The probability that the number of residents that recognize the brand is not 4 is 0.86 , the probability that at least 7 people will recognize the brand is 0.29 and the probability that at most 5 people will recognize the coffee shop is 0.39.
Given Recognition rate of brand in town of Coffleton is 57% and sample size is 10.
We have to use binomial distribution:
P(X=x)=[tex]C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]C_{n,x} =C!/r!(C-r)![/tex]
A) The parameters are as under:
x is the number of successes.
n is the number of trials which is 10 in this question.
p is the probability.
In this problem :
The brand name of a certain chain of coffee shops has 57% recognition rate in the town of coffleton , hence p=0.53.
There is a sample of 10 residents, n=10.
Probability that the no. of people that recognize the brand name is not 4 is as under:
P(X≠4)=1-P(X=4)
P(X=4)=[tex]C_{10,4}(0.53)^{4} (0.43)^{6}[/tex]
=0.1395
P(X≠4)=1-0.1395
=0.8605
B) P(X>=7)=[tex]C_{10,7} (0.57)^{7} (0.43)^{3} +C_{10,8} (0.57)^{8} (0.43)^{2} +C_{10,9} (0.57)^{9} (0.43)^{1} +C_{10,10} (0.57)^{10} (0.43)^{0}[/tex]
=0.18012+0.081+0.0258+0.0036
=0.29
C)P(X<=5)=[tex]C_{10,1} (0.57)^{1} (0.43)^{9} +C_{10,2} (0.57)^{2} (0.43)^{8} +C_{10,3} (0.57)^{3} (0.43)^{7} +C_{10,4} (0.57)^{4} (0.43)^{6} +C_{10,5} (0.57)^{5} (0.43)^{5}[/tex]
=0.00285+0.0146205+0.0432+0.126+0.21168
=0.3983.
Hence the probability that the number of residents that recognize the brand is not 4 is 0.86 , the probability that at least 7 people will recognize the brand is 0.29 and the probability that at most 5 people will recognize the coffee shop is 0.39.
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A toilet is leaking at the rate of 1 fluid ounces per minute. How many gallons is
the toilet leaking per hour?
O 0.47 gal/hr
O 0.94 gal/hr
O 28.13 gal/hr
O 2.13 gal/hr
1 gallon (gal) = 128 fluid ounce (fl oz)
1 hour (hr) = 60 minutes (min)
Convert 1 fl oz/min to gal/hr.
[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]
tengo 2/3 de lo que cuesta una computadora ¿Cuanto vale la computadora si me faltan solo 318 dolares para comprarla?
How many solutions does this system of equations have? x² + y² = 25
x² - 6=0
The system of equation have one solution.
How to solve system of equation?x² + y² = 25
x² - 6 = 0
x² = 6
x = √6
Therefore, let's substitute the value of x in equation (i)
x² + y² = 25
(√6)² + y² = 25
y² = 25 - 6
y² = 19
hence,
y = √19
Therefore, the system of equation have one solution.
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Please answer with everything needed i appreciate everyones help:0
A scenario that would best model the graph on Holly, her home, and school is:
Holly was trying to get to school from home but fell ill when 4 miles from home. Holly waited to catch her breath and gain some strength. Holly reached school and reported her condition. The school allowed her to go home.What happened Holly's journey to school?As Holly was heading to school, she felt uneasy and had to wait for 10 mins to catch her breath.
After doing so, she then continued to school which was 6 miles from her home. When she got there, she went to the nurse's office.
She waited in school for 15 minutes and was then told to go home to rest and recuperate. She then made the journey back home in a car and arrived in 10 minutes.
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Use your graphing calculator to find the equation of the trend line for the scatterplot below.
The equation of the trend line is y = 3x + 15
How to determine the equation of the trend line?Start by entering the table of values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 21Sum of Y = 153Mean X = 3.5Mean Y = 25.5Sum of squares (SSX) = 17.5Sum of products (SP) = 52.5The equation of the trend line is represented as:
y = bx + a
Where
b = SP/SSX = 52.5/17.5 = 3
a = MY - bMX = 25.5 - (3*3.5) = 15
This gives
y = 3x + 15
Hence, the equation of the trend line is y = 3x + 15
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Find the missing side length of the triangle
Answer:
b = 24 meter
Step-by-step explanation:
Using Pythagoras theorem:
a² + b² = c²
Here given: a = 10 m, b = ?, c = 26 m
Insert values
10² + b² = 26²
b² = 26² - 10²
b² = 676 - 100
b² = 576
b = √576
b = 24
Answer:24
Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.
so according to formula,h squared=b squared+p squared
so,26 squared=10 squared+p squared.
in order to find p
p squared=26 squared -10 squared
which gives us 576
and p squared =576
the square on the p will go on the other side and become an underroot.
take the underoot of 576
which gives us p=24.
so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula
(3.5x0.71) ÷ √8.2-7.5
24.85
Step-by-step explanation:
First find the square root of 8.2 and subtract from the square root of 7.5. Multiply 3.5 by 0.71, the answer you get divide it by the answer you get after finding the square root.
how can i do scientific notifacation please
The unit digit of a two digit number is one less than the ten digit number. If the number is increase by 8 and then divided by the unit of the digits, the results is 8. Find the number.
The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
Lets simplify the problem,
Let assume the "tens" digit be x
Then the "units" difference = (x-1), according to the condition.
Hence, the number itself is N = 10x + (x-1).
Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.
From the last statement of the problem, we have this equation
[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]
Simplify and find "x"
[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].
Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
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Jen has collected information about the students in her class and the month they were born.
Which of the following statements would be true about this information?
It is both a relation and a function.
It is not a relation, but it is a function.
It is a relation but not a function.
It is neither a relation nor a function.
The true statement about this information is that: A. It is both a relation and a function.
What is a function?A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population.
In this context, we can infer and logically deduce that the true statement about this information collected by Jen is that it's both a relation and a function because it indicates a relationship between two variables.
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Answer:
It is both a relation and a function.
Step-by-step explanation:
Jason bought 10 of the 30 raffle tickets for a drawing. assuming that he chooses the winning ticket each time, what is the probability that jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away?
Answer: 2.96% rounded
Step-by-step explanation: 10/30) x (9/29) x (8/28) = 720 / 24,360 = 6/203 = 2.96%
If T -1 (x, y) (½x, y - 5), then T(x, y) ( x, y + 5) (2 x, y + 5) ( x - ½, y + 5)
The coordinates of the function will be T (x , y ) = (2 x, y + 5) ; Option B is the answer.
What is a Function ?A function is a mathematical statement that relates an independent and a dependent variable .
An inverse of a function is given
T⁻¹ (x, y) : (½x, y - 5)
T(x, y) : ?
As the inverse in given , to find the function , the reverse of all the transformation has to be done .
The x coordinate has been halved , so the original function will be double.
The y coordinate has 5 subtracted to it , so it will be added to the coordinate.
So the coordinates of the function will be
T (x , y ) = (2 x, y + 5)
Therefore Option B is the answer.
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Answer:
B. y = x + 2; y = 5
Step-by-step explanation:
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TIME REMAINING
53:34
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Option 3 and 4. The two options that shows the correct representation of the inequality are:
- 6x + 15 < 10 - 5xAn open circle is at 5 and a bold line starts at 5 and is pointing to the right How to solve the inequality–3(2x – 5) < 5(2 – x)
We have to open up the brackets by multiplying the sides
= -6x + 15 < 10 - 5x
Hence the third option is certified to be correct.
Next this inequality has to be shown on a number line.
To do this we have to solve the inequality completely
From -6x + 15 < 10 - 5x
we have to take like terms
-6x+5x < 10 - 15
-x < -5
x<5
The sign of inequality has to be reversed given that the coefficient of x was negative.
Hence x>5. The number line would start from the right and it would move towards the right
From the solution here, we can see that the two correct options are
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You have a machine that can add exactly 46,899 pieces of candy per scoop to a giant vat and another machine that can remove exactly 13,576 pieces of candy with a different scoop from the giant vat. You have a total supply of 600,000 pieces of candy. Your giant vat starts out empty. The first machine adds scoops of candy, and then the second machine removes scoops of candy. When these two machines are done, there is only one piece of candy left in the vat. How many scoops of candy did the first machine add to the vat?
The first machine has added maximum 25 scoops of candies.
Given Machine 1 can add 46899 pieces of candies in the giant vat and machine 2 can add 13576 pieces of candies in the giant vat to form total supply of 600000.
let the number of scoops added by first machine be x and number of scoops added by second machine is y.
The equation will be as under:
46899x-13576y=600000
It can be solved logically. Because other machine is removing the candies from the giant vat so the value of 13576y is minimum 600000-13576=586424. Because it atleast withdrawn 1 scoop.
So the value of 46899x is maximum 1186424 which can bewhen the number of scoops is =1186424/46899=25 approximately.
Hence the number of scoops added by first machine is maximum 25.
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Question contains an error as the line related to left over 1 candy should be deleted.
how do u write 99.09 - 98.29 in a long subtraction line by line and where do u put the answer?
The computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.
How to calculate the value?It should be noted that the subtraction line is simply used to subtract numbers.
In this case, the computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.
When subtracting the numbers on the number line, we will move towards the left hand side of the number line.
An illustration of the number line is given.
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Is this a function or not because there’s a vertical line but the plots also go above each other .
Answer:
not a function because it doesn't pass the vertical line test
Step-by-step explanation:
even though they have different y coordinates they still don't pass the test
THAT IS THE QUATION OF Y=7X+300
Answer:
Slope=14.000/2.000=7.000
x-intercept = 300/-7 = -42.85714
y-intercept = 300/1 = 300.00000
Step-by-step explanation:
Robin was just hired at Groceries & More as a cashler. They pay her $12 an hour. She works 20 hours a week and is going to save all her money to buy a new cell phone that costs $950 The amount of deductions from her weekly paycheck is $34. How many weeks will Robin have to save for in order to buy the new computer? Enter your answer rounded to the nearest whole number.
Answer:
5 weeks
Step-by-step explanation:
We know that she works at a rate of $12 an hour, she also works 20 hours a week.
The total amount she makes per week is $240 (12 x 20). However, that is without deductions. We have to subtract $34 from the $240.
$240 - $34 = $206.
$206 is the amount she makes in a week and she wants to save $950. How many weeks does she have to save? Well, let's divide.
$950 / $206 = 4.6 weeks. However, if we have to round up to 5 weeks.
(b) An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Also find:
(i) how many use only Radio?
(ii) how many use only Television?
(iii) how many use Television and Magazine but not radio?
Answer:
Here you go with your correct answer
Line l contains points (2,4) and (5,1). Point P has coordinates (1,1). Find the distance from P to l.
The least distance from point P to line l is approximately equal to 3.536 units.
How to find the least distance between a line and a point outside the line
There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:
Vector parallel to the line l
[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]
[tex]\overrightarrow{AB} = (3, - 3)[/tex]
A vector from one point on the line l to the point P
[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]
[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]
Now we proceed to find the vector distance by using the following vectorial formula:
[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]
[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]
[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]
[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]
[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]
The magnitude of the vector distance is determined by Pythagorean theorem:
[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]
d ≈ 3.536
The least distance from point P to line l is approximately equal to 3.536 units.
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Which equations are true for x = –2 and x = 2? Select two options
x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0
The equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16
How to determine the true equations?We have:
x = -2 and x = 2
Rewrite as:
x + 2 = 0 and x - 2 = 0
Multiply both equations
(x + 2)(x - 2) = 0
This gives
x^2 - 4 = 0 --- option (a)
Add 4 to both sides
x^2 = 4
Multiply by 4
4x^2 = 16 --- option (d)
Hence, the equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16
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Which property best describes the conditional statement
below?
If AABC = ADEF, then ADEF= AABC
OA. Reflexive property
B. Transitive property
C. Symmetric property
D. Associative property
The congruence property that shows that if ΔABC ≅ ΔDEF, then ΔDEF ≅ ΔABC is; A: Reflexive Property
How to Identify properties of Congruent Segments?In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.
Now, since we are told that ΔABC is congruent to ΔDEF, then it means that by the reflexive property of congruence we can equally say that ΔDEF are congruent to angles of ΔABC
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A pencil cost $1.20 and a pen cost $2.90. Jasmiah bought an equal number of such pencils and pens. She spent $32.30 more on the pens than on the pencils. How many pencils and pens did she buy altogether?
Answer:
38
Step-by-step explanation:
hope it helps good day.
Answer:
38 pencils and pens
Step-by-step explanation:
Given
Cost of pencil= $1.20
Cost of pen= $2.90
Difference in cost
= $2.90 -$1.20
= $1.70
Since she bought an equal number of pens and pencils, the additional amount of money spent on pens is due to the difference in price of a pen as compared to a pencil. Let one pen and one pencil be a set.
Number of sets
= $32.30 ÷$1.70
= 19
Since there are 19 sets,
total number of pencils and pen
= 19(2)
= 38
Drag a statement or reason to each box to complete this proof.
If −3(x+8)=−21, then x=−1.
Drag a statement or reason to each box to complete this proof.
If 3x−4=14, then x=6.
Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.
How to utilize properties of Algebra?Statement 1; −3(x + 8) = −21
Reason 1; Given
Statement 2; −3(x + 8)/-3 = −21/-3
Reason 2; Division property of Equality
Statement 3; x + 8 - 8 = 7 - 8
Reason 3; Subtraction Property of Equality
Statement 4; x = -1
Reason 4; Given
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Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
330. (11 − b)(11 + b)
Answer:
The product is the difference of squares is [tex]$$\left(11-b\right)\left(11+b\right)=121-{{b}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (11-b)(11+b).We have to multiply the given expression.Square the first term 11. Square the last term b.[tex]$$\begin{aligned}&(11-b)(11+b)=(11)^{2}-(b)^{2} \\&(11-b)(11+b)=121-b^{2}\end{aligned}$$[/tex]
can someone please help me
Answer:
The answer is C. U=3x and V=2y^3
Step-by-step explanation:
3x*3x=9x^2
2y^3*-2y^3=-4y^6
Other variables cancel each other out
Reina walked 1/2 of a mile in 1/4 of an hour. What was Reina's rate of speed in miles per hour?
Help please! I already tried doing this but I didn't get the answer right, and I don't know where I went wrong
I think factorizing everything you can first will make the simplification ... well, simpler.
[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x(x+7)}{(x+7)(x+9)}[/tex]
The factors of [tex]x+7[/tex] in the second rational expression cancel:
[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x}{x+9}[/tex]
Now, use the property
[tex]\dfrac ab \div \dfrac cd = \dfrac ab \times \dfrac dc[/tex]
(this is the property of multiplication having to do with multiplicative inverse, or "inverting the divisor" as the question calls it) to write
[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \times \dfrac{x+9}x[/tex]
and we see some more cancellation, namely of the factors of [tex]x[/tex] and [tex]x+9[/tex].
[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \boxed{\dfrac{x-3}{x+4}}[/tex]
3)If the interior angle of a regular polygon is 35" how many sida does it have?A)5. B) 8 C)6 D) 7
The number of sides the regular polygon has is: B. 8.
How to Find the Interior Angle of a Regular Polygon?A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.
Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.
Given the following information about the regular polygon:
Interior angle of the regular polygon = 135 degrees.
Plug this into the given formula for finding the interior angle of a polygon:
135 = (n - 2)180/n
Multiply n by both sides of the equation
135 × n = (n - 2)180/n × n
135n = (n - 2)180
Open the bracket
135n = 180n - 360
Subtract both sides by 180n
135n - 180n = 180n - 360 - 180n
-45n = -360
Divide both sides by -45
-45n/-45 = -360/-45
n = 8
Thus, the number of sides that the regular polygon has is: B. 8 sides.
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John ate a whole pizza which has 2,368 Cal. If he burns 125 Cal by walking for 30 minutes, how long would it take to burn off the entire pizza by walking
The time taken to burn off the entire pizza by walking is 568.32 minutes.
Time taken to burn caloriesTotal calories in pizza = 2,368Total calories burnt per 30 minutes walk = 125Number of 30 minutes walk to burn all calories = w2,368 = 125 × w
2,368 = 125w
w = 2,368 / 125
w = 18.944
Total time needed to burn all calories = 30 minutes × 18.944
= 568.32 minutes
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