For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.
The average total number of shoppers on a grocery store in 1 day is 506; the standard deviation is 115.
The number of shoppers is normally distributed.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 506 and standard deviation of 115.
Then, we can say that,
Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P(X<200)
[tex]=P(Z < \frac{200-506}{115})[/tex]
=P(Z<-2.66)
Where, Z is the standard normal variate.
ρ = -0.266
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.0039
For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.
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Jordan and his children went into a restaurant and he bought $26 worth of drinks
and tacos. Each drink costs $2.50 and each taco costs $2. He bought 4 more tacos
than drinks. Write a system of equations that could be used to determine the number
of drinks and the number of tacos that Jordan bought.
The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's assume that number of drinks that Jordan and his children bought is x while the number of tacos is y.
The cost of drinks = 2.50x
Cost of tacos = 2y
Total cost 2.5x + 2y
2.5x + 2y = 26
Given that,
He bought 4 more tacos than drinks.
Therefore,
y = x + 4.
Hence "The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4".
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A wise man once said, "300 reduced by 3 times my age is 84." What is his age?
Answer:
his age would be 72.
300-84=216
216÷3 is 72
What values of u and v make △QRS≅△IKJ?
The values of u and v that makes △QRS and △IKJ congruent triangles are u = 7 and v = 3
How to determine the values of u and v?The triangles are given as
△QRS and △IKJ
The statement △QRS≅△IKJ means that
The triangles △QRS and △IKJ are congruent triangles
This means that the corresponding sides are congruent
So, we have the following equations:
v + u + 15 = 10u - 15v
-4u + 2v + 99 = 7v + 8u
Evaluate the like terms
So, we have
9u - 16v = 15
12u + 5v = 99
Make u the subject in 12u + 5v = 99
So, we have
u = (-5v + 99)/12
Substitute u = (-5v + 99)/12 in 9u - 16v = 15
9(-5v + 99)/12 - 16v = 15
So, we have
9(-5v + 99) - 192v = 180
Open brackets
-45v + 891 - 192v = 180
Evaluate the like terms
-237v = -711
Divide by -237
v = 3
Substitute v = 3 in u = (-5v + 99)/12
u = (-5 x 3 + 99)/12
Evaluate
u = 7
Hence, the values are u = 7 and v = 3
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The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x+4, y+6), give the vertices of △A′B′C′.
PLEASE HELPPPP
Answer:
A' = (6, 3)
B' = (1, 1)
C' = (8, 7)
Step-by-step explanation:
Vertices of triangle ABC:
A = (2, -3)B = (-3, -5)C = (4, 1)Given mapping rule:
(x, y) → (x + 4, y + 6)
This notation tells you that the x-coordinate is translated 4 units to the right, and the y-coordinate is translated 6 units up.
Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':
⇒ A' = (2 + 4, -3 + 6) = (6, 3)
⇒ B' = (-3 + 4, -5 + 6) = (1, 1)
⇒ C' = (4 + 4, 1 + 6) = (8, 7)
Find the measure of
Answer:
50 degrees
Step-by-step explanation:
Line CDF is 180 degrees
76 and 54 and some part of the 180 degrees
1. add 76+54 = 130
2. subtract 180-130 = 50
Cost of 100 grams. Cereal=49p
Pasta=14p
Leah buys 400 grams of cereal and 250 grams of pasta.
Work out the total cost in £
PLEASE HELP ASAP!!
The table describes the quadratic function h(x).
x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
What is the equation of h(x) in vertex form?
h(x) = (x + 2)2 − 3
h(x) = (x + 1)2 − 2
h(x) = (x − 1)2 + 2
h(x) = (x − 2)2 + 3
The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that the values of x and h (x) for the quadratic function is given by;
x = -3, -2, -1, 0, 1, 2, 3,
h (x) = -2, -3, -2, 1, 6, 13, 22
Consider the quadratic function as;
h (x) = ax² + bx + c
Now Substitute x = -3 and h (x) = -2 in quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-3)² + b × -3 + c
- 2 = 9a - 3b + c
And, Plug x = -2 and h (x) = -3 in function we get;
h (x) = ax² + bx + c
- 3 = a × (-2)² + b × -2 + c
- 3 = 4a - 2b + c
And, plug x = -1 and h (x) = -2 in function we get;
h (x) = ax² + bx + c
- 2 = a × (-1)² + b × -1 + c
- 2 = a - b + c
After solving we get:
a = 1 , b = 4 and c = 1
Then
h (x) = ax² + bx + c
h (x) = 1 × x² + 4x + 1
h (x) = x² + 4x + 1
h (x) = x² + 4x + 4 - 4 + 1
h (x) = (x + 2)² - 3
Hence, The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3
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Don’t get how to do this
Answer:
1. 1.4, 1 5/8, 12/5, 8/8
2. 0.88
3. 1/4 and 8/8
4. 12/5 and 2/100
5. 1 5/8 and 1.625
6. 1 1/2
PLEASE HELP! This is due tomorrow!
Determine whether the equation represents a linear or nonlinear function. Explain.
I just need help with these, I have a busy day today :(
The categories of the functions are:
Linear functions: (16) y = 7 - x (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|Nonlinear functions: (15) y = x² + 13 (18) y = x . x . x (20) 7 - y = 2ˣ (22) |x| + 12 = yHow to categorize the functions?The category of the functions are given as
Linear functionsNonlinear functionsAs a general rule, linear functions can take any of the following forms
y = a x = by = xy = mxy = mx + cy - y1 = m(x - x1)Ax + Bx = CWhere the variables a, A, m, b, B, c and C are real numbers
Any equation that do not have the above form is considered a nonlinear function
Using the above forms as a guide, we have the linear equations to be
(16) y = 7 - x (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|
All other equations are nonlinear equations
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Enter a term in the box to make an equation that has infinitely many solutions.
3x+______= 3x+14-6
Answer:
3x+6-14
Step-by-step explanation:
the measure of the angles of a triangle are shown in the figure below. solve for x
64°
x°
40°
Answer:
Sum of angles in a triangle add up to 180°.
x = 180 - 64 - 40
= 76°
What is x and y and how do I solve for it in the future?
The values of x and y in the triangle are 15 and 88 degrees.
How to find the angles of a triangle?A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.
A triangle can be classified base on its sides and angles as equilateral triangle, isosceles triangle and scalene triangles.
An equilateral triangle has three of its sides and angles equal to each other.
An isosceles triangle has 2 sides and angles equal to each other.
A scalene triangle has no sides equal to each other.
Therefore,
The other triangle on the left side is an equilateral triangle.
Therefore, all it sides and angles are equal.
Hence, each angle of the triangle is 60 degrees.
A traversal line cut across the sides of the parallel lines of the triangles formed.
Therefore,
60° = 4x
x = 60 / 4
x = 15
Therefore,
60 + y + 32 = 180(sum of angles in a triangle)
y = 180 - 92
y = 88°
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HELPO PLSS
16. A snack mix contains toasted oat cereal,
pretzels, and nuts in a ratio of 2:2:1 by
mass. What mass of each ingredient is
needed to make the following amounts of
snack mix?
a) 330 g
b) 210 g
c) 500 g
d) 750
Answer:
a) 132 g oat cereal, 132 g pretzels, 66 g nuts
b) 84 g oat cereal, 84 g pretzels, 42 g nuts
c) 200 g oat cereal, 200 g pretzels, 100 g nuts
d) 300 g oat cereal, 300 g pretzels, 150 g nuts
Step-by-step explanation:
a) 330 = 5x
x=66
132 oat cereal
132 pretzels
66 nuts
(And repeat for all masses)
:] Tell me if this is incorrect!
(Brainliest would help a lot lol)
a student group plans to donate school supplies for children in an orphanage. if notebooks that are normally 59 cents each are on sale two for 99 cents, how much can be saved by purchasing ten notebooks at the sale price?
The amount that can be saved by purchasing ten notebooks at the sale price is 95 cents.
What will the price be?The information stated that the notebook are in sale for 2 at 99 cents. The cost for each notebook will be:
= 99 cents / 2
= 49.5 cents
The amount they can be saved will be:
= (59 × 10) - (49.5 × 10)
= 590 - 495
= 95 cents
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When the summer started, Janie needed to fill her empty pool. At first, she used a garden hose to fill the pool, but this was taking too long. She got tired of watching the pool fill so slowly, so she turned off the water and went for a walk. She spotted a truck in the neighborhood that was filling pools and flagged them down to come fill her pool too. They were able to fill the pool at a faster rate. Which graph best represents this situation?
The statement mentions that the pool started empty, which implies that the graph must start at the point (0,0).
Then, the pool slowly filled, so the amount of water in the pool remained constant when Janie turned off the water and went for a walk.
Finally, thanks to a truck in the neighborhood the pool filled up quickly, and when it was filled the amount of water remained constant.
Therefore, the graph that best represents this situation is the one shown in option B.
Find the value of each variable
Answer:
Step-by-step explanation:
since they are verticle angles:
8x+7=9x-4
subtract 8x and add 4
x=11
Assume that a sample is used to estimate a population mean μ . Find the 99% confidence interval for a sample of size 891 with a mean of 20.8 and a standard deviation of 17.6. Enter your answer as a tri-linear inequality accurate to 3 decimal places.19.281Incorrect < μ < 22.319
Solution:
The confidence interval is expressed as
where
[tex]\begin{gathered} \bar{x}\text{ or }\mu\Rightarrow sample\text{ mean} \\ z\Rightarrow confidence\text{ level value} \\ s\Rightarrow sample\text{ standard deviation} \\ n\Rightarrow sample\text{ size} \end{gathered}[/tex]Given a 99% confidence interval for a sample size of 891 with a mean of 20.8 and a standard deviation of 17.6, this implies that
[tex]\begin{gathered} \bar{x}=20.8 \\ s=17.6 \\ n=891 \\ z=2.576 \end{gathered}[/tex]By substituting these values into the above equation, we have
[tex]\begin{gathered} CI=20.8\pm(2.576\times\frac{17.6}{\sqrt{891}}) \\ =20.8\pm1.518866748 \\ Thus,\text{ } \\ \Rightarrow lower\text{ bound:} \\ 20.8-1.518866748=19.28113325 \\ \Rightarrow upper\text{ bound:} \\ 20.8+1.518866748=22.31886675 \end{gathered}[/tex]Hence, we have
[tex]19.281<\mu<22.319[/tex]kx = wv + yx solve for x also please dont change letters around it confuses me
Answer:
[tex]x=\frac{vw}{k-y}[/tex]
Step-by-step explanation:
if f(x)=2x+a what is the value of A satasfying f(2)=2
Answer:
-2
Step-by-step explanation:
Substitute x with 2 and y with 2
2 = 2 * 2 + a
2 = 4 + a
subtract 4 on both sides
2 = 4 + a
-4 -4
-2 = a
i inserted a picture of the question answers to choices A 5/2B 2/5C -2/5D -5/2
If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. Given a value, a/b, the negative reciprocal of a/b is - b/a.
From the information given, the slope of the red line is 2/5. This means that the slope of the green line which is perpendicular to the red line is - 5/2
Option D is correct
on average, 12 customers use the bank's atm during the noon lunch hour. what is the probability that exactly 10 customers will use the atm during the next noon lunch hour? assume the poisson distribution applies.
The probability that exactly 10 customers will use the atm during the next noon lunch hour is 0.0948
How to determine the probability the number of customers is 10From the question, we have the following parameters:
Average number of customers = 12
Number of customers = 10
The above parameters means that:
x = 10
λ = 12
The probability of a Poisson distribution is represented as
P(x) = λˣe⁻λ/x!
This gives
P(x = 12) = 10¹² * e⁻¹⁰/12!
Evaluate
P(x = 12) = 10¹² * e⁻¹⁰/479001600
Solving further, we have
P(x = 12) = 0.0948
Hence, the probability is 0.0948
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The table shows the votes of 900 people in the last elections.
Political
Party
Labour
Conservative
Lib Democrat
Other
Frequency
345
480
60
15
Angle in
Complete the table and draw a pie chart
to represent this information.
Note: Please draw your pie chart in a 'clockwise' direction from the line already drawn
and follow the order from the table (Labour, then Conservative etc...).
The angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.
The table shows the votes of 900 people in the last elections.
Political Party Frequency Angle in
Labour 345
Conservative 480
Lib Democrat 60
Other 15
345 + 480 + 60 + 15 = 900
The total angle in a pie chart is 360
The angle for labour is = 360 (345 / 900) = 138 degree
The angle for Conservative is = 360 (480 / 900) = 192 degree
The angle for Lib democrate is = 360 (60 / 900) = 24 degree
The angle for others is = 360 (15 / 900) = 6 degree
Therefore, the angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.
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if tan 1/3 and cos is less than 0 was in the sin of x
Answer:
[tex] \frac{1}{ \sqrt{10} } [/tex]
The vertices of Triangle FGH are F(-4, -5), G(-3, -2), and H(-1, -3). What are F’G’H’ for a dilation by scale factor of 1/2?
The coordinates of the triangle FGH after dilating by 1/2 is F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)
How to determine the coordinates of FGH after the dilation?From the question, the given parameters are the vertices of Triangle FGH
The vertices are represented as
F(-4, -5), G(-3, -2), and H(-1, -3).
Also, from the question, we have
The scale factor of dilation is
k = 1/2
The above implies that
k represents the scale factor of dilation
The coordinates after the dilation is calculated as
Image of dilation = Vertices of the triangle x Scale factor
Substitute the known values in the above equation
So, we have
Image of dilation = [F(-4, -5), G(-3, -2), and H(-1, -3)] x 1/2
Evaluate the products
So, we have
Image of dilation = F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)
Hence, the image after the dilation is F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)
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Find the midpoint of CD
C=(1,9) and D=(7,-7)
Answer:
(4, 1 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = C (1, 9 ) and (x₂, y₂ ) = D (7, - 7 ) , then
midpoint = ( [tex]\frac{1+7}{2}[/tex] , [tex]\frac{9-7}{2}[/tex] ) = ( [tex]\frac{8}{2}[/tex] , [tex]\frac{2}{2}[/tex] ) = (4, 1 )
Dilate the figure by the scale factor. Then enter
the new coordinates.
C(-1, 1)
B(1, -2)
A(3, 3)
K=9
A'([?], [])
B'([],[])
C'([],[_])
Answer: b (-1,1)
Step-by-step explanation:
when writing a repeating decimal as a fraction why does the fraction always have only 9’s or 9’s and 0’s as digits in the denominator
When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .
Repeating Decimal is a decimal in which after certain point a particular digit or sequence of digit repeats itself infinitely .
For Example : 0.66666666...
When in a fraction the numerator is divided by the denominator , it is not at all necessary that the denominator will always have 9’s or 9’s and 0’s .
We can understand more with the help of an example .
example : 1/3 = 0.3333... is a repeating decimal , which does not have a 9 , 0 in the denominator .
(ii) 5/3 = 1.666666.... is a repeating decimal , which does not have a 9 , 0 in the denominator .
Therefore , When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .
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What is the midpoint between (-3,-2) and (4-7)
The midpoint between the given figures are -2.5 and 5.5 respectively.
What is a midpoint ?A midpoint is defined as that particular point that divides two separate figures into two equal halves or the centre of two endpoints on a number line.
That is;
point a + point b/2
The figures given are :
Point a = -3
Point b = -2
= -3 + -2/ 2
= -5/2
= -2.5
For points 4 and 7 ;
= 4 + 7 / 2
= 11/2
= 5.5
Therefore, the middle or midpoint of -3 and -2 is -2.5 and the midpoint for 4 and 7 is 5.5.
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The Smiths have decided to put a paved walkway of uniform width around their swimming pool. The pool is a rectangular pool that measures 12 feet by 20 feet. The area of the walkway will be 60 square feet. Find the width of the walkway.
***NOTE*** This is a Quadratic Word Problem, so please the Quadratic Method!! Extra 20 BRAINLIST will be reward if work is shown step by step CORRECTLY!!
Answer:
Step-by-step explanation:
12 times 2 =24 60 into 10 so i think it will be 6
The Mendez Family consists of two adults and two children. Their current monthly income is $4800. Calculate the percentage of the total budget for each category.
Percentage spent on transportation is 12%
Percentage spent on Property tax is 11%
Percentage spent on utilities is 9%
Percentage spent on food is 20%
Percentage spent on mortgage payment is 30%
Percentage spent on entertainment is 8%
Percentage spent on miscellaneous is 10%
What are the percentages?
Percentage is the fraction of a number expressed as a number out of 100. In order to convert a number of fraction to percentage, multiiply by 100. The sign that is used to represent percentage is %.
Percentage spent on transportation = (576 / 4800) x 100 = 12%
Percentage spent on Property tax = (528 / 4800) x 100 = 11%
Percentage spent on utilities = (432 / 4800) x 100 = 9%
Percentage spent on food = (960 / 4800) x 100 = 20%
Percentage spent on mortgage payment = (1440 / 4800) x 100 = 30%
Percentage spent on entertainment = (384 / 4800) x 100 = 8%
Percentage spent on miscellaneous = (480 / 4800) x 100 = 10%
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