the 95% confidence interval for the proportion of all dies that pass the probe is [0.513,0.616].
What is sample proportion?Sampling is frequently used to estimate the percentage of population that possesses a particular attribute, such as the percentage of all faulty goods which come off an assembly line or the percentage among all buyers that enter a store and make a purchase before leaving. The population proportion is indicated p, while the sample proportion is written p. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.
The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance. When seen as a random variable, it will be represented by the letter P.
How to solve?
An article reported that in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 169 of these passed the probe.
So,p'=201/356=0.56460
The 95% confidence interval for the proportion of all dies that passed the probe will be,
p∈[p'±zα/2√p'(1−p')/n]
p∈[0.56460±1.96×√0.56460(1−0.56460)356]
p∈[0.513,0.616]
So the 95% confidence interval is [0.513,0.616].
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9/10 times 0.5 in fraction form
Answer:
9/20
Step-by-step explanation:
(9/10)*(1/2)
(9/20) times
Answer: tis answer would be 9 over 20
Step-by-step explanation:
if you mix 3 ounces of blue paint and 2 ounces of yellow paint and decided to make 20 ounces how much of the yellow paint will there be?
8 ounce of yellow color required.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
if you mix 3 ounces of blue paint and 2 ounces of yellow paint.
So, we have the composition ratio as 2:3
Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.
Thus, yellow = 2/5 x 20= 8 ounce
Blue= 3/5 x20 = 12 ounce
Hence, 8 ounce of yellow color required.
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let x denote the number of canon slr cameras sold during a particular week by a certain store. the pmf of x is x 0 1 2 3 4 px(x) 0.1 0.2 0.3 0.25 0.15
P(X = 4, Y = 2) = 0.055131
P(X = Y) = 0.35607
From the information given:
X represent no of Canon SLR
The PMF is given as:
X : 0 1 2 3 4
p(x) : 0.1 0.2 0.3 0.25 0.15
p = P(customers that purchase the camera & also purchase an extended warranty.
As a result, the conditional distribution Y provided X approaches a Binomial distribution with n = x and p = 0.55 as the parameter.
[tex]\frac{Y}{X}[/tex] ~ Bin ( n= x , p =0.55) y
= 0.1 ........ x and X = 0,1,2,3,4.
The condition probabilities Y given X is:
[tex]P (\frac{Y = 0}{X = 0} ) =1[/tex]
[tex]P (\frac{Y = 0}{X = 1} ) = 0.45 and P (\frac{Y = 1}{X = 1} ) =0.55[/tex]
[tex]P (\frac{Y = 0}{X = 2} ) = 0.2025 and P (\frac{Y = 1}{X = 2} ) =0.495, P (\frac{Y = 2}{X = 2} ) =0.3025[/tex]
[tex]P (\frac{Y = 0}{X = 3} ) = 0.091125 and P (\frac{Y = 1}{X = 3} ) =0.334125, \\P (\frac{Y = 2}{X = 3} ) =0.408375 and P (\frac{Y = 3}{X = 3} ) = 0.166375[/tex]
[tex]P (\frac{Y = 0}{X = 4} ) = 0.0.041006 and P (\frac{Y = 1}{X = 4} ) =0.0.200475, P (\frac{Y = 2}{X = 3} ) =0.367538[/tex]
[tex]P (\frac{Y = 3}{X = 4} ) = 0.299475 and P (\frac{Y = 4}{X = 4} ) =0.091506[/tex]
Now, the joint P.D (probability Dist.) of X & Y is expressed as:
[tex]P (\frac{Y = y}{X = x} ) = P (\frac{Y = y. X = x}{X = x} )[/tex]
[tex]P( X = x , Y = y) = P(\frac{Y = y}{X =x} ) * P(X =x)[/tex]
The Joint P.D is;
Y Total
0 1 2 3 4
X 0 0.1 0 0 0 0 0.1
1 0.09 0.11 0 0 0 0.2
2 0.06075 0.1485 0.09075 0 0 0.3
3 0.022781 0.083531 0.102094 0.041594 0 0.25
4 0.006151 0.030071 0.055131 0.044921 0.013726 0.15
Total 0.279682 0.372103 0.247974 0.086515 0.013726 1
(a)
P(X=4,Y=2)
From the table above:
P(X=4,Y=2)
= 0.055131
(b)
P(X= Y)
= (P = 0 , Y = 0) + P( X =1, Y =1) + P( X=2, Y=2) + P(X=3,Y=3) + P(X=4,Y=4)
= 0.1 + 0.11 + 0.09075 + 0.041594 + 0.013726
= 0.35607
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If the experiment called for the temperature of the liquid to change by -3\4°c each hour, what would the temperature be at noon? Explain.
The temperature of the liquid at noon would be of:
-2.25ºC.
What is the linear function?The linear function in this problem is defined in the slope-intercept format, as follows
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope, representing the rate of change of the temperature.b is the y-intercept, representing the initial temperature.The values of these coefficients are given as follows:
m = -3/4, b = 0.
Then the function that gives the temperature in x hours after 9 A.M. is of:
y = -3/4x.
Noon is three hours after 9 A.M., hence the estimate is given as follows:
y = -3/4(3) = -9/4 = -2.25ºC.
Missing InformationThe problem states that the initial temperature is of 0ºC at 9 A.M.
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Which expression is equivalent to x 6 – 16x 2
Answer:
Below
Step-by-step explanation:
x^6 -16x^2 = x^2 ( x^4 - 16 ) is one possibility
( you didn't include choices)
Which system of linear equations has a solution of (1, –1)? y1 and y2 y1 and y3 y2 and y3 y2 and y4
The system of linear equations which has a solution of (1,-10) is y2 and y4
What are the 3 types of systems of a linear equation?Dependent: There are countless possible solutions to the system. The same lines are depicted on the equation graphs.
Independent: There is only one solution to the problem. The equations' graphs come together at a single point.
Inconsistent: There is no fix for the system.
What are the 3 solutions of systems of linear equation?There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method
line y2 cross line y4 at (1,-1)
Hence the solution is y2 and y4
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4% of what number is 1.48?
well, is really "x", which oddly enough is the 100%, but we also know that 4% of "x" is 1.48, hmmm what the heck is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.48& 4 \end{array} \implies \cfrac{x}{1.48}~~=~~\cfrac{100}{4} \implies \cfrac{ x }{ 1.48 } ~~=~~ 25\implies x=37[/tex]
The diameter of a cylindrical water tank is 11 ft, and Its height is 8 ft. What is the volume of the tank?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
11 ft
8 ft
Answer:
760ft
Step-by-step explanation:
Use the formula: πr^2h where r = radius(diameter/2) and h = height
radius: 11/2 = 5.5
pi: 3.14
Height: 8
3.14*5.5^2*8
= 759.88
Rounded: 760 ft
A faucet is used to add water to a large bottl that already contained some water. After 25 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 60 ounces of water. Let y be the amount of water in the bottle x t was turned on write a linear equation that models the amount of water in the bottle in terms of x. Oa. Y--5? 45 1 121 o d. Y-5x 49.
We insert m and c values inside the slope-intercept form to get a linear equation that expresses the volume of water in the bottle in terms of t: w = 5t + 5.
Explain Slope-Intercept Form of a Line?A line's equation can be expressed in standard form, slope-intercept form, and point-slope form.The slope-intercept form of the line passing through the points; (x1, y1) and (x2, y2) is; y = mx + cWhere x and y are really the coordinate points, c is really the y-intercept, and m is the slope of the line; m = (y2 - y1)/(x2 -x1).Let w be the quantity of water in the bottle after turning on the faucet.
The following points can be drawn from the provided statement:
(t1, w1) = (4, 25)
(t2, w2) = (11, 60)
The equation of a line's slope-intercept form is:
w = mt + c
Put the values to find slope m.
m = (w2 - w1)/(t2 -t1)
m = 60 - 25 / 11 - 4
m = 5
Put m = 5, t = 4 and w = 2 in equation of the line;
w = mt + c
25 = 5(4) + c
c = 5
We insert m and c values inside the slope-intercept form to get a linear equation that expresses the volume of water in the bottle in terms of t:
w = 5t + 5
Thus, the linear equation that models the amount of water in the bottle is w = 5t + 5.
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Given log_5 2≈0.4308 and log_527≈2.0478, evaluate the expressions. Note: you must use the given values and not values obtained from a calculator for those logarithms.
log_5 3
log_5 (27/50)
The solutions to the logarithm equations are;
1) Log₅3 = 0.6826
2) Log₅(27/50) = -0.383
How to solve logarithm Equations?
There are different rules of logarithm such as;
Product rule which is; Log a + Log b = Log (ab)
Quotient rule which is; Log a - Log b = Log(a/b)
Power rule which is; Log aˣ = x log a
We are given that;
Log₅2 = 0.4308
Log₅27 = 2.0478
We know that 27 = 3³. Thus;
Log₅27 = Log₅3³
Using power rule, we have;
Log₅3³ = 3Log₅3
Thus;
Log₅27 = 3Log₅3 = 2.0478
1) We want to solve Log₅3
We have;
3Log₅3 = 2.0478
Thus;
Log₅3 = 2.0478/3 = 0.6826
2) Log₅(27/50)
Using quotient rule, we have;
Log₅27 - Log₅50
This can also be expressed as;
Log₅3³ - Log₅ (25 * 2)
= 3Log₅3 - [2Log₅5 + Log₅2]
= 2.0478 - 2 - 0.4308
= -0.383
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The Terra family sold its heavily wooded land to
a lumber company for $350,000 at a rate of $700
dollars per acre. If the property averages 8 trees
per acre, which of the following is closest to the
number of trees on the land?
A.
63
B. 500
C. 3,500
D. 4,000
E. 5,608
Answer:
B
Step-by-step explanation: It is very simple. All you have to do is to do 350 000 divided by 700 which gives you 500. That's your answer!
the board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 5.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 41 randomly selected calls. the mean wait time was calculated to be 5.61 minutes. assuming the population standard deviation is 2.50 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 5.00 minutes with a 98% level of confidence?
In this case, the standard error would be standard error = 2.50 / sqrt(41) = 0.342 and the z-score would be z = (5.61 - 5.00) / 0.342 = 1.71
What is the z-score value?A z-score value is the numerical measured value of the relationship of a value to the mean of a group of values and it is measured in the terms of standard deviations from mean value.
What is the formula to measured the z-score value?The z-score is measured by formula z=(x- μ)/ a where x is the raw score, μ is the population mean and a is the population standard deviation. So to calculate z-score, we subtract the population mean from the raw score and divide it by the population standard deviation.
standard error = population standard deviation / sqrt(sample size)
standard error = 2.50 / sqrt(41) = 0.342
Next, you would need to calculate the z-score for the observed mean wait time of 5.61 minutes.
z = (observed mean - population mean) / standard error
z = (5.61 - 5.00) / 0.342
z= 1.71
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the chi-square goodness of fit test assesses whether the observed counts of a categorical variable .
The chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.
The chi-square fit test of goodness assesses whether the proportions of a category or individual outcome in a sample follow a hypothetical proportion population distribution.
In other words, if you take a random sample, the observed proportions follow the values suggested by theory.
Analysts often use the goodness-of-fit chi-square test to determine whether the proportions of categorical results are equal. Alternatively, the analyst can specify the proportions to include in the test.
Alternatively, this test can assess whether observed results follow a discrete probability distribution, for example, Poisson distribution.
As a hypothesis test, the chi-square test of goodness can be used to infer the entire population based on a sample.
Thus, it is true that the the chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.
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Write an equivalent expression by distributing the "-" sign outside the parentheses: 8.2r - (-7s− 1)
Answer:
8.24 + 7s + 1
Step-by-step explanation:
You negate everything in the parentheses, so --7s and --1, which turns into 7s and 1.
Why does the following equation have no solutions? 5-4x-7-10x=-8x-4-6x-10
There are no solutions to linear equations of the following equation
5-4x-7-10x=-8x-4-6x-10, because if they have the same variable term but different constant values on opposite sides of the equation.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation.
The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Given equation is ,
5-4x-7-10x=-8x-4-6x-10
-14x-2=-14x-14
If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
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In January and February of this year, the store made $2,500 from sales of accessories and services. a. Let x represent the amount the store will make from sales of computer products from March through December. Write an equation (slope-intercept form) that represents the predicted amount y that the store will make from sales of accessories and services x for the entire year. Y = 0.05x+2,500 b. If Enrique predicts sales from accessories and services for the entire year will be $5,000, use your equation to determine how much money must be made from computer product sales from March through December. Just your answer by showing our work on explaining our thinking
The equation that represents the predicted amount y that the store will make from sales of accessories and services x for the entire year is y = 0.05x + 2500
As it is given that Enrique can make extra money from the sales of services and accessories for computer products sold by his store and the store makes x dollars selling computer products, he predicted to the store will make 0.05x dollars ($0.05) from selling accessories.we consider x to be dollars of selling computer products, in the month of January and February of this year, the stored made $2,500 from sales of accessories and services.
so the linear equation will be : y = 0.05x + 2500
If sales from accessories and services for the entire year will be $5,000, then the equation will be :
y = 0.05x + 5000
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what is the domain and range for a parabola with the equation y=x^2-x-2
The quadratic equation y = x² - x - 2 has a domain with all real numbers and a range with all values equal to or greater than - 9 / 4.
How to determine the domain and the range of the parabola
The domain of a function is the set of values of x that belongs to the functions and the range of the function corresponds to its set of values of y. In this case we find the definition of a quadratic equation, of which we must determine its domain and range. A brief manner to determine them is modifying the function by deriving its vertex form:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.First, write the quadratic equation:
y = x² - x - 2
Second, modify the equation into its vertex form:
y + 1 / 4 = x² - x + 1 / 4 - 2
y + 9 / 4 = x² - x + 1 / 4
y + 9 / 4 = (x - 1 / 2)²
The domain of all quadratic functions is all real numbers and the range of the quadratic function y = x² - x - 2 is y ≥ - 9 / 4 as the vertex constant is greater than zero.
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FILL IN THE BLANK. In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that _____.
If the slope of a basic regression analysis—in which y is the dependent variable and x is the independent variable—is positive, then there must be a positive correlation between x and y.
What is regression analysis?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A statistical technique that demonstrates the link between two or more variables is regression analysis. The approach examines the connection between a dependent variable and independent variables, often represented in a graph. A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
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In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of a?a = 3a = 8a = 18a = 33.
A linear function with a rate of change of +5 is depicted in the table as m = 13 + 5 = 18.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
We will discover what a linear function is in this article, along with information on its graph, domain, and range.
Additionally, we will learn how to recognize a linear function and how to calculate its inverse.
According to our question-
The graph in the table shows a linear function.
The linear function's general equation is y = ax+b, where a denotes slope and b denotes a constant.
Finding the equation of the linear function at x = 3 y = 13 and at x = 5 y = 23 13 = 3a+b by utilizing the first and third points from the table (1)
23 = 5a+b → (2) find a and b by resolving (1) and (2)
Consequently, a = 5 and b = -2; y = 5x – 2
After then, the equation of y = y = 5*4-2 = 18 was changed by substituting x = 4 in it.
m = 18
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A local charity has put together 20 care packages for
people. Each package contains $15 worth of goodies
and $2.50 per food satchel added to it. If the charity
spent $800 on the care packages how many food
satchels were in each package? Write and solve an
equation for this scenario.
Answer:
The equation is 15x + 2.50y = 800, where x is the number of care packages and y is the number of food satchels. Solving for y, we get y = 32. Therefore, each package contained 32 food satchels.
Step-by-step explanation:
A factory make heet of metal that are 1/2 of an inch thick. If a worker at the factory make a tack of 10 of the heet, how many inche thick will the tack be
We know that the stack of 10 sheets will be 5 inches thick using simple mathematical operations.
What do we mean by mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).
So, we know that:
Each sheet is 1/2 inch thick.
The worker prepares a stack of 10 sheets.
Then, calculate the thickness of the tack as follows:
1/2 * 10
1 * 5
5 inches
Therefore, we know that the stack of 10 sheets will be 5 inches thick using simple mathematical operations.
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which could be the sides of a right triangle? a 2.5 cm, 6.5 cm, 6 cm b 2 cm, 2 cm, 5 cm c 1.5 cm, 2.5 cm, 4 cm d 2 cm, 3 cm, 5 cm
The option that could be the sides of a Right Triangle is 2.5 cm, 6.5 cm, 6 cm , the correct option is (a) .
In the question ,
it is given that ,
four options are given that have the three sides of the triangle ,
we have to select the sides that forms a right triangle .
If the sides form a right triangle , then
square of the longest side is equal to square of the other two sides .
In option (a) the sides are given as 2.5 cm, 6.5 cm, 6 cm .
So ,
(6.5)² = 6² + (2.5)²
42.25 = 42.25
Since LHS = RHS ,
So , Yes , the sides given in option (a) forms a right triangle .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Which could be the sides of a right triangle ?
(a) 2.5 cm, 6.5 cm, 6 cm
(b) 2 cm, 2 cm, 5 cm
(c) 1.5 cm, 2.5 cm, 4 cm
(d) 2 cm, 3 cm, 5 cm
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a subcommittee of the citys planning dept suggests a different plan for the walkways in a city's new park. in the revised blueprint shown below, the walkways are shown in blue and parallel lines indicated by red arrowheads.The right angles of the rectangular park are marked, and the other two angle measures are given in red, find the measure of each numbered angle in the blueprint
The angles are ∠1=42°
∠2=48°
∠3=90°
∠4=42°
∠5=48°
∠6=132°
∠7=90°
∠8=48°
∠9=90°
∠10=132°
∠11=90°
∠12=90°
∠13=48°
∠14=48°
∠15=90°
∠16=90°
∠17=90°
∠18=48°
∠19=48°
∠20=90°
∠21=48°
∠22=42°
What is an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. Angles formed by two rays are located in the plane that contains the rays.
An angle in Plane Geometry is a figure formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, while the common endpoint is referred to as the vertex.
In Euclidean geometry, an angle is the figure formed by two rays known as the sides.
∠1=42°
∠1+∠2=90°
∠2=48°
In ΔABF,
∠2+∠3+42°=180°
48°+∠3+42°=180°
∠3=90°
∠4=42°
Now, ∠3+∠4+∠5=180°
90°+42°+∠5=180°
∠5=48°
∠5+∠6=180°
∠6=132°
∠7=90°
∠8=48°
∠7+∠9=180°
∠9=90°
∠10=132°
∠11+∠3=180°
∠11=90°
∠11+∠12=180°
∠12=90°
∠16=∠11=90°
∠12=15=∠90°
∠13=48°
∠14=48°
∠17=90°
∠1+∠17+∠18=180°
42°+90°+∠18=180°
∠18=48°
∠19=48°
Now, ∠19+∠20+42°=180°
∠20=90°
∠21=48°
Now, ∠21+∠22=90°
∠22=42°
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The volume of a rectangular prism is with height x + 2. Using synthetic division, what is the area of the base?.
The solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.
What is synthetic division?Synthetic division, which is frequently used to determine a polynomial's zeros, is described as a streamlined method of dividing a polynomial with another polynomial equation of degree 1. Comparatively easier to calculate than the long division method, this division method is carried out manually.
we know that the volume of a rectangular prism as where V is volume ,A is area ,H is height
Now, we are given
V=[tex]2x^{3}+9x^{2} -8x-36[/tex]
h=x+2
now, we can find A
V=A*h
A=V/h
now, we can plug it
[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2}[/tex]
now, we can use synthetic division method
so, we can write it as
A=[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2} = 2x^{2} +5x-18[/tex]
So the area of base=[tex]2x^{2} +5x-18[/tex]
Therefore ,the solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.
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let x represent the full length of a certain species of newt. assume that x has a normal probability distribution with mean 110.6 inches and standard deviation 4.9 inches. you intend to measure a random sample of n
If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.
Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.
Sampling distribution of the sample mean:
using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.
The standard deviation of the population is σ = 3.1 and the sample size is n =103, people
The standard deviation σ/√n= 3.1/√103 =0.31.
As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.
x-bar ≈ N (216, 0.31)
μ_{x-bar} = 216
σ_{x-bar} =0.31
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(complete question)
Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.
Marta buys x candles and y books at a store.
• Each candle costs $6, and each book costs $14.
• She spends no more than $65.
• She buys more than 8 items total.
Create two inequalities using x and y to model the situation.
The two inequalities that models the situation are as follows:
6x + 14y ≤ 65
x + y > 8
How to use inequalities to model a situation?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Marta buys x candles and y books at a store.
Each candle costs $6, and each book costs $14.She spends no more than $65.She buys more than 8 items totalTherefore,
x = number of candlesy = number of booksHence, the inequalities are as follows:
6x + 14y ≤ 65
x + y > 8
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the weights for newborn babies is approximately normally distributed with a mean of 5.6 pounds and a standard deviation of 1.2 pounds. consider a group of 1100 newborn babies: 1. how many would you expect to weigh between 4 and 7 pounds? 2. how many would you expect to weigh less than 6 pounds? 3. how many would you expect to weigh more than 5 pounds? 4. how many would you expect to weigh between 5.6 and 8 pounds? hint: do not round until you get your final answer.
The answer to the parts for the given standard deviation are 859, 629 , 308, 477.
What is standard deviation?
Standard Deviation may be a live that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists
Main body:
1 )
mean=5.6
sd=1.2
total number 1000 find number weight between 4 to 9 pounds
z=x-mue/sd
⇒ 4-5.6/1.2=-1.6/1.2 =-1.33
z value by table = 0.09176
⇒z=7-5.6/1.2=1.4/1.2 = 1.666
z value by table =0.95154
effective value 0.95154 -0.09176 = 0.8598
number of children =1000 x 0.8598=859.8
babies expect to weigh between 4 and 7 pounds are 859.
2)
less than 6 pounds
z=6-5.6/1.2=0.4/1.2=0.333
z value by table = 0.62930
number of children born less than 7 pounds =0.62930 x 1000=629.3
means 629 children less than 6 pounds
3)
more than 5 pounds
z=5-5.6/1.2= -0.6/1.2= -0.5
z value as per table -0.5 = 0.30854
number of children born 1000 x 0.30854=308.5
number of children born more than 5 pounds are 308
4)
weight between 5.6 to 8 pounds
z=5.6-5. 6/1.2=0/1.2 =0
value of z by table 0.5
z=8-5. 6/1.2=2.4/1.2 = 2
value of z by table 0.97725
0 value will be 0.97725-0.5000=0.4772
number of children born between 5.6 to 8 pounds=0.4772 x 1000 = 477.2 means 477.
Hence the value are as follows
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Solve the equation. Check for extraneous solutions. 9 |9−8x|=2x+3 please show steps
Answer:
x = 0.6 , x = 2
Step-by-step explanation:
the absolute value function always gives a positive value, that is
| - a | = | a | = a
the expression inside the bars, however , can be positive or negative, so
9 - 8x = 2x +3 ( subtract 2x from both sides )
9 - 10x = 3 ( subtract 9 from both sides )
- 10x = - 6 ( divide both sides by - 10 )
x = 0.6
Or
- (9 - 8x) = 2x + 3
- 9 + 8x = 2x + 3 ( subtract 2x from both sides )
- 9 + 6x = 3 (add 9 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
As a check
substitute these values into the equation and if both sides are equal then they are the solutions.
x = 0.6
left side = | 9 - 8(0.6) | = | 9 - 4.8 | = | 4.2 | = 4.2
right side = 2(0.6) + 3 = 1.2 + 3 = 4.2= left side
-------------------------------------------------------
x = 2
left side = | 9 - 8(2) | = | 9 - 16 | = | - 7 | = 7
right side = 2(2) + 3 = 4 + 3 = 7 = left side
the solutions to the equation are x = 0.6 and x = 2
in a random sample of 38 restaurants it was found that the mean number of employees was 12.6 with a standard deviation of 2.4 employees. find the critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level.
Critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level is - 2.431
What is standard Deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The variation from the mean of each data point is used to determine the standard deviation, which is equal to the square root of variance.
What is mean ?It is basically the average of the given numbers.
The given data is
Sample Size = n = 38
Sample mean = X = 12.6
Sample Standard deviation = S = 2.4
= n - 1 = 38 - 1 = 37
μ₀ = μ ≥ 15
μ₁ = μ < 15 ( left tailed )
d = 0.01
Hence, Critical value = - 2,431
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How would you solve this?
The irregular hexagon has an area of 147 square units. (Correct choice: A)
How to find the area of an irregular polygon
In this problem we have an irregular hexagon that is the result of subtracting a small rectangle from a great rectangle. Likewise, the area of this hexagon is the result of subtracting the area of the small rectangle from the area of the great rectangle. From geometry we know that the area formula for the rectangle is:
A = w · h
Where:
A - Area of the rectangle, in square units.w - Width of the rectangle, in units. h - Height of the rectangle, in units.Now we proceed to determine the area of the irregular polygon:
A'' = A - A'
A'' = 13 · 12 - 3 · 3
A'' = 156 - 9
A'' = 147
The area of the irregular hexagon is equal to 147 square units.
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