For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50
This means that [tex]p = 0.5[/tex]
Sample of 14 customers
This means that [tex]n = 14[/tex]
Probability that at least 7 will order a nonalcoholic beverage
This is:
[tex]P(X \geq 7) = 1 - P(X < 7)[/tex]
In which
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001[/tex]
[tex]P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009[/tex]
[tex]P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056[/tex]
[tex]P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222[/tex]
[tex]P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611[/tex]
[tex]P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222[/tex]
[tex]P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833[/tex]
So
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954[/tex]
[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046[/tex]
0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.
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5/2 + 6g = 11/4 solve it
Answer:
g = [tex]\frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{2}[/tex] + 6g = [tex]\frac{11}{4}[/tex]
Multiply through by 4 to clear the fractions
10 + 24g = 11 ( subtract 10 from both sides )
24g = 1 ( divide both sides by 24 )
g = [tex]\frac{1}{24}[/tex]
if sin150=1/2 then find sin75
Answer:
0.966
Step-by-step explanation:
When typed into a calculator, sin75 = -0.3877816354
Upon converting to degrees, the full answer is 0.96592582628
Write the first 4 terms of the arithmetic sequence. The first term is - 1 and the
common difference is 3.
Answer:
-1, 2,5,8
Step-by-step explanation:
nth term =a+(n-1) *d
-1+(n-1) *3
-1+3n-3
3n-4
t2 =3*2-4
6-4
2
t3=3*3-4
9-4
5
t4=3*4-4
12-4
8
Which option is correct and how would one solve for it?
Answer:
102
Step-by-step explanation:
We have the sum for k = 1 to 4 of 3 ^ ( k-1) * ( k-1)
k =1 3 ^ (1-1) * ( 1-1) = 3^0 * 0 = 0
k =2 3 ^ (2-1) * ( 2-1) = 3^1 * 1 = 3
k =3 3 ^ (3-1) * ( 3-1) = 3^2 * 2 = 9*2 = 18
k =4 3 ^ (4-1) * ( 4-1) = 3^3 * 3 = 27 *3 = 81
Add these together
0+3+18+81 =102
━━━━━━━☆☆━━━━━━━
▹ Answer
102
▹ Step-by-Step Explanation
Convert the notation into a sum and substitute values from 1-4:
(3¹⁻¹ *(1 - 1)) + (3²⁻¹ * (2 - 1)) + (3³⁻¹ * (3 - 1)) + (3⁴⁻¹ * (4 - 1))
0 + 3 + 18 + 81
= 102
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are not closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial. Reset Submit
Answer:
f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.
Step-by-step explanation:
The set of all polynomials is closed under addition, subtraction, and multiplication, because performing any of these operations on a pair of polynomials will give a polynomial result.
__
Comment on the question
The wording is a bit strange, because f(x) and g(x) are elements of a set (of polynomials), so cannot be said to be "closed." "Closed" is a property of a set with respect to some function, it is not a property of an element of the set.
Answer:
f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.
Step-by-step explanation:
Its correct trust
A box is dragged across 20 meters with a force of 60 Newtons, which are kg*m/s^2
Answer:
Mass= 6kg
Acceleration= 10 ms^-2
Work done = 1200Nm
Step-by-step explanation:
kg*m/s^2 represent the force.
The kg represent the mass
The m/s^2 represent the acceleration
The acceleration here will be due to gravity force= 10 ms^-2
Then the mass= 60/10
Mass= 6 kg
The force = 60 Newton
Distance covered in the direction of the the force= 20 Meters
The work done in the direction of the force= force* distance
The work done in the direction of the force=60*20
The work done in the direction of the force=1200 Nm
Answer: 20 • 60
Step-by-step explanation:
The midterm exam will have a total of 108 marks and there are twice as many 05 marks questions than 02 marks questions. Each question is worth either 02 marks or 05 marks”. Find out how many questions of each value there are in the online test?
Answer: 9 (2 mark question) and 18 (5 marks questions)
Step-by-step explanation:
Given: Total mark = 108
Let the 2 marks questions be x
Therefore 5 mark question = 2x
ATQ
⇒5(2x)+2(x) = 108
⇒10x+2x =108
⇒12x = 108
⇒x = 108/12
⇒x = 9
Total two mark questions are 9 and 5 mark questions are 18.
please click thanks and mark brainliest if you like :)
PLZZZZZZZZZZZZZZ HELP I WILL GIVE BRAINLIEST TO THE FIRST TO ANSWER
Answer:
B
Step-by-step explanation:
-(-a)/b = a/b
Option A is not equal to a/b
But Option B is, after cancelling out the negative sign
Answer:
[tex]\large \boxed{ \mathrm{B.} \ - \frac{a}{-b} }[/tex]
Step-by-step explanation:
[tex]\displaystyle -\frac{-a}{b} =-(- \frac{a}{b} ) = \frac{a}{b}[/tex]
The first option is not equivalent to a/b.
[tex]\displaystyle \frac{a}{-b}\neq \frac{a}{b}[/tex]
The second option is equivalent to a/b.
[tex]\displaystyle -\frac{a}{-b} =\frac{-a}{-b} = \frac{a}{b}[/tex]
a is inversely proportional to (b - 4).
If a = 8 and b = 22, express a in terms of b.
Answer:
Step-by-step explanation:
a is expressed in terms of b as a = 144/(b - 4).
If A is inversely proportional to (b - 4), we can express this relationship using the formula:
A = k/(b - 4),
where k is the constant of proportionality.
To determine the value of k, we can use the given information when a = 8 and b = 22:
8 = k/(22 - 4).
Simplifying the equation:
8 = k/18.
To isolate k, we multiply both sides of the equation by 18:
8 * 18 = k.
k = 144.
Now that we know the value of k, we can rewrite the equation in terms of b:
A = 144/(b - 4).
Therefore, a is expressed in terms of b as a = 144/(b - 4).
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7 1/4 x−x=9 3/8 HELLLLPPPPP PLLSSSS
-1.5
Step-by-step explanation:
So, you do 7.25 - 1 (because it is) and you get 6.25. Make it a fraction inton 25/4 and divide bu 75/8 (9 3/8 simplified) and you get -1.5 voila.
Answer:
x = 3/2
Step-by-step explanation:
7 1/4 = 7 + 1/4 = 28/4 + 1/4 = 29/4
9 3/8 = 9 + 3/8 = 72/8 + 3/8 = 75/8
then:
7 1/4 x = 29x/4
29x/4 - x = 75/8
29x/4 - 4x/4 = 75/8
25x/4 = 75/8
x = (75/8)/(25/4)
x = (75*4)/(8*25)
x = 300/200
x = 3/2
Checking:
(29/4)(3/2) = (29*3)(4*2) = 87/8
87/8 - 3/2 = 75/8
3/2 = 12/8
then:
87/( - 12/8 = 75/8
a ball is thrown upward with an initial height of 3 feet with an initial upward velocity 37 ft/s the balls heigh in feet after t second is given by h=3=+37t-16t^2
Answer:
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
Step-by-step explanation:
Given
[tex]h=3+37t-16t^2[/tex]
Required
Find all values of t when height is 23 feet
To solve this, we simply substitute 23 for h
[tex]23=3+37t-16t^2[/tex]
Collect like terms
[tex]16t^2 - 37t - 3 + 23=0[/tex]
[tex]16t^2 - 37t +20=0[/tex]
Solve t using quadratic formula;
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where a = 16, b =-37 and c = 20
[tex]t = \frac{-(-37)\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{1369 - 1280}}{32}[/tex]
[tex]t = \frac{37\±\sqrt{89}}{32}[/tex]
[tex]t = \frac{37\±9.43}{32}[/tex]
[tex]t = \frac{37+9.43}{32}[/tex] or [tex]t = \frac{37-9.43}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
Line A passes through the point (-1,2). Which of the
following CANNOT be the equation of line A?
A y=1 - 2
B
y = x +1
C
X = -1
D y=x+3
Answer:
b
Step-by-step explanation:
y = x + 1
The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).
Option B is correct.
Given:
Line A passes through the point [tex](-1,2)[/tex].
To find:
Which of the given equations cannot be the equation of line A.
Solution:
If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point
In option A, consider the given equation is:
[tex]y=1-x[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=1-(-1)[/tex]
[tex]2=1+1[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.
Similarly, check for the other options.
In option B,
[tex]y=x+1[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+1[/tex]
[tex]2=0[/tex]
This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.
In option C,
[tex]x=-1[/tex]
It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.
In option D,
[tex]y=x+3[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.
Therefore, the correct option is B.
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Find out the Time Zone for UAE and its neighboring countries. Express them as positive or negative rational numbers with reference to Greenwich Mean Time. Note down the time of few of your daily activities such as breakfast, school time, lunch time, etc. Compare the same time with GMT.anyone please answer this.
Answer:
UAE is in the Gulf Standard Time zone.
It is GMT + 4
Breakfast: 7 am; GMT 3 am
School time 8 am: GMT 4 am
Lunch time: 12:30 pm; GMT 8:30 am
Step-by-step explanation:
UAE is in the Gulf Standard Time zone.
It is GMT + 4
Breakfast: 7 am; GMT 3 am
School time 8 am: GMT 4 am
Lunch time: 12:30 pm; GMT 8:30 am
y''+y'=3 hihihihihhihihihihihihih
Answer:
Maaf Saya Tidak Tahu
Step-by-step explanation:
Maaf Maaf
If the areas of the given pairs of shapes are equal, find the value of x.
Answer:
X= 8cm
Step-by-step explanation:
area of the square = s×s = 16×16 = 256cm
area of the rectangle = l×b = 32×x = 32x
Given , area of triangle = area of square
32x = 256
x= 256/32
x= 8cm
Answer:
[tex]x = 8cm[/tex]
Step-by-step explanation:
we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e
the area of the square equal to the area of the rectangletherefore,
[tex] \displaystyle \rm A _{square } = A _{rect}[/tex]
recall the formula of the area of square and rectangle so,
[tex] \displaystyle {s}^{2} = lw[/tex]
now assign variables
[tex]s \implies16cm[/tex][tex]l \implies32cm[/tex][tex]w \implies x[/tex]thus substitute:
[tex] \displaystyle 32cmx = {16cm}^{2} [/tex]
simplify square:
[tex] \displaystyle 32cmx = 256cm^2[/tex]
divide both sides by 32:
[tex] \displaystyle \boxed{x = 8cm}[/tex]
and we're done!
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
The length of a rectangle is twice its width. If the area of the rectangle is 72in², find its perimeter
Let breadth be x
Length=2x[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto 72=2x(x)[/tex]
[tex]\\ \sf\longmapsto 2x^2=72[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{72}{2}[/tex]
[tex]\\ \sf\longmapsto x^2=36[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
Length=6×2=12inBreadth=6in[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(12+6)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(18)[/tex]
[tex]\\ \sf\longmapsto Perimeter=36in[/tex]
WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWERLenora wants to buy granola bars for her hiking trip. Eight bars cost $2.40. She wants to buy 12 bars. How much will 12 bars cost?
Answer:
$3.60
Step-by-step explanation:
2.40/8=.30
$.30 per bar
.3 x 12= $3.60
Answer:
$3.60
Step-by-step explanation:
Proportions
8 bars ⇔ $2.4
12 bars ⇔ $W
W = 12*2.4/8
W = $3.6
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x→9 x − 9 x2 − 81
Without resorting to L'Hopitâl's rule,
[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac{x-9}{(x-9)(x+9)}=\lim_{x\to9}\frac1{x+9}=\frac1{18}[/tex]
With the rule, we get the same result:
[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac1{2x}=\frac1{18}[/tex]
consider the bevariate data below about Advanced Mathematics and English results for a 2015 examination scored by 14 students in a particular school.The raw score of the examination was out of 100 marks.
Questions:
a)Draw a scatter graph
b)Draw a line of Best Fit
c)Predict the Advance Mathematics mark of a student who scores 30 of of 100 in English.
d)calculate the correlation using the Pearson's Correlation Coefficient Formula
e) Determine the strength of the correlation
Answer:
Explained below.
Step-by-step explanation:
Enter the data in an Excel sheet.
(a)
Go to Insert → Chart → Scatter.
Select the first type of Scatter chart.
The scatter plot is attached below.
(b)
The scatter plot with the line of best fit is attached below.
The line of best fit is:
[tex]y=-0.8046x+103.56[/tex]
(c)
Compute the value of x for y = 30 as follows:
[tex]y=-0.8046x+103.56[/tex]
[tex]30=-0.8046x+103.56\\\\0.8046x=103.56-30\\\\x=\frac{73.56}{0.8046}\\\\x\approx 91.42[/tex]
Thus, the Advance Mathematics mark of a student who scores 30 out of 100 in English is 91.42.
(d)
The Pearson's Correlation Coefficient is:
[tex]r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot \sum X^{2}-(\sum X)^{2}][n\cdot \sum Y^{2}-(\sum Y)^{2}]}}[/tex]
[tex]=\frac{14\cdot 44010-835\cdot 778}{\sqrt{[14\cdot52775-(825)^{2}][14\cdot 47094-(778)^{2}]}}\\\\= -0.7062\\\\\approx -0.71[/tex]
Thus, the Pearson's Correlation Coefficient is -0.71.
(e)
A correlation coefficient between ± 0.50 and ±1.00 is considered as a strong correlation.
The correlation between Advanced Mathematics and English results is -0.71.
This implies that there is a strong negative correlation.
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57
the temp fell 3 degrees every hour for 5 hours what's the change in temperature
Answer:
-15
Step-by-step explanation:
If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees
Simplify the product. 7(–9)
Answer:
have a great day
god is great
A rotating light is located 16 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
Answer:
a
Step-by-step explanation:
answer is a on edg
henry incorrectly said the rate 1/5 pound/ 1/20 quart can be written as the unit rate 1/100 pound per quart. What is the correct unit rate? What error did Henry likely make?
Answer:
4 pounds per quart
Step-by-step explanation:
Henry divided by 20 instead of multiplying by 20.
1/5 pound is the numerator and 1/20 quart is the denominator. To make the denominator equal to 1 quart, you need to multiply by 20.
So 1/5 x 20 = 4 pounds.
Literally, a unit rate means a rate for one.
The unit rate is 4 pounds per quartHenry used the wrong arithmetic operatorThe rate is given as:
[tex]\mathbf{Rate = \frac{1}{5}\ pound\ per\ \frac{1}{20}\ quart}[/tex]
Per means divide.
So, the expression becomes
[tex]\mathbf{Rate = \frac{1}{5}\ pound\ \div \frac{1}{20}\ quart}[/tex]
Express as products
[tex]\mathbf{Rate = \frac{1}{5}\ pound\ \times \frac{20}{1\ quart}}[/tex]
Simplify
[tex]\mathbf{Rate = \frac{1}{1}\ pound\ \times \frac{4}{1\ quart}}[/tex]
Rewrite as:
[tex]\mathbf{Rate = \frac{4\ pound}{1\ quart}}[/tex]
So, the unit rate is 4 pounds per quart
Henry's error is that: He multiplied 1/5 by 1/20, instead of dividing 1/5 by 1/20
Read more about unit rates at:
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.966 grams and a standard deviation of 0.315 grams. Find the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less.
Answer:
The probability is [tex]P(X \le 0.305 ) = 0.01795[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.966 \ grams[/tex]
The standard deviation is [tex]\sigma = 0.315 \ grams[/tex]
Given that the amounts of nicotine in a certain brand of cigarette are normally distributed
Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )[/tex]
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )[/tex]
From the z-table(reference calculator dot net ) value of [tex]P(Z >-2.0984 ) =0.98205[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205[/tex]
=> [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795[/tex]
=> [tex]P(X \le 0.305 ) = 0.01795[/tex]
Write an equation showing the relationship between the lengths of the three sides of a right triangle.
Answer:
Below
Step-by-step explanation:
First triangle)
This triangle is a right one so we will apply the pythagorian theorem.
● 25 is the hypotenus
● 25^2 = b^2 + 24^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Seconde triangle)
Again it's a right triangle
x is the hypotenus.
● x^2 = 12^2 +5^2
● 12^2 = x^2-5^2
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This is a right triangle
AC is the hypotenus.
● AC^2 = BC^2 + BA^2
Notice that: BC = BE+EC and BA=BD+DA
● AC^2 = (BE+EC)^2 + (BD+DA)^2
Answer: 2) b = 7 3) x = [tex]\sqrt{119}[/tex]
Step-by-step explanation:
Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²
2) b² + 24² = 25²
b² + 576 = 625
b² = 49
[tex]\sqrt{b^2}=\sqrt{49}[/tex]
b = 7
3) 5² + x² = 12²
25 + x² = 144
x² = 119
[tex]\sqrt{x^2}=\sqrt{119}[/tex]
[tex]x=\sqrt{119}[/tex]
NEED IT ASAP
Tony is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 10% sales tax plus a state-mandated $45 fee for disposing of his old tires. If Tony has determined that he will spend less than $559.80 total, then what is the price range he can spend on the tire set?
Select one:
a. Less than $468
b. At least 472
c. $468 or more
d. Less than 473
Answer:
A
Step-by-step explanation:
Let:
Total price be T
And price of tire set be x
T<559.80 ---(1)
T=x +(10% of x)+ 45. ——(2)
T=x+(1/10)x+45
T=(11/10)x+45
Substitute T into equ. 1
T<559.80
(11/10)x +45<559.80
(11/10)x < 514.80
11x < 5148
x < 468
Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 2, −5 is the only other zero, leading coefficient is 3.
Answer:
Step-by-step explanation:
Hello, just apply the instructions as below.
[tex]3(x-2)^2(x+5)^3[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you