Answer:
The probability that exactly 2 buyers would prefer red car is 0.0317.
Step-by-step explanation:
Let the random variable X represent the number of buyers would prefer red car.
The probability of the random variable X is, p = 0.40.
A random sample of n = 14 buyers are selected.
The event of a buyer preferring a red car is independent of the other buyers.
The random variable X thus follows a Binomial distribution with parameters n = 14 and p = 0.40.
The probability mass function of X is:
[tex]P(X=x)={14\choose x}(0.40)^{x}(1-0.40)^{14-x};\ x=0,1,2,3...[/tex]
Compute the probability that exactly 2 buyers would prefer red car as follows:
[tex]P(X=2)={14\choose 2}(0.40)^{2}(1-0.40)^{14-2}[/tex]
[tex]=91\times 0.16\times 0.0021768\\=0.031694208\\\approx 0.0317[/tex]
Thus, the probability that exactly 2 buyers would prefer red car is 0.0317.
A plumber wishes to cut a piece of pipe
32 inches long into two parts so that the
larger part is 4 inches less than three
times the smaller part. What are the
lengths of the two parts of the pipe?
Answer:
9 and 23
Step-by-step explanation:
Let x be smaller length in inches.
x+3x-4=32
4x=36
x=9
9*3-4=23
So they're 9 and 23 inches long.
The lengths of the two parts of the pipe are 9 and 23 inches long.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Let x be the smaller length in inches.
x + 3x - 4 = 32
4x = 36
x =9
Now substitute;
9*3 - 4 = 23
Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.
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ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
f(x) = 2(x –3)²
Step-by-step explanation:
f(x) = 2x² – 12x + 18
The vertex form of the above expression can be obtained as follow:
f(x) = 2x² – 12x + 18
Factorise
f(x) = 2(x² – 6x + 9)
Next, we shall simplify x² – 6x + 9 by factorisation method.
This is illustrated below:
x² – 6x + 9
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.
The factors are –3x and –3x
Next, replace –6x with –3x and –3x in the equation above as shown below:
x² – 6x + 9
x² – 3x –3x + 9
Factorise
x(x – 3) –3(x –3)
(x –3)(x –3)
(x –3)²
f(x) = 2x² – 12x + 18
f(x) = 2(x² – 6x + 9)
f(x) = 2(x –3)²
Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is
f(x) = 2(x –3)²
Complete the equation that describes c, the number of cats and g, the number of gold bars put into the machine.
c=?g
Answer:
C= 3g
Step-by-step explanation:
The net of the figure shown is made of which set of
shapes?
3 triangles and 1 square
3 triangles and 1 rectangle that is not a square
4 triangles and 1 square
4 triangles and 1 rectangle that is not a square
Answer:
Step-by-step explanation:
The sides of the base are each 5 inches. We see 4 right angles so that we are dealing with a square.
The triangles look to be isosceles. In any event there are 4 of them. So the answer is the 3rd one down.
Answer:
C
Step-by-step explanation:
A random sample is drawn from a normally distributed population with mean μ = 31 and standard deviation σ = 1.9. Calculate the probabilities that the sample mean is less than 31.6 for both sample sizes
Answer:
For sample size n = 39 ; P(X < 31.6) = 0.9756
For sample size n = 76 ; P(X < 31.6) = 0.9970
Step-by-step explanation:
Given that:
population mean μ = 31
standard deviation σ = 1.9
sample mean [tex]\overline X[/tex] = 31.6
Sample size n Probability
39
76
The probabilities that the sample mean is less than 31.6 for both sample size can be computed as follows:
For sample size n = 39
[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]
[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]
[tex]P(X < 31.6) = P(Z< 1.972)[/tex]
From standard normal tables
P(X < 31.6) = 0.9756
For sample size n = 76
[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]
[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]
[tex]P(X < 31.6) = P(Z< 2.75)[/tex]
From standard normal tables
P(X < 31.6) = 0.9970
What is 7/35 converted into a decimal??
Answer:
0.2
Step-by-step explanation:
it works out to be 0.2 as a decimal and 20% as a percentage.
Answer:
.2
Step-by-step explanation:
The arm and blade of a windshield wiper have a total length of 30 inches. The blade is 24 inches long and the wiper sweeps out an angle of 125 degrees.
Answer:
942.5 in²
Step-by-step explanation:
The formula for the area (A) of a sector of a circle is
A = ½r²θ
where θ is the angle in radians.
1. Convert the angle to radians
θ = 125°
[tex]\theta = 125^{\circ} \times \dfrac{\pi \text{ rad }}{180^{\circ}} =\frac{25}{36} \pi\text{ rad}[/tex]
2. Area swept out by wiper arm
A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²
3. Area missed by wiper
A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²
4. Area covered by wiper
A = 450 θ in² - 18 θ in² = 432 θ in²
5. Insert the value of θ
A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²
The area swept out by the wiper blade is 942.5 in².
Write the algebric expression of the difference of 'a' and 'b'
Step-by-step explanation:
An algebraic expression haa atleast one variable and operator sign such as (+,-,×,÷)
According to the question, an algebraic expression should be made from difference of 'a' and 'b'
so, the expression is (a - b) or a - b.
Hope it helps!!!!
8/15 simplify the quotient to get ?
Answer:
0.5333333333 or 0.53 when simplified.
Step-by-step explanation:
8/15 is simply 8÷15
15 into 8 is not possible so you annex a zero and write a decimal point.The 8 now becomes 80. We now say 80÷15,the answer is 5 because 15x5=75.The remainder is five.We annex another zero and it becomes 50,50÷15=3
I hope this helps.
√ (952.695) + √0.00195 – 5.382 please help Thank you to whoever helps
Answer:
25.52791653032955454422437424679625318128649677442393276098...
Step-by-step explanation:
You can just paste this into wolframalpha.
Answer: 970.72312
Step-by-step explanation:
Straightforward operation.
YoIn a sale, the normal price of a book is reduced by 30%. The sale price of the book is £2.80 Work out the normal price of the book.
Answer: £4
Step-by-step explanation:
From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.
Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.
Let the normal price of the book be y.
70% of y = £2.80
70/100 × y = £2.80
0.7 × y = £2.80
0.7y = £2.80
y = £2.80/0.7
y = £4
The normal price of the book is £4.
write an equation for the translation of x^2 + y^2 = 49 by 7 units right and 4 units up
Answer:
(x - 7)² + (y - 4)² = 49
Step-by-step explanation:
Given
Equation: x² + y² = 49
Required:
New Equation when translated 7 units right and 4 units up
Taking it one step at a time.
When the equation is translated 7 units right, this implies a negative unit along the x axis.
The equation becomes
(x - 7)² + y² = 49
When the equation is translated 4 units up, this implies a negative unit along the y axis.
(x - 7)² + (y - 4)² = 49
The expression can be further simplified but it's best left in the form of
(x - 7)² + (y - 4)² = 49
Help please!! Thanks!!!
Answer:
your answer is k
Step-by-step explanation:
not all the isosceles triangles are similar
A collection of 108 coins containing only quarters and nickels is worth $21. A table titled Coin Collection showing Number of Coins, Value, and Total. The first row shows Nickels, and has n, 0.05, and 0.05 n. The second row shows, Quarters, and has q, 0.25, and 0.25 q. The third row shows total, and has not entries. Which value could replace q on the chart? 21 108 21 – n 108 – n
Answer:
q = 108-n
Step-by-step explanation:
Given: 108 coins containing only quarters and nickels
q = 108-n
since total number of coins is 108, and n= number of nickels
If you want to know how many of each kind of coin, read on:
First solve the number of quarters and nickels.
If all 108 coins are quarters, the value is 108*0.25 = $27
Since this value exceed the actual by 27-21 = $6,
we replace a number of quarters by nickels.
Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.
So it will take 6/0.2 = 30 replacements.
Therefore there are 108-35 = 78 quarters and 30 nickels.
The solution is : q = 108-n, is the value could replace q on the chart.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Given:
108 coins containing only quarters and nickels
q = 108-n
since total number of coins is 108, and n= number of nickels
If you want to know how many of each kind of coin, read on:
First solve the number of quarters and nickels.
If all 108 coins are quarters, the value is 108*0.25 = $27
Since this value exceed the actual by 27-21 = $6,
we replace a number of quarters by nickels.
Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.
So it will take 6/0.2 = 30 replacements.
Therefore there are 108-35 = 78 quarters and 30 nickels.
The solution is : q = 108-n, is the value could replace q on the chart.
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Simplify.
N4 x N7 over n5
Answer:
[tex]n^6[/tex].
Step-by-step explanation:
[tex]n^4 * \frac{n^7}{n^5}[/tex]
= [tex]n^4 * n^{7 - 5}[/tex]
= [tex]n^4 * n^2[/tex]
= [tex]n^{4 + 2}[/tex]
= [tex]n^6[/tex].
Hope this helps!
The hypotnuse of a right triangle is three times the length of its first leg. Theblength of the other leg is four feet. Find the lengths of the first leg and the hypotnduse and enter them in the below squares in this order. For non-integer answer(s), round your answer(s) to the nearest tenth.
Answer:
Length of first leg = 1.4feet
Hypotenuse = 4.2feet
Explanation:
Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.
Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.
From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.
Also the other leg is four feet i.e c= 4
Substituting this values into the Pythagoras formula;
a²=b²+c²
(3b)² = b²+4²
9b² = b²+16
9b²-b² = 16
8b² = 16
b² = 16/8
b² = 2
b = √2
b = 1.4
Since a = 3b
a = 3(1.4)
a = 4.2
Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.
I need help with solving this problem 4x-c=k
Answer:
x=1/4c+1/4k
Step-by-step explanation:
4x-c=k
move c over
4x=c+k
then divide by 4
x=1/4c+1/4k
hope this helps
A pole that is 2.5 M tall cast a shadow that is 1.72M lawn dart at the same time a nearby tower cast a shadow that is 50.5 M long how tall is the tower round answer to the nearest meter
Answer:
The tower is 73.4 m tall
Step-by-step explanation:
The height of the pole = 2.5 m
The shadow cast by the pole = 1.72 m
Shadow cast by tower = 50.5 m
To find the height of the tower, we proceed by finding the angle of elevation, θ, of the light source casting the shadows as follows;
[tex]Tan\theta =\dfrac{Opposite \ side \ to\ angle \ of \ elevation}{Adjacent\ side \ to\ angle \ of \ elevation} = \dfrac{Height \ of \ pole }{Length \ of \ shadow} =\dfrac{2.5 }{1.72}[/tex]
[tex]\theta = tan ^{-1} \left (\dfrac{2.5 }{1.72} \right) = 55.47 ^{\circ}[/tex]
The same tanθ gives;
[tex]Tan\theta = \dfrac{Height \ of \ tower}{Length \ of \ tower \ shadow} =\dfrac{Height \ of \ tower }{50.5} = \dfrac{2.5}{1.72}[/tex]
Which gives;
[tex]{Height \ of \ tower } = {50.5} \times \dfrac{2.5}{1.72} = 73.4 \ m[/tex]
Evaluate the following: 3 to the power 2 ÷ (2 + 1). 2 3 4 5
Answer:
3
Step-by-step explanation:
Solve the following quadratic equation by completing the square ✓3x^2 + 10x + 7✓3 = 0
[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]
Simplifying Rational Expressions: I need answers for both 7 and 8 below. Answers for just one or the other is also fine.
Answer:
1. Option A 2. Option DStep by step explanation
1. [tex] \frac{1}{1 - x} + \frac{x}{ {x}^{2} - 1} [/tex]
Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] to rewrite the fractions
[tex] - \frac{1}{x - 1} + \frac{x}{(x - 1)(x + 1)} [/tex]
Write all numerators above the Least Common Denominator ( X - 1 ) ( X + 1 )
[tex] \frac{ - (x + 1) + x}{(x - 1)(x + 1)} [/tex]
When there is a ( - ) in front of an expression in parentheses , change the sign of each term in the expression
[tex] \frac{ - x - 1 + x}{(x - 1)(x + 1)} [/tex]
Using [tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex] , simplify the product
[tex] \frac{ - x - 1 + x}{ {x}^{2} - 1 } [/tex]
Since two opposites add up to zero, remove them from the expression
[tex] \frac{ - 1}{ {x}^{2} - 1} [/tex]
So, Option A is the right option.
___________________________________
2.
[tex] \frac{ {x}^{2} - x - 12}{ {x}^{2} - 16} - \frac{1 - 2x}{x + 4} [/tex]
Write - X as a difference
[tex] \frac{ {x}^{2} + 3x - 4x - 12 }{ {x}^{2} - 16 } - \frac{1 - 2x}{x + 4} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression
[tex] \frac{ {x}^{2} + 3x - 4x - 12 }{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]
Factor the expression
[tex] \frac{x(x + 3) - 4(x + 3)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]
Factor out X+3 from the expression
[tex] \frac{(x + 3)(x - 4)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]
Reduce the fraction with x-4
[tex] \frac{x + 3}{x + 4} - \frac{1 - 2x}{x + 4} [/tex]
Write all the numerators above the common denominator
[tex] \frac{x + 3 - ( 1- 2x)}{x + 4} [/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \frac{x + 3 - 1 + 2x}{x + 4} [/tex]
Collect like terms
[tex] \frac{3x + 3 - 1}{x + 4} [/tex]
Subtract the numbers
[tex] \frac{3x + 2}{x + 4} [/tex]
Undefined at,
X + 4 = 0
Move constant to R.H.S and change its sign
[tex]x = 0 - 4[/tex]
Calculate
[tex]x = - 4[/tex]
So, the answer is :
[tex] \frac{3x + 2}{x + 4} [/tex] , undefined at X = -4 and 4
Hope this helps..
Best regards!!
Please help this is a new topic for me.
Answer:
last answer
Step-by-step explanation:
P' (2, -4)
Q' (-2, -5)
R' (1, -8)
Answer:
C. P'(2, -4) Q'(-2, -5) R'(1, -8)
Step-by-step explanation:
When you reflect something across the y-axis you change (x,y) to (-x,y).
For each point, change the x to a negative x.
P(-2, -4) --> P'(2, -4)
Q(2, -5) --> Q'(-2, -5)
R(-1, -8) --> R'(1, -8)
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Suppose $600 is compounded yearly for 20 years. If no other deposits are made, what rate is needed for the balance to triple in that time? Round your answer to the nearest hundredth of a percent.
Answer:
5.65%
Step-by-step explanation:
Principal=$600
Time=20 years
FV=600*3=$1800
n=1
r=?
r= n[(A/P)^1/nt - 1]
=1{(1800/600)^ 1/1*20 - 1}
={(3)^1/20-1}
=3^0.05-1
=1.0565-1
=0.0565
rate=0.0565*100
=5.65% to the nearest hundredth percent
Please help urgently ❤️❤️❤️
Greetings from Brasil...
Here we have application of Trigonometry
COS β = adjacent side ÷ hypotenuse (H)
bringing to our problem....
COS A = AC ÷ H
But we dont have AC.... We have to use Pitagoras:
AB² = AC² + BC²
AC² = AB² - BC²
AC = √(AB² - BC²)
AC = √(10² - 8²)
AC = √(100 - 64)
AC = √36
AC = 6So
COS A = AC ÷ H ⇔ COS A = AC ÷ AB
COS A = 6/10
COS A = 3/5Answer: B) 3/5
Step-by-step explanation:
Cos = adjacent/hypotenuse
Thus, the cos is AC/AB.
Because of Pythagorean Theorem, AC^2=AB^2-BC^2. Let AC be x.
[tex]x^2=10^2-8^2\\x^2=100-64\\x^2=36\\x=6[/tex]
Thus, the cos is 6/10, or 3/5
find the coordinates of the point whose ordinate is -7 and lies on y axis
Answer:
(0,-7)
Step-by-step explanation:
If nay point is form (x,y)
x is abscissa can be also called x axis coordinate
y is ordinate can be also called y axis coordinate
ordiantes are points lying on y axis.
For any point lying on y axis, its x-axis coordinate will be 0
given that ordinate is -7. it means that value of y coordinate is -7
Thus, coordinates of the point is (0,-7)
please answer this A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. This is called a company’s overhead. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even? A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. This is called a company’s overhead. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?
Answer: The store must sell 40 bikes.
Step-by-step explanation:
y=60x+2400
y=120x
120x=60x+2400
-60x on both sides
60x=2400
divide 60 on both sides
2400/60=40
x=40
The electromotive force V of an alternating current circuit at time t can be describe by the
following function, where V is volts and t is in seconds. V(t) = 220sin(180πt). How many cycles
will the circuit run through in 1 minute?
Answer:
5400 cycles
Step-by-step explanation:
You have the following function:
[tex]V(t)=220sin(180\pi t)[/tex]
where t is in seconds.
In order to find the number of cycles in 1 minute, you first calculate the frequency of the function, which is given by:
[tex]f=\frac{180\pi}{2\pi}=90s^{-1}[/tex]
The number of cycles is then given by:
[tex]n=ft=(90s^{-1})(60s)=5400\ cycles[/tex]
There are 5400 cycles in 1 minute
work out the shaded area.
plzzzz
Answer:
Shaded area: 70cm^2
Step-by-step explanation:
Whole=120cm^2
White Square=
10-2.5-2.5=5
12-1-1=10
5✖️10=50cm^2
Whole-white=70cm^2
Please help with 4.)
WILL MARK BRAINLIEST X
Answer:
a) More.
b) Less.
c) More.
Step-by-step explanation:
a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.
b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.
c) The same exact thing as part a.
Hope this helps!
Clarise evaluated this expression.
(66.3 – 14.62) ÷ 0.6 – 0.22
(51.68) ÷ 0.6 – 0.22
(51.68) ÷ 0.42
51.68 ÷ 0.16
32.3
Which errors did Clarise make?
Answer:
(66.3-14.62)/0.6-0.22
(51.68)/0.6-0.22
(51.68/0.6)-0.22
(86.14667)-0.22
85.92667