 0.036288 miles
Speed= 90mph
Time taken = distance/speed
Time taken= 0.036288/90
Time = 4.032*10^-4 hour
Time = 4.032*10^-4*60*60
Time = 1.45152 seconds
if (ax+b)(x-3) = 4x^2+cx-9 for all values of x, what is the value of c? a) -9 b) -6 c) 6 d) 9
Answer:
c=-9
Step-by-step explanation:
Hello,
[tex](ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9[/tex]
We can identify the like terms so:
a = 4
b-3a = c
3b = 9 <=> b = 3
So c = 3 - 3*4 = 3-12 = -9
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
