The sample size that should be used is 43.
Given that;
The weight of a cereal box is measured as part of a statistical quality control process for the manufacture of cereal. It is understood that the population standard deviation is 0.06 ounces. To attain a margin of error of and a confidence level of 97% 0.02 ounces.
By considering the confidence level scenario, we get to solve how large a sample should be utilized.
The significance level is (α) = 0.03 ( 97% confidence level )
The critical value is (z*) = 2.17 ( From z-table )
The population standard deviation (σ) = 0.06
The margin of error (E) = 0.02
Therefore, the required sample size is;
n = [(z* × σ)/E ]²
n = 42.383
n ≅ 43
Finally, the sample size that should be used is 43.
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Write an equation of the line in slope-intercept form.
Ay
4
y =
(0, 2)
2
(3, 3)
4
AX
Equation of line in slope-intercept form is [tex]y = (\frac{1}{3})x + 2[/tex].
Given in graph,
A(0,2) and B(3,3)
Slope-intercept form => y = mx + c
Slope, m = [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{3-2}{3-0}[/tex]
= [tex]\frac{1}{3}[/tex]
Therefore, y = (1/3)x + c
Put A(0,2) in above equation
2 = (1/3)*0 + c
2 = c
Hence, y = (1/3)x + 2.
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Use the real number line shown below to complete each statement.
The letter best represents −0.1525.
The letter best represents 9
5
.
The letter best represents −1
5
.
A number line goes from negative 0.5 to positive 1.8 and shows points negative 0.5, 0, positive 0.5, 1, and 1.5. Marks divide the space between each number into 5 equal parts. Point a is on the third mark and point b is halfway between the third and fourth mark to the right of negative 0.5, point c is on the second mark after 0, point d is between the second and third mark after positive 1, point e is on positive 1.5, and point f is on the third mark after positive 1.5.
Based on the real number line shown below, each statement should be completed as follows:
The letter b best represents −0.1525.The letter f best represents 9/5.The letter a best represents −1/5.What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Therefore, both -0.1525 and -1/5 would be represented by the letters that are on the left hand side of the real number line while 9/5 would be represented by a letter that is on the right hand side, which are letters b, a, and f respectively;
Letter b ⇒ -0.1525Letter a ⇒ -1/5Letter f ⇒ 9/5Read more on number line here: brainly.com/question/21832213
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according to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?
There should be 12 emails total.
7.200 and 2.683 are the variance and standard deviation, respectively.
What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.Calculation of expected number of emails, variance and standard deviation:
Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683Learn more about variance here:
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13. In the figure, PSR is a straight line. Find RSQ and PQS.
The angle RSQ = 105° and angle PQS = 78°
Given,
In the question:
In the figure,
PSR is a straight line .
To find the angle RSQ and angle PQS.
Now, According to the question;
In ΔQRS,
we know that :
Sum of angle of triangle is 180 degree.
Angle (SQR + QRS + RSQ) = 180°
In the figure,
Angle (23° + 52° + RSQ) = 180°
75° + ∠RSQ = 180°
∠RSQ = 180 - 75
∠RSQ = 105°
We have to find the ∠PQS
Now, PSR is a straight line
In Triangle PSQ
Find the ∠S
105 + ∠S = 180° (Linear Pair)
∠S = 75°
In ΔPQS
Angle(SPQ + PQS + QSP) = 180°
Angle(27° + PQS + 75° ) = 180°
∠PQS = 180 - 102
∠PQS = ∠78°
Hence, The angle RSQ = 105° and angle PQS = 78°
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What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?
Answer:
-15, 9
Step-by-step explanation:
Substituting into the distance formula,
[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]
in rocky mountain national park, many mature pine trees along highway 34 are dying due to infestation by pine beetles. scientists would like to use a sample of size 200 to estimate the proportion of the approximately 5000 pine trees along the highway that have been infested. describe how to select a systematic random sample of 200 pine trees along highway 34.
The given alternate possible way given in the question is not good as the sample does not follow the conditions of the definition of SRS in the study.
SRS is a group or sample size of "n" objects in a population of "n" objects in which all the possible samples would have equal chances to occur or happen.
In the alternate case, There 200 trees sample is taken from near the highway, that can have fewer chances to be infected or can have more infected.
The fact that the sample was not taken randomly and has not been selected in such a way that each tree has equal chances to happen.
The SRS is not possible to obtain as it does not follow the term and conditions of SRS.It creates a bias in the study.Hence we get the required answer.
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Example of a slope intercept form equation with a negative slope and y-intercept of 0
Answer:
An example would be y = -x.
Step-by-step explanation:
Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.
Hope this helps.
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Someone help
Given the function f(x) = 1 + 1/2x³, find the value of f(-4) in simplest form.
Answer: -62.5
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Step-by-step explanation:
to test whether the overall regression equation is statistically significant one uses a. the r2-statistic. b. the standard error statistic. c. the f-statistic. d. the t-statistic.
One can use the f-statistic to test whether the overall regression equation is statistically significant, one uses the f-statistic.
A reasonably high R-squared score makes sense if your regression model includes independent variables that are statistically significant. According to the statistical significance, shifts in the dependent variable are correlated with changes in the independent variables.
The ratio of two variances is known as an F-statistic, and it bears Sir Ronald Fisher's name. Variances gauge how widely apart the data points are from the mean. When the individual data points tend to deviate further from the mean, there are more variances.
The F-test determines that it is unlikely that all of the coefficients will equal zero by adding the predictive power of all independent variables. But it's likely that none of the variables are individually important enough to be statistically significant.
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Calculate (8.42 x 109) − (2.35 x 108).
Answer:
Step-by-step explanation:
663.98
Answer: 663.98
Step-by-step explanation:
(8.42*109)=917.78
(2.35*108)=253.8
917.78-253.8=663.98
A chess board is made using the ratio of square length to king's height, 2.5 inches to 4.5 inches. If a chess board is made with a king's height of 2.25 inches, what is the length of the square? 0.75 inch 1.25 inches 2.25 inches 4.75 inches
The length of the square, given the height of the King, can be found to be 1.25 inch.
How to find the height?The chessboard is made such that its square length as a ratio would be 2 . 5 inches to 4 . 5 inches for the King's height.
If the King's height is 2. 25 inches, the square length of the chess board can be found by the formula:
= ( King's height x Ratio of square length ) / Ratio of King's height
Solving gives us:
= (2 . 25 x 2 . 5 ) / 4.5
= 5.625 / 4. 5
= 1.25 inches
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The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 side touching. What is the total number of white cubes that were used to build the prism?
Answer:34?
Step-by-step explanation: not too sure but yeah
Can anyone write the equation of the graph?
The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.
How to Determine the Equation of the Graph of an Absolute Value Function?The equation that represents the absolute value function is expressed in in vertex form as y = a|x – h| + k, here, the vertex of the graph of the absolute value function is (h, k), while the value of a determines if the graph opens up or opens down.
The point (3, 5) is the vertex of the graph, therefore:
(h, k) = (3, 5)
Plug in h = 3 and k = 5 into, y = a|x – h| + k:
y = a|x - 3| + 5
Find the value of a, by substituting the values of the coordinates of a point on the graph, (x, y) = (5, 7), into the equation y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 = 2a + 5
2 = 2a [subtraction property]
1 = a [division property of equality]
a = 1
Substitute the value of a into the equation y = a|x - 3| + 5:
y = |x - 3| + 5 [equation of the graph].
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What is a counterexample for the conjecture?
If the area of a rectangle is 80 square units, the perimeter must be greater than 35.9 units.
A) A rectangle with length 39.5 units and width 0.5 unit has a perimeter of 80 units and an area of 19.75 square units.
B) A rectangle with length 8 units and width 10 units has a perimeter of 36 units and an area of 80 square units.
C) A rectangle with length 8 units and width 9 units has a perimeter of 34 units and an area of 72 square units.
D) A square with a side length of √80 units has a perimeter of approximately 35.8 units and an area of 80 square units.
The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.
What is counterexample?An instance or example that refutes the proposition is referred to as a counterexample. To determine if a statement is true or not, logic uses this. Counterexamples typically offer strong arguments in opposition to the assertion under discussion.The goal of the inquiry is to demonstrate any possible relationship between the area and perimeter of a rectangle.acc to our question-
The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.
The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.
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For the equation if the parabola y=3x^2-x-2 find the extremum and determine whether it is a minimum or a maximum
PLEASE PLEASE PLEASE
Format: The minimum is y(__)=__
The extrema of the quadratic equation is at the vertex, and it is a minimum at:
y = -1.75
How to find the extremum of the parabola?Here we have the following quadratic equation:
y = 3x^2 - x - 2
We can see that the leading coefficient (the coefficient in the term with the largest exponent) is positive, this means that the parabola opens upwards.
This means that the vertex of the quadratic equation will be a minimum.
Remember that for a quadratic equation:
y = a*x^2 + b*x + c
The vertex is at:
x = -b/2a
So for our quadratic, the vertex is at:
x = -1/(2*3) = -1/6
Evaluating the quadratic equation there we get:
y = 3*(-1/6)^2 - (-1/6) - 2
y = -1.75
That is the minimum of the quadratic.
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What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust
write the inverse: if the 2 smallest sides sum to be larger than the 3rd side, then it is a triangle.
Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."
The statement is given as if the sum of two sides is greater than the third side then it is a triangle.
Now for the inverse we have to convert the given line into double negative.
Hence we get:
If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle
Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.
the various types of conditional statements are:
When the conditional statement's hypothesis and conclusion are both untrue, it is referred to as an inversion of the statement.If both a hypothesis and a conclusion are false at the same time, the statement is contrapositive.A statement is said to be biconditional when it is both conditional and converse at the same time, satisfying both conditions as true.Top learn more about inverse of a statement visit:
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Find the value of the variables in each figure. Explain your reasoning.
The value of the variables x and y in each figure are 28 and 46.3 respectively.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.
Therefore,
5x + 40 = 180,
5x = 180 - 40
5x = 140
x = 28
Also,
(3y-1 ) and 40 are corresponding angles, thus
40 + 3y - 1= 180 ,
3y = 180 - 40 + 1
3y = 139
y = 46.3
Thus, the value of the variables x and y in each figure are 28 and 46.3 respectively.
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help me please
Ayuda pro favor
The values of x after applying congruency to solve the complete shape is 3.5.
What are congruent shapes?Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.
To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.
Comparing ΔQHG and ΔQFE, we can deduce that
ΔQHG ≅ ΔQFETherefore,
x+8 = 3x+13x-x = 8-12x = 7x = 7/2x = 3.5Hence, the values of x in is 3.5.
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Match the following definitions with the correct term.
Answer:
that's biology but
Step-by-step explanation:
autotrophs make their owner food
heterotrophs can't make their own food
photosynthesis is the 3rd one
photosynthesis happens in the chloroplast
photosynthesis makes glucose
I can go in depth about any of these, ask me if needed
3c + bc - 2a if a=6,b=4, and c=10
Answer:58
Step-by-step explanation:
Triangles UVW and VUX are congruent identifier common sides are angles.
Answer:
Common side: UV
Step-by-step explanation:
Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
Question 20 options:
f(–5) = 10, f(0) = 0
f(–5) = 12, f(0) = 5
f(–5) = –20, f(0) = –2
f(–5) = 20, f(0) = 10
Answer:
D
Step-by-step explanation:
f(-5) = 2|-5-5|
f(-5) = 2|-10|
f(-5) = 2 * 10
f(-5) = 20
f(0) = 2|0-5|
f(0) = 2|-5|
f(0) = 2 * 5
f(0) = 10
Please help! The total cost after tax to buy floor tiles is represented by 14f+0.096(14f), where f represents the number of square feet of tile are need to cover the floor.
a. What part of the expression represents the amount of tax that must be paid? Explain. (3 pts)
b. What would the expression be if the cost per square foot was $15 (plus tax)? (3 pts)
Considering the expression in this problem, it is found that:
a) The part of the expression that gives the amount of taxes that has to be paid is: 0.096(14f).
b) The expression would be of: C(f) = 15f + 0.096(15f).
What is the meaning of the expression?The expression for the total cost in this problem is presented as follows:
C(f) = 14f + 0.096(14f).
The meaning of each term is given as follows:
14f means that the cost of each square feet of tile is of 14 f.0.096 x 14f means that an additional 0.096 = 9.6% is paid of tax for each square feet of tile purchased.If the cost per square foot was of $15 instead of $14, the complete expression would be as follows:
C(f) = 15f + 0.096(15f).
That is, the two instances of 14 in the equation were replaced by 15.
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Math 8
Writing Equations from a Graph
Date
Find the slope, y intercept and two points on each line. Then write the equation for each line.
Answer:
1. y=2x+4
2. y=x
3. y=-1/2x+1
4. y=-x+1
Step-by-step explanation:
the formula for these are y=mx+b. Your slope would be m and y intercept would be b. so y=2x+4 would mean that the slope is 2 and y intercept is 4. you can find the points by checking what points are on the blue line.
Which statement is true about 67?
A. its a prime number
B. its a composite number
C. its neither prime or composite
Answer:
a. its a prime number cuz as far as ik 67 has one factor 67x1
Answer:
Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself
help quick!!
Find the equation of the Axis of symmetry and the coordinates of the vertex of the graph of each function
y = 4x² – 2
Answer: (0,-2)
Step-by-step explanation: just multiply
a shipment of 12 television sets contains 3 defective sets. in how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?
The hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the defective sets.
Define the term combination?Combinations are mathematical operations that count the total number of possible configurations for a set of elements is when order of said selection is irrelevant.As per the stated question.
You can select five television from a possible twelve in the sample space.
To acquire at least 2 faulty, therefore:
¹²C₅ = 12!/(7!)(5!) =12*11*10*9*8/(5*4*3*2*1)
¹²C₅ = 11*9*8
Obtaining two or three defective items. (At least 2).
2 defective items are-
(³C₂)(⁹C₄) = 3*9*8*7*6/(4!)
(³C₂)(⁹C₄) =9*7 =63
Three defective items equal -
(³C₃)(⁸C₂) = 1*8*7/2!
(³C₃)(⁸C₂) = 56
Total defective items is 63+56= 119 ways.
Probability = 119/(11*9*8)
Probability = 119/792
Thus, a hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the flawed sets.
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x³+10<9 help pls pls pls pls pls pls
Answer:
x< -1
Step-by-step explanation:
x^3 < 9 - 10
x^3 < -1
x< -1
Answer:
x < -1
Step-by-step explanation:
x³<9-10
x³<-1
x < -1
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Please help i need this today.
Answer:
option c this is no solution for the equations
Answer:
x=5 y=-8 the calc are in the photo