the clock lost 2 seconds per day
Question 3 (4 marks)
A certain retail outlet found that 40% of all customers walking into their store will buy at least one item on
that occasion. Customers make a purchase independently from one another. Calculate the following
probabilities correct to 4 decimal places.
3.1. (2 marks) What is the probability that one or two out of the next four customers will make a purchase?
3.2. (2 marks) What is the probability that at least one out of the next four customers do not make a purchase?
Answer:
3.1 0.6912 = 69.12% probability that one or two out of the next four customers will make a purchase.
3.2 0.9744 = 97.44% probability that at least one out of the next four customers do not make a purchase
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they make a purchase, or they do not. The probability of a customer making a purchase is independent of any other customer. This 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.
40% of all customers walking into their store will buy at least one item on that occasion.
This means that [tex]p = 0.4[/tex]
4 customers:
This means that [tex]n = 4[/tex]
3.1 What is the probability that one or two out of the next four customers will make a purchase?
This is:
[tex]P(1 \leq X \leq 2) = P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.4)^{1}.(0.6)^{3} = 0.3456[/tex]
[tex]P(X = 2) = C_{4,2}.(0.4)^{2}.(0.6)^{2} = 0.3456[/tex]
So
[tex]P(1 \leq X \leq 2) = P(X = 1) + P(X = 2) = 0.3456 + 0.3456 = 0.6912[/tex]
0.6912 = 69.12% probability that one or two out of the next four customers will make a purchase.
3.2. What is the probability that at least one out of the next four customers do not make a purchase?
This is:
[tex]P(X \leq 4) = 1 - P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.4)^{4}.(0.6)^{0} = 0.0256[/tex]
[tex]P(X \leq 4) = 1 - P(X = 4) = 1 - 0.0256 = 0.9744[/tex]
0.9744 = 97.44% probability that at least one out of the next four customers do not make a purchase
four of the angle of a Pentagon are 70°,90°,100° and 145°. What is the side of a fifth angle?
Answer: 135°
Step-by-step explanation:
The sum of the angles in a pentagon is equal to 540°, and the sum of the first four angles is 405°.
70 + 90 + 100 + 145 = 405
540 - 405 = 135
A square has a perimeter of 88 yd. What is the length of each side
Answer:
22 yards
Step-by-step explanation:
p = 4s
88 = 4s
22 = s
Name the three labeled segments that are parallel to EF
Answer:
Answer D
Step-by-step explanation:
The answer here is D since all of the other ones have at least one option that is perpendicular to segment EF.
An investment of $8500 increases in value by 4.5% every year. How long until the investment reaches about $17323.
Answer:
It would take 16 years and 64 days until the investment reaches about $ 17323
Step-by-step explanation:
Given that an investment of $ 8500 increases in value by 4.5% every year, to determine how long it would take until the investment reaches about $ 17323, the following calculation must be performed:
8,500 x (1 + 0.045 / 1) ^ X = 17,323
8,500 x 1,045 ^ X = 17,323
1,045 ^ X = 17,323 / 8,500
1.045 ^ X = 2.038
1,045 ^ 16,175 = 2,038
X = 16.175
1 = 365
0.175 = X
0.175 x 365 = X
63.875 = X
Therefore, it would take 16 years and 64 days until the investment reaches about $ 17323
Find the equation of a circle that is centered at the origin and is tangent to the circle (x−6)^2+(y−8)^2=25
Center: ( 6 , 8 )
Radius: 5
Answer:
[tex] x^2 +y^2 = 25 [/tex]
Step-by-step explanation:
Center of the required circle = (0, 0)
Center of the given circle = (6, 8)
Radius of the given circle = 5 units
Distance between the centers of both the circles
[tex] =\sqrt{(6-0)^2 +(8-0)^2} [/tex]
[tex] =\sqrt{(6)^2 +(8)^2} [/tex]
[tex] =\sqrt{36 +64} [/tex]
[tex] =\sqrt{100} [/tex]
[tex] =10\: units [/tex]
Since, required circle is tangent to the given circle with radius 5 units.
Therefore,
Radius of required circle = 10 - 5 = 5 units
Now, Equation of required circle can be obtained as:
[tex] (x - 0)^2 +(y - 0)^2 = 5^2 [/tex]
[tex] (x)^2 +(y)^2 = 25 [/tex]
[tex] x^2 +y^2 = 25 [/tex]
Decrease £2123 by 8%
Give your answer rounded to 2 DP
The Decreased amount of £2123 by 8% is approximately; £1953.16
How to find percentage decrease a value?We want to decrease £2123 by 8%.
We can do this by the following formula;
Decreased amount = 2123 * (100% - 8%)
Decreased amount = 2123 * 92%
Decreased amount = £1953.16
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Find the surface area of the rectangular prism
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Page 11 of 4
Question 11 (1 point)
Rock musician Donny West is paid 20% on his CD sales and tour video sales.
Last year, he sold one million CDs and 650,000 videos.
The CDs were sold to music stores for $5.25 each and the videos for $6 each.
How much did Donny West receive in royalties last year?
a) $780,000
b) $1,050,000
c) $1,830,000
d) $200,000
e) $130,000
Answer:
dony west receive $1830000
Can someone plz help with this? Thank you so much.
Answer:
A. 3
Step-by-step explanation:
[tex]y = 3x - 8 \\ at \: (6, \: 1) \\ \frac{dy}{dx} = 3 \\ at \: (x, \: y) \\ gradient = \frac{y - 1}{x - 6} \\ 3 = \frac{y - 1}{x - 6} \\ y - 1 = 3(x - 6)[/tex]
In triangle ABC, the complement of < B is < A.
Which statement is not always true?
Answer:
[tex](c)\ \tan B = \sin A[/tex]
Step-by-step explanation:
Given
[tex]\angle A + \angle B = 90[/tex] --- Complement angles
See attachment for complete question
Required
Which is not always true
To do this, we simply test each option
[tex](a)\ \sin A = \cos B[/tex]
The above is always true, if A and B are complements.
Examples are:
[tex]\sin(40) = \cos(50)[/tex]
[tex]\sin(90) = \cos(0)[/tex]
etc
[tex](b)\ \sec A = \csc B[/tex]
The above is always true, if A and B are complements.
The expression can be further simplified as:
[tex]\frac{1}{\cos A} = \frac{1}{\sin B}[/tex]
Cross Multiply
[tex]\sin B = \cos A[/tex]
This is literally the same as (a)
[tex](c)\ \tan B = \sin A[/tex]
The above is not always true, if A and B are complements.
The expression can be further simplified as:
[tex]\frac{\sin B}{\cos B} = \sin A[/tex]
Cross multiply
[tex]\sin B = \sin A * \cos B[/tex]
If A and B are complements. then
[tex]\sin A = \cos B[/tex]
So, we have:
[tex]\sin B = \sin A * \sin A[/tex]
[tex]\sin B = \sin^2 A[/tex]
The above expression is not true, for values of A and B
[tex](d) \cot B = \tan A[/tex]
The above is always true, if A and B are complements.
An example is:
[tex]\cot (55) = \tan (25) = 0.7002[/tex]
etc.
So lost. How do I find the area when the height isn’t shown.
Answer:
By taking the height as x most probably
Step-by-step explanation:
Que sucede cuando dividimos un numero entre si mismo
Answer:
no pasa nada
Step-by-step explanation:
espero que eso te ayude:)
Answer:
Cualquier número dividido entre si mismo da como resultado 1
A triangle has sides of lengths 24, 143, and 145. Is it a right triangle? Explain.
Answer:
Yes, the given triangle is right angled
Step-by-step explanation:
To confirm if the given triangle is right angled, we have to apply pythagoras theorem. It states, if a triangle is right angled then
Hypotenuse² = Base² + Perpendicular²
We know that the longest side is hypotenuse.
ie; (145)² = (143)² + (24)²
(145)² = 20449 + 576
21025 = 21025
As LHS = RHS, it is clear that the given triangle with sides 24, 143 and 145 units is right angled
What is 17% of 13.00
Answer:
The answer is 2.21
Step-by-step explanation:
Answer:
2.21
Step-by-step explanation:
13(.17)
A is a set containing five different numbers. B is a set containing
four different numbers, all of which are members of A. Which of
the following statements CANNOT be true?
Answer:
"the median of a is equal to the median of b" cannot be true.
Step-by-step explanation:
The statement "the range of A is less than the range of B. cannot be true.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
The given statements are:
The mean of A is equal to the mean of B,The median of A is equal to the median of B,The range of A is equal to the range of B,The range of A is less than the range of B.The range of A < the range of B --> the range of a subset cannot be more than the range of a whole set.
Thus, the statement "the range of A is less than the range of B. cannot be true.
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Write the expression 53.7124 x 10 x 3 as a single number.
Answer:
The aswer is buy a rabbit
Step-by-step explanation:
Answer:
1611.372
Step-by-step explanation:
Plssss help I’ll mark u brainliest!!!
Answer:
The answer to the question is C
Somebody knows how to do that?
Answer:
p(g) (85 if 3g)
p(g) (135 if 3g)
p(g) (195 if 6g)
lets move p fwd so that 3+3+2 = 8
8 games = 3(85) + 3(135) + 2(195)
= 255 + 405 + 390
= 1050 yards
Statement would be something like > more than 1000 or designed around a division as proof to prove average or mean per game = 1050/8 = 131.25 mean or even the range 405-255 = 150 range whilst the median would be 135
Last question asks '' How many games has James played when he has scored 85 yards? '' The answer would be 1 game can be shown as g or 1g.
Let me know what the statement choices are and I'd be happy to help.
Step-by-step explanation:
What the answer please help me
Answer:
It's c
Step-by-step explanation:
[tex] \sqrt{ {15}^{2} + {8}^{2} } = 17 \\ \sin(x) = \frac{8}{17} \\ \cos(x) = \frac{15}{17} [/tex]
Write an equation of the line below in the picture?
Answer:
0,-1, -7-2 is the correct answer
Alex collects coins that appreciate (increase in) value. At the store he has found three coins that he likes and can afford. Help Alex decide which coin to buy by selecting two coins and comparing their values over time. 1. Which two coins are you going to compare? Circle the two coins you picked. Coin A Coin B Coin C Finding Equations for the Values 2. What are the current values and appreciation rates of the two coins you selected? (2 points: 1 point for each of 2 coins) Coin Current Value Annual Appreciation Rate 3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use the formula: V(t) = P(1 + r)t, where V(t) is the value of the coin in t years, P is the initial investment, and r is the growth rate. For each of the coins you selected, identify P and r, then set up an equation to find the value of the coin at any t. (2 points: 1 point for each coin) Coin P r Function V(t) = V(t) = Interpreting Exponential Expressions 4. In the coin value formula, V(t) = P(1 + r)t, which part(s) form the base of the exponential function? Which part(s) form the constant, or initial value? Which part(s) form the exponent? (4 points: 1 point for each answer below) Base: Constant, or initial value: Exponent: In this function, if the value of r were to increase, would the value represented by P also increase or stay the same? Why? Explain your answer using terms such as "rate of growth" and "initial value" in the context of the coin problem. 5. Find the value of the coins after 10, 20, 30, and 60 years. Use the function you identified in question 3 to calculate the value. (8 points: 1 point for each time interval) Coin A Coin B Coin C Initial Value 10 years 20 years 30 years 60 years Determining the More Valuable Coin 6. Which coin is more valuable after 10 years? 20 years? 30 years? 60 years? Which coin would you purchase if you intended to keep it longer than 60 years, and why? (Hint: Loo
Answer:
Coin A:
10:$46.18
20:$96.74
30:$190.31
60:$1448.66
Coin B
10:$65.16
20:$106.13
30:$172.88
60:$466.98
Coin C
10:$88.81
20:$131.47
30:$194.60
60:$631.18
I think these are right. I've rounded the answers to the nearest 10th place.
Find the surface area of the sphere.
r = 3 cm
Formulas for Spheres
S.A. = 4tr2
V = grur S.A. = [?] cm2
Round to the nearest tenth.
The surface area of the sphere is 113 square cm
How to determine the surface area?The radius is given as:
r = 3 cm
The surface area is calculated as:
[tex]A = 4\pi r^2[/tex]
So, we have:
[tex]A = 4\pi * 3^2[/tex]
Evaluate the product
A = 113
Hence, the surface area of the sphere is 113 square cm
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Answer: 113
Step-by-step explanation: SA formula is = 4*pi*r^2, input our own values into that, and we get 4*3.14*5^2 = 113.04, round down, and you get 113
What data display would be best for a persons income based on age?
Answer:
where are the answers to select from?
Step-by-step explanation:
HELP PLEASE
The gift shop at a science museum sells lollipops that are made to look like the planets. Each lollipop is shaped like a sphere and has a radius of 121212 mm.
What is the volume of each lollipop?
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Answer:
[tex]V=7.45\times 10^{15}\ mm^3[/tex]
Step-by-step explanation:
The radius of each lollipop is 121212 mm
We need to find the volume of each lollipop. The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Put all the values,
[tex]V=\dfrac{4}{3}\times 3.14\times (121212 )^3\\\\V=7.45\times 10^{15}\ mm^3[/tex]
So, the volume of each lollipop is equal to [tex]7.45\times 10^{15}\ mm^3[/tex].
PLssssssssssssssssssssss help.
What is the product?
StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction
StartFraction x (x minus 4) (x minus 1) Over 2 (x + 4) EndFraction
StartFraction x (x minus 1) Over 2 EndFraction
StartFraction (x + 4) (x minus 4) Over 2 x (x minus 1) EndFraction
StartFraction (x minus 4) (x minus 1) Over 2 x (x + 4) EndFraction
Answer:
A
Step-by-step explanation:
The product of the expression [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
What is an expression?An expression is an algebraic term used for a mathematical statement that include variables and mathematical operations
Below is how to calculate the product
The product expression is given as:
[tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Express x^2 - 16 as a difference of two squares
[tex]\frac{(x - 4)(x + 4)}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Divide the expression
[tex]\frac{x - 4}{2} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Factorize the other fraction
[tex]\frac{x - 4}{2} * \frac{x(x^2 - 2x + 1)}{(x -1)(x + 4)}[/tex]
Further factorize
[tex]\frac{x - 4}{2} * \frac{x(x- 1)(x - 1)}{(x -1)(x + 4)}[/tex]
Divide
[tex]\frac{x - 4}{2} * \frac{x(x- 1)}{x + 4}[/tex]
Multiply the fractions
[tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Hence, the product of [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
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Factor y2 - 5y - 1y+ 5 by grouping.
A) (y + 1)(y – 5)
B) (y - 1)(y – 5)
C) (y - 1)(y + 5)
D) (y + 1)(y + 5)
Answer:
C
Step-by-step explanation:
gghiruufkfhfjttyyyyyy
Answer:
the answer is (y-1) (y-5)
Which sequence of transformations would create an image that is incongruent to the original pre-image? O A translation 4 units to the left followed by a dilation by 2 O A rotation of 90- followed by a translation of 2 units to the right O A reflection across the y-axis followed by a rotation of 180- O A rotation of 270 followed by a reflection across the x-axis.
Answer: Choice A
A translation 4 units to the left followed by a dilation by 2
=============================================================
Explanation:
The following transformations will make the pre-image and image congruent to one another:
ReflectionRotationTranslationIf you apply any of those transformations mentioned above, then the image is an identical copy of the pre-image. Nothing about the figure has changed other than it has been shifted, rotated, or reflected in some way. The figure retains its original size and shape. These transformations are called isometries.
A dilation on the other hand does not preserve the size. "Dilation by 2" means the scale factor is 2, so the image will be twice as large compared to the pre-image, in terms of linear dimension. This means there is no way the image is congruent to the pre-image if a dilation has occurred.
Based on all this, choice A is the answer. Choices B, C, and D only involve the three isometries mentioned earlier and no dilation at all, so they can be ruled out.
plz help 5th grade work
Answer:
I don't see where the question is...
Step-by-step explanation: