The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.
What is binomial probability?Binomial probability is the probability based on the binomial distribution.
The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.
The binomial distribution formula is:
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
P = binomial probability
x = number of times for a specific outcome within n trials
{ⁿ \ ₓ} = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
Random sample, n = 8
Specific outcome within n trials = 4
pˣ = 0.5⁴
= 0.0625
qⁿ = (1 - 0.5)⁸ ⁻ ⁴
= 0.5⁴
= 0.0625
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
= 8/4 x 0.0625 x 0.0625
= 2 x 0.0625 x 0.0625
= 0.0078125
= 0.008
Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.
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which expression is equivalent to 19÷6•3+2
19/6 * 3+2, expression is equivalent to 19÷6•3+2
What are equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances.
When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
We may be given equations with algebraic expressions on both sides in some situations.
The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F
Hence, 19/6 * 3+2, expression is equivalent to 19÷6•3+2
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Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles ---- Total Fee
2 Miles ---------------- $15.00
5 Miles ---------------- $19.50
7 Miles ---------------- $22.50
10 Miles ---------------- $27.00
15 Miles ---------------- $34.50
What does the y-intercept mean in this situation?
A) When the cab travels 0 miles, the total fee will be $1.50.
B) When the cab travels 0 miles, the total fee will be $12.00.
C) For every additional mile the cab travels, the total fee increases by $1.50.
D) For every additional mile the cab travels, the total fee increases by $12.00.
The meaning of the y-intercept in this situation is ,
''For every additional mile the cab travels, the total fee increases by $12.00.''
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
From the table, we have the following parameters:
Points (x, y) = (2, 5) and (15.00, 19.50)
So, we would calculate the slope as follows:
Slope = (19.50 - 5)/(15.00 - 2)
Slope = 14.50/13
Slope = 1.11
Hence, We get;
Fixed fee = $15 - (1.12 x 2)
= $15 - 2.24 ≈ $12.00
So, We get;
For every additional mile the cab travels, the total fee increases by $12.00.
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Carlos filled up a 15 gallon bucket with water in 150 seconds. At what rate, in gallons per second, did Carlos fill the bucket?
Answer:
Every 10 seconds is 1 gallon
Given f(x) = 2x2 - 2x - 4, find f(3).
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~[tex]\qquad \sf \dashrightarrow \: f(x) = 2 {x}^{2} - 2x - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 2(3) {}^{2} - 2(3) - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 2(9) {} - 6- 4[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 18{} - 10[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 8[/tex]
What’s 30/50 in simplest for?
Answer:
Step-by-step explanation:
3/5 because 10 is their GCF
Answer:
The answer is 3/5
Step-by-step explanation:
30/50 > 6/10 >3/5
Just divide 30/50 (both numbers by 5) and then divide 6/10 (both numbers by 2). Hope this helped :)
determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
y=-2x
2x+y=3
Answer:
parallel
Step-by-step explanation:
solve for the second equation so y is by itself
y=-2x+3
their slopes are the same so they're parallel
What is the circumference of a circle whose diameter is 15 niches
The circumference of a circle with a given diameter of 15 inches is equal to 15pi which is equal to 47.12 inches.
What is the circumference of a circle?The circumference of a circle is the distance around the edge of the circle.
What is the formula for calculating the circumference of a circle?The formula for calculating the circumference of a circle is given by,
C = 2πr = πd
Where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle and d is the diameter.
It is also known as the perimeter of the circle.
In the question above, we're given,
Diameter of the circle (d ) = 15 inches.
So, using the formula for the circumference of the circle,
Circumference (c) = π d
= π * 15
= 47.12 inches
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jason paid 12.75 for 5.5 pounds of hamburger. how many dollars per pound
Answer: ≈2.32
Step-by-step explanation: So, we can solve this in 2 ways:
1) 12.75 / 5.5 (easiest way)
= 2.3181818181818183
(Rounded to the nearest hundredth) ≈ 2.32
2) Set up a proportional relationship:
[tex]\frac{12.75}{5.5}[/tex] = [tex]\frac{?}{1}[/tex]
Now, divide 12.75 by 5.5, and get about 2.32
Now, let's check our answer:
2.32 x 5.5 = 12.76
So, he paid about 2.32 per pound.
I hope this helped!
Which statement is correct
The yard is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches.
Since 1959, it has been precisely standardised to 0.9144 metres per international agreement. The word "yard" comes from the Old English word "gerd," "gyrd," etc., which was used for measuring sticks, staves, and branches.
The term first appears in the late 7th-century regulations of Ine of Wessex where "yard of land" refers to the yardland, an ancient English tax assessment unit equivalent to one-fourth of a hide.
Around the same time, it was substituted for a branch moved by the wind in the Lindisfarne Gospels description of the messengers from John the Baptist in the Gospel of Matthew. In addition to the yardland, surveying lengths of 15 feet (4.6 m) or 16.5 feet were also referred to as "yards" in Old and Middle English (5.0 m).
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Answer:The correct statement among the given options is:
StartFraction 1 inch Over 2.54 centimeters EndFraction = StartFraction 7 inches Over 17.68 centimeters EndFraction SO 1 is the answer.
Can someone please tell me how do we solve this? Thank you.
Answer:
C
Step-by-step explanation:
find the vertices of this hyperbola 36x^2-y^2-216x+10y+261=0
The required vertices of hyperbola is given as (3, 5±√38).
What is an hyperbola?Hyperbola is part of conic section, and its equation is given as,
[tex](x - h)^2/a^2 + (y - k)^2/b^2 = 1[/tex], where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.
Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1
From above equation,
h = 3 k = 5 a = √38/6 and b = √38
Vertices of the hyperbola is given as,
(h, k ± b) = (3, 5±√38)
Thus, the required vertices of hyperbola is given as (3, 5±√38).
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if bd = 7x - 10, BC= 4x - 29, and cd
= 5x - 9, find x
In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.
BD = 88
BC = 27
CD = 61.
How to find the calculation?Given that BD is equal to 7x, BC is equal to 4x, and CD is equal to 5x,
It is evident from the above figure that Points B, C, and D are parallel. On line segment BD, point C is located.
BD = BC + CD
In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.
7x - 10 = (4x - 29) + (5x - 9)
When we combine similar phrases, we obtain
7x - 10 = (4x + 5x) + (-29 - 9 )
7x - 10 = 9x - 38
38 plus 38 on either side.
7x - 10 + 38 = 9x
7x + 28 = 9x
Take 7x away from both sides.
28 = 9x - 7x
28 = 2x
By 2, divide both sides.
14 = x
Consequently, x has a value of 14.
BD = x - 10 = 7(14) - 10 = 88
88 units are BD's worth.
BC = 4x - 29 = 4(14) - 29 = 27
BC has a value of 27 units.
CD = 5x - 9 = 5(14) - 9 = 61.
The CD is worth 61 units.
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Classify the given scenarios as an observational study, an experiment, or a sample survey.
Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production.
Scenario B: Eight students were chosen at random from the cafeteria and asked if their favorite sport was soccer.
Scenario C: To determine which drug is most effective in treating the common cold, drug A or drug B, cold patients were randomly given one of the two drugs and the results were compared.
Scenario D: To determine which hair growth treatment was most effective in regrowing hair, GrowHair or ReGain, participants were assigned a treatment to determine which showed the most new hair growth.
Scenario E: Students who were taught reading by two different methods are compared in terms of their reading standardized test scores.
Scenario F: Ten employees are randomly selected and asked whether they would be in favor of a new management position in their department.
Classifying the scenarios as an observational study, an experiment, or a sample survey.
Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.
Scenario B: Eight students were chosen at random from the cafeteria and asked if their favorite sport was soccer- a sample survey
Scenario C: To determine which drug is most effective in treating the common cold, drug A or drug B, cold patients were randomly given one of the two drugs and the results were compared- a sample survey.
Scenario D: To determine which hair growth treatment was most effective in regrowing hair, GrowHair or ReGain, participants were assigned a treatment to determine which showed the most new hair growth- experiment.
Scenario E: Students who were taught reading by two different methods are compared in terms of their reading standardized test scores observational study.
Scenario F: Ten employees are randomly selected and asked whether they would be in favor of a new management position in their department- a sample survey.
What is a sample survey, observational study and experiment ?Sample Survey can be defined as the way in which people are randomly choose or pick from a large population so as to draw or reach a conclusion.
Observational study is a type of research method in which people are be observed before conclusion are drawn.
Experiment study is research method in which something is been tested before conclusion are reach.
Therefore Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.
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below you are given a partial excel output based on a sample of 16 observations
(tables)
The estimated regression equation is
a. Ey) = Bo + B1x12x2
b. y Bo + B1x1 + B₂X2 + €
c. 94.425 +2.63 x₁ + 12.56 x2
d. 9 = 12.924-3.682 x + 45.216 x2
The estimated regression equation is :
ŷ = 12.924 - 3.682[tex]x_{1}[/tex] + 45.216[tex]x_{2}[/tex]
S0, option(d) is the correct answer.
In statistics, an estimated regression equation is an equation constructed to model the relationship between dependent and independent variables.
The least squares method is the most widely used method for developing estimates of the model parameters.
For simple linear regression, the least squares estimates of the model parameters β0 and β1 are indicated [tex]b_{0}[/tex] & [tex]b_{1}[/tex]. Using these approximates, an estimated regression equation is constructed: ŷ = [tex]b_{0} + b_{1} x[/tex] . The graph of the estimated regression equation for simple linear regression is a straight-line approximation of the relationship between y and x.
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B varies directly as m. A study shows that m= 6 when b = 5.
The value for the proportional constant, for given data, is 5/6.
What is a Linear Function?A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.
Given that b varies directly as m
so b ∝ m
it says b is directly proportional to m,
removing the proportional sign apply a constant k,
b = km
where k is the proportional constant,
and m = 6 and b = 5
5 = 6k
k = 5/6
Hence the value of the constant is 5/6.
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two functions f and g are defined over the set r of real numbers as follows: f:x > x^2-2x-1 and g:x > x-1. find the value of x for which f(x)=g(x)-2
The values of x for which f(x) = g(x) - 2 are given as follows:
x = 1 and x = 2.
How to solve the equation?The functions for this problem are defined as follows:
f(x) = x² - 2x - 1.g(x) = x - 1.The equation is given as follows:
f(x) = g(x) - 2.
Replacing the values, we have that:
x² - 2x - 1 = x - 1 - 2
x² - 2x - 1 = x - 3
x² - 3x + 2 = 0.
We can factor the equation as follows:
(x - 2)(x - 1) = 0.
Hence the solutions are obtained as follows:
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2x < 8 I need help with this question please
The required solution of the given inequality 2x < 8 is x < 4.
What is Inequality?A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given inequality is
2x < 8
According to given question we have
Write inequality
2x < 8
Divide both sides by 2 we get,
x < 4
Therefore, the required solution of the given inequality 2x < 8 is x < 4.
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Evaluate the following expression if w= 9, x= 7, and y= 1.
11y-5
106
16
6
7
Answer:
357
Step-by-step explanation:
statistical methods that use sample data to answer general questions about a population are called
Inferential statistics is a branch or method of statistics that makes the use of various analytical tools to draw or conclude inferences about the population data from sample data. Apart from inferential statistics, another part is descriptive statistics forms another branch of statistics.
Inferential statistics help to make conclusions about the population while descriptive statistics summarizes the features of the data set.
Inferential statistics helps to develop a good grasp of the population data by analyzing the samples obtained from it.
It helps in making concept about the population by using different analytical tests and tools.
Inferential statistics can be classified into two types of hypothesis testing and regression analysis. Hypothesis testing also includes the use of belief intervals to test the parameters of a population.
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Aimee is estimating 315 x 47 by first
rounding to 1 s.f.
Which of these calculations should Aimee
use?
300 × 0
300 × 50
320 × 0
315 × 50
320 × 50
315x0
300 × 47
315x47
320 × 47
For estimation, she have to make calculation as 320x50/
How do I round to the nearest significant digit?Using one significant figure as an example 3692 should be converted to one square foot (s.f.). The number 3 is the first significant digit because it is the first non-zero digit.6 exceeds 5 in number.We round up because 6 is greater than 5 One plus three equals four, and 3692 is four thousand square feet.
How are estimates calculated?each number to the nearest significant figure.Use the 'approximately equal to' symbol to build the new estimated calculation.Consider units when calculating and use the rounded numbers to provide an approximation.
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Which inequality represents the phrase “A number plus 5 is greater than 12?”
Answer:
the solution and explanation/work is in the images
Answer:
x+5 > 12
Step-by-step explanation:
A number plus 5 is greater than 12 represents x + 5 > 12.
How much solutions does this equation have
y= 1/4x+1
y=1/4x-1
Answer: No Solution
Step-by-step explanation:
There is no solution.
A set of equations with the same slopes and different y-intercepts have no solution.
a florist has 133 roses.she sold 5/7 of them how many roses are left with her
A. 58
B. 38
C. 57
D. 19
Factor completely, use the formula
a³ - 6³ = (a - b)(a² + ab + b²)
3
8m³ - 1
Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1).
What is factor?Factors are the positive integers that can divide a number evenly in mathematics. Say we want to create a product by multiplying two numbers. The factors of the product are the number that is multiplied. Each number has its own factor.
Examples of factors in real life include putting candies in a box, arranging numbers in a pattern, giving chocolates to kids, and many more.
Factors are the figures that can divide an amount precisely. As a result, there is no remainder after division. Factors are the sums of numbers that you multiply to produce another number. A factor is therefore the divisor of another number.
Using the formula
a³ – b³ = (a – b)(a² + ab + b²)
8m³ - 1³ = (8m – 1)(8m² + 8m + 1²)
8m³ - 1³ = (8m – 1)(8m² + 8m + 1²)
8m³ - 1³ = (8m – 1)((8m)² + 8m + 1²)
8m³ - 1³ = (8m – 1)(64m² + 8m + 1)
8m³ - 1³ = (8m – 1)(64m² + 8m + 1)
Thus, Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1)
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What is the measure
Answer:
Angle FSM = 92° OPTION B
Step-by-step explanation:
[tex]5x+32=7x+8[/tex]
[tex]5x-7x=8-32[/tex]
[tex]-2x=-24[/tex]
[tex]x=\frac{-24}{-2} =12[/tex]
Angle FSM:
[tex]FSM=7x+28=7(12)+8=84+8=92[/tex]
Hope this helps
Solve the following problem using the substitution method.
y= (-3x -2)
6x - 2y = 1
Answer:
(x,y) = (-1/4, -5/4)
Step-by-step explanation:
To solve the system of equations using the substitution method, we can start by solving one equation for one variable in terms of the other. Let's start by isolating y in the first equation:
y = -3x - 2
Now we can substitute this expression for y into the second equation:
6x - 2(-3x - 2) = 1
Simplifying this, we get:
6x + 6x + 4 = 1
12x + 4 = 1
12x = -3
x = -3/12 = -1/4
Now we can substitute this value of x back into the first equation to solve for y:
y = -3(-1/4) - 2 = 3/4 - 2 = -5/4
So the solution of this system of equations is (x,y) = (-1/4, -5/4)
You can check this solution by substitute these values back into the original equation and check that both are correct.
Tell me if this helped :)
Answer:
( - [tex]\frac{1}{4}[/tex], [tex]\frac{-5}{4}[/tex] )
Step-by-step explanation:
Substitute -3x - 2 for y
6x - 2y = 1
6x -2(-3x - 2) = 1
6x + 6x + 4 = 1 Combine like terms
12x + 4 = 1 Subtract 4 from both sides
12x + 4 - 4 = 1 - 4
12x = -3 Divide both sides both sides by 12
[tex]\frac{12x}{12}[/tex] = [tex]\frac{-3}{12}[/tex]
x = - [tex]\frac{1}{4}[/tex]
Substitute - [tex]\frac{1}{4}[/tex] for x to solve for y
y = -3x - 2
y = (-3)[tex]\frac{-1}{4}[/tex] - 2
y =[tex]\frac{3}{4}[/tex] - 2
y = [tex]\frac{3}{4}[/tex] - [tex]\frac{8}{4}[/tex]
y = [tex]\frac{-5}{4}[/tex]
In ΔRST, m < R = 100°, r = 20, and t = 12. Find the m < S, to nearest degree.
The measure of angle S in ΔRST to the nearest degree is 44°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know sine rule of a triangle ABC is, a/sinA = b/sinB = c/sinC.
Given, In ΔRST, m < R = 100°, r = 20, and t = 12.
Therefore,
r/sinR = t/sinT.
20/sin100° = 12/sinT.
20.30 = 12/sinT.
sinT = 12/20.3.
sinT = 0.59.
T = sin⁻¹(0.59).
T = 36°.
We know the sum of all the interior angles in a triangle is 180°.
Therefore, m∠R + m∠T + m∠S = 180°.
100° + 36° + m∠S = 180°.
m∠S = 180° - 136°.
m∠S = 44°.
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which set of ordered pairs best represents the linear function f(x) = 1/2x + 2 ?
The set of ordered pairs that best represents the linear function f(x) = (1/2)x +2 is the third option.
H { (-4, 0), (-1, 1.5), (2, 3), (4, 4)}
Which set of ordered pairs best represents the linear function?We want to see which one of the given sets best represents the linear function:
f(x) = (1/2)x +2
To identify the correct option, we need to see which set of ordered pairs only includes points that are on the linear equation.
For example, the first set starts with the point (-4, -7.5)
Replacing these values in our function we will get:
-7.5 = (1/2)*-4 + 2
-7.5 = -2 + 2
-7.5 = 0
This is false, so we can discard the first equation.
(We also can see that f(-4) = 0, so we can also discard the second option).
Now let's look at the third option, the second point is (-1, 1.5)
f(-1) = 1.5 = (1/2)*-1 + 2
1.5 = -0.5 + 2
1.5 = 1.5
This point belongs to the functions graph.
(and on the other set we have the point (-1, 3), that point clearly does not belong to the graph, so we can also discard this option).
Finally, the only remaining option is the third one, H.
{ (-4, 0), (-1, 1.5), (2, 3), (4, 4)}
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What is 5 ÷ 3 in standard form?
The expression, 5 ÷ 3, in standard form, would be 1. 67 x 10⁰.
How to write in standard form?For the purposes of representing large or small numbers in mathematics, a standard form of a number is essentially mentioned. To represent such numbers in standard form, we employ exponents.
It would be easier to understand the correct definition of standard form if you used decimal numbers and adhered to specific restrictions. As is well known, fractions are expressed more simply as decimal numbers.
Basically, in standard form, we try to ensure that only one digits is to the left of the decimal point and then to the right are the rest of the digits in the number. The position of the number is then reflected as a power of 10.
First, solve 5 ÷ 3 :
= 5 / 3
= 1. 667
The result already has only one number to the left of the decimal so the power of 10 would be 0:
= 1. 667 x 10⁰
This is because every number to the power 0, is 1 and so 1.667 x 10⁰ would be the same as 1. 667 x 1 which is correct.
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What’s the numerator for the following rational expression?s/t +7/t =?/t
The numerator of the indicated expression is s+7.
What are the common factors that make up 7?The numbers 7, 14, 21, 28, 35, and 42 are the multiples of 7. 3 and 7 only share 21 as their smallest common number. 21 is the least common denominator as a result. The denominators can be multiplied by one another to find the common denominator for two or more fractions.
We were given the following rational expression:
where p is the numerator and q is the denominator, is the general representation of the rational expression.
So, the expression we provide is:
Assuming the LCM, the following expression can be rewritten as
Comparing (1) with the above-mentioned general rational expression
The numerator of the given expression is p=s+7.
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