Answer:
the slope is 1.75
Step-by-step explanation:
Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight. For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb
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
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:
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]
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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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.
Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
(one-half, seven-quarters)
(one-half, three-halves)
(1, 1)
(1, 3)
Answer:
[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2 - x +2[/tex]
Required
The vertex
We have:
[tex]f(x) = x^2 - x +2[/tex]
First, we express the equation as:
[tex]f(x) = a(x - h)^2 +k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
So, we have:
[tex]f(x) = x^2 - x +2[/tex]
--------------------------------------------
Take the coefficient of x: -1
Divide by 2: (-1/2)
Square: (-1/2)^2
Add and subtract this to the equation
--------------------------------------------
[tex]f(x) = x^2 - x +2[/tex]
[tex]f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2[/tex]
[tex]f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}[/tex]
Expand
[tex]f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}[/tex]
Factorize
[tex]f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]
Factor out x - 1/2
[tex]f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}[/tex]
Compare to: [tex]f(x) = a(x - h)^2 +k[/tex]
[tex]h = \frac{1}{2}[/tex]
[tex]k = \frac{7}{4}[/tex]
Hence:
[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]
Question: Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
Answer: A or 1/2 , 7/4
Step-by-step explanation:
did it on an assignment on EDGE
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
Mrs. Nickel puts a variety of wrapped chocolate candies in a bag. There are 5 silver-wrapped candies, 1 purple-wrapped candy, 2 striped candies, and 4 gold-wrapped candies. If 15 students select one candy at a time out of the bag, without looking, and replace the candy after each draw, how many students would be expecting to select a gold-wrapped candy from the bag?
Answer:
5 students would be expecting to select a gold-wrapped candy from the bag.
Step-by-step explanation:
Since Mrs. Nickel puts a variety of wrapped chocolate candies in a bag, and there are 5 silver-wrapped candies, 1 purple-wrapped candy, 2 striped candies, and 4 gold-wrapped candies, if 15 students select one candy at a time out of the bag, without looking, and replace the candy after each draw, to determine how many students would be expecting to select a gold-wrapped candy from the bag, the following calculation must be performed:
5 + 1 + 2 + 4 = 12
4 gold-wrapped candies out of 12 in total
4/12
15 x 4/12 = X
15 x 0.333 = X
5 = X
Therefore, 5 students would be expecting to select a gold-wrapped candy from the bag.
PLssssssssssssssssssssss help.
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
ANSWER FAST I JUST NEED ANSWER
Answer: 18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
The graph shows 180 pages on it, and if you go over and down then it shows chapter 18.
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].
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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Sarah and all of her siblings have brown hair. She concludes that if her parents have another child, he or she will have brown hair. Is this an example of inductive or deductive reasoning?
a) Deductive.
b) Inductive.
c) Both deductive and inductive.
d) Neither deductive nor inductive.
Answer:
b) Inductive
Step-by-step explanation:
It is correct to say that this is an example of inductive reasoning, because the reasoning is based on a situational perception and not on actual logic. Sarah based her reasoning on a premise that if she and her brothers have brown hair, then if she had another brother, he would also have brown hair.
Plssss help I’ll mark u brainliest!!!
Answer:
The answer to the question is C
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:
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Answer:
the answer is (y-1) (y-5)
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
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:
plz help 5th grade work
Answer:
I don't see where the question is...
Step-by-step explanation:
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]
Write an equation of the line below in the picture?
Answer:
0,-1, -7-2 is the correct answer
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
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:
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]
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.
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.
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)
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
c = 9.76165m
c = 9.8m
Step-by-step explanation:
The formula for this is [tex]a^{2} +b^{2} =c^{2}[/tex]
or [tex]c = \sqrt{a^{2} +b^{2} }[/tex]
Need help with using the graph to find the numbers
Assignment is about evaluating composition of functions from graphs anything helps
Answer:
f(2) = -3
g(-3) = -5
Step-by-step explanation:
----------------------
Find the surface area of the rectangular prism