If we repeated a hypothesis test 1000 times, the number of times we would expect to commit a Type I error, assuming the null hypothesis were true, would depend on the significance level (α) of the test.
A Type I error occurs when we reject the null hypothesis when it is actually true. The significance level of a test (α) is the probability of making a Type I error when the null hypothesis is true. In other words, if we set a significance level of α = 0.05, we are saying that we are willing to tolerate a 5% chance of making a Type I error.
Assuming a significance level of α = 0.05, if we repeated the test 1000 times, we would expect to make a Type I error in approximately 50 tests (0.05 x 1000 = 50). This means that in 50 out of the 1000 tests, we would reject the null hypothesis even though it is actually true.
However, it is important to note that the actual number of Type I errors we make in practice may differ from our expectation, as it depends on the specific characteristics of the population being tested and the sample sizes used in each test.
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suppose vi pays its phone reps $12 per hour. how many phone reps should it employ if it wants to maximize profit?
Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.
Here,
The formula below can be used to determine the ideal amount of phone representatives:
=> MR = MC
Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.
The following results are obtained by taking the derivative of revenue and cost with regard to n:
=> MR=dR/dn = k
=> dC/dn = 12 for MC.
When we set MR equal to MC, we obtain:
=> k = 12
Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
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write down a model that allows the variance of u to differ between men and women. the variance should not depend on other factors.
The model will be as follows: y = b0 + b1x1 + b2x2 + u
To write a model that allows the variance of u to differ between men and women, the best option is to use the heteroscedasticity model. This model will enable the variances to differ between the genders without depending on other factors.
The model will be as follows: y = b0 + b1x1 + b2x2 + u, Where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model. However, this model does not allow the variance of u to differ between men and women.
To achieve this, we need to modify the model to allow the variance of u to differ between men and women. This can be done by using the weighted regression model. The model will be as follows: y = b0 + b1x1 + b2x2 + u, where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model.
The weights can be represented as: wi = 1/σ^2i, where: wi = weight for observation, iσi = standard deviation of the ith observation. This model will allow the variance of u to differ between men and women without depending on other factors.
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a study was conducted to evaluate the stress level of senior business students at a particular college. forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). for the forty students, the mean emg (electromyogram) activity was found to be 35.8 microvolts. in addition, the standard deviation of the emg readings was found to be 2.5 microvolts. what would be the 99% confidence interval on the true mean emg activity for all seniors in the class? (you should be using statistical software such as statcrunch.) group of answer choices [34.7296, 36.8704] [34.7296, 36.7804] [34.7456, 36.0566] [34.9672, 36.7840]
The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]
To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula
CI = X ± Zα/2 (σ/√n)
where
X = sample mean = 35.8
Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.
σ = sample standard deviation = 2.5
n = sample size = 40
Substituting these values into the formula, we get
CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].
Therefore, the correct option is (a) [34.7296, 36.8704]
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Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes. with the valley floor. If necessary, round to the nearest degree.
The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
What is grade?The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.
To find the angle we use the trigonometric functions:
tan(θ) = grade = rise/run
Given that, the grade of the incline is 78%, then grade = 0.78.
θ = arctan(0.78) ≈ 38.7 degrees.
Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
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Sarah has 43 bananas, she gives Steve 10. How many bananas does she have left?
Answer:
33
Step-by-step explanation:
43-10=33 sarah has 33 bananas ledt
does anyone know the answer??
The point that partitions segment AB in a 1:4 ratio is (-1, -0.4).
How to determine the coordinates of point Q?In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 4.
In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:
Q(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
Q(x, y) = [(1(7) + 4(-3))/(1 + 4)], [(1(-10) + 4(2))/(1 + 4)]
Q(x, y) = [(7 - 12)/(5)], [(-10 + 8)/5]
Q(x, y) = [-5/5], [(-2)/(5)]
Q(x, y) = [-1, -2/5]
Q(x, y) = [-1, -0.4]
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Rewrite the expression 2(10+12) using the distributive property of multiplication over addition
The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.
The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c
a( b + c ) = ab + ac
Using this property, we can rewrite the expression 2(10+12) as
2( 10 + 12 ) = 2(10) + 2(12)
Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:
2(10+12) = 20 + 24
Simplifying further, we get
2(10+12) = 44
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7(x+4)= -21 i need help pls help me its hard 8th grade btw
The given equation is 7(x+4) = -21 . Therefore, the value of x is 7
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation is made up of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Many times the right side of the equation is assumed to be zero. Assuming this does not reduce generality, this can be achieved by subtracting the right side from both sides.
According to the Question:
The given equation is:
7(x+4)= -21
⇒ 7x + 28 = -21
⇒ 7x = -49
⇒ x = 7
Complete Question:
Solve the Equation : 7(x+4)= -21
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when researching a population where it is impossible or impractical to compile a list of the elements, which sampling technique is appropriate to use?
When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique
Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.
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Determine the equation of the circle graphed below.
Answer:
Step-by-step explanation:
Circle centre: (4,7)
Radius: 3
Equation is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (where (h,k) is center, r is radius)
[tex](x-4)^2+(y-7)^2=3^2[/tex]
[tex](x-4)^2+(y-7)^2=9[/tex] (This is the general standard form )
in expanded form,
[tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]
[tex]x^2+y^2-8x-14y+56=0[/tex]
Note: Unless stated either form is an acceptable answer.
w(x)= -5(x-8)(x+4)
What is the maximum height that the stone will reach?
Answer:
(2, 180)
Step-by-step explanation:
w(x)=-5x^2+20x+160
a=-5 b=20
x=-20/2x(-5)
x=2
w(2)=180
2, 180
1. The orthocenter is outside the triangle. 2. An altitude is the same line segment as an angle bisector. 3. If the perpendicular bisector of one side of a triangle intersects the opposite vertex, then the triangle is isosceles
The solution of the match is
(1) Orthocenter (C) The point at which the altitudes of a triangle
meet.
(2) Centroid (D) The point at which the medians of a triangle
meet.
(3) Circumcenter (A) The point of intersection of the perpendicular
bisectors of the sides of a triangle.
(4) Incentre (B) The point at which the three angle bisectors
of a triangle meet.
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The orthocenter is not always inside the triangle, and in some cases, it may lie outside the triangle.
The centroid of a triangle is the point where the three medians of the triangle intersect. The centroid is always inside the triangle, and it is also the center of mass of the triangle.
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. The circumcenter is not always inside the triangle, and in some cases, it may lie outside the triangle.
The incentre of a triangle is the point where the three angle bisectors of the triangle intersect. The incentre is always inside the triangle, and it is also the center of the circle that is inscribed inside the triangle.
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Complete Question:
Match the following.
(1) Orthocenter (A) The point of intersection of the perpendicular
bisectors of the sides of a triangle.
(2) Centroid (B) The point at which the three angle bisectors of
a triangle meet.
(3) Circumcenter (C) The point at which the altitudes of a triangle
meet.
(4) Incentre (D) The point at which the medians of a triangle
meet.
What is the area of this figure? Do not include a label. Number only.
Therefore, the area of the polygon is 24 square units.
What is coordinate?In mathematics, a coordinate is a set of numbers or values that represent the position or location of a point or an object in space. Typically, coordinates are used to describe points in two-dimensional (2D) or three-dimensional (3D) space.
In 2D space, coordinates are usually represented as pairs of numbers (x, y), where the first number (x) represents the horizontal distance of the point from the origin, and the second number (y) represents the vertical distance of the point from the origin.
by the question.
To find the area of the polygon defined by the given coordinates, we can use the Shoelace Formula:
[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|[/tex]
where?[tex](x_{1} ,y_1), (x_2,y_2), ..., (x_n,y_n)[/tex] are the coordinates of the vertices listed in order.
Plugging in the given coordinates in order, we get:
[tex]Area = 1/2 * |(-12 + -5(-3) + (-5)(-5) + (-2)(-2) + 22 + 4(-2)) - (4*(-5) + (-5)(-5) + (-3)(-2) + (-2)2 + 2(-1) + 2*(-5))|= 1/2 * |-2 - 125 + 25 - 4 + 8 + 8 + 20 + 10 + 2 + 10|= 1/2 * |-48|=24[/tex]
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What the answer to this problem?
The coordinates of point Q in the parallelogram is (2b + 2a,2c)
1)How to determine the coordinates of Q?The coordinates are given as:
P(2b, 2c) Q(?, ?) S(0, 0) R(2a, 0)
The parallelogram form of the object indicates that the distances PQ and RS are equal.
The distance RS is calculated as:
RS = ( 2a - 0, 0)
This gives
RS = (2a, 0)
Coordinate Q is calculated as:
Q = P + RS
This gives
Q = (2b,2c) + (2a,0)
Evaluate the sum
Q = (2b + 2a,2c)
Hence, the coordinates of point Q is (2b + 2a,2c)
2)To prove: SQ and PR bisect each otherMidpoint of SQ=(b+ a ,c)
Midpoint of PR=(a+ b, c)
hence, SQ and PR bisect each other.
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12. STEM An engineer is designing solar
panels for a rover that will explore
Mars. The solar panel unfolds to an
isosceles trapezoid. The length of
one leg is 0.1.x -0.5 meters, and the
length of the other leg is 0.3.x-2.1
meters. What is the length of each of
the legs of the solar panel?
Answer:
Step-by-step explanation:
Let's call the length of the shorter leg of the isosceles trapezoid "a" and the length of the longer leg "b".
From the problem, we know that:
a = 0.1x - 0.5 (length of one leg is 0.1.x - 0.5 meters)
b = 0.3x - 2.1 (length of the other leg is 0.3.x-2.1 meters)
Since we know that the trapezoid is isosceles, we know that a = b. So we can set the two expressions equal to each other:
0.1x - 0.5 = 0.3x - 2.1
Now we can solve for x:
0.2x = 1.6
x = 8
Now that we know x, we can substitute it back into the expressions for a and b to find their lengths:
a = 0.1(8) - 0.5 = 0.3 meters
b = 0.3(8) - 2.1 = 0.3 meters
Therefore, each of the legs of the solar panel are 0.3 meters long.
The difference of -12 - 45 will be?? postive or negitive or equle
Answer:33
Step-by-step explanation:45-12=33
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."
What is variability?
To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.
To calculate the range, we subtract the smallest value from the largest value:
Largest value: 58
Smallest value: 10
Range = Largest value - Smallest value = 58 - 10 = 48
Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."
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Helppp.. also show work pls
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
8. A rectangular room is shown.
4x - 1
--x
2
3x + 6
A. (4x-1)-2x
B. (3x2+6) + (4x - 1) + x
C. (4-1)-(3x² + 6)
(3x2+6) + 2(4x - 1) + 2x
Door
X
4x - 1
Port A: Which of the following expressions represents the perimeter of the room without th
door?
(3x²+6)+(x-1)x2+²x = (3x²+6) + 2(9x-=
Port B: What is the perimeter of the room without the door in simplest form? Show you
work.
I only need part b
Answer: 14x + 10
Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:
Perimeter = 2(4x-1) + 2(3x+6)
Simplifying and combining like terms, we get:
Perimeter = 14x + 10
Therefore, the perimeter of the room without the door in simplest form is 14x + 10.
if a random sample of size 555 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 5% ? round your answer to four decimal places.
The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:
σ = sqrt((p*(1-p))/n)
where n is the sample size.
Substituting the values given in the question, we have:
σ = sqrt((0.5*(1-0.5))/555) = 0.0258
To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:
P(|p_hat - p| < 0.05)
where p_hat is the sample proportion.
We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:
P(|p_hat - p|/σ < 0.05/σ)
P(-0.97 < Z < 0.97)
where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:
P(-0.97 < Z < 0.97) = 0.8327
Rounding to four decimal places, we have:
P(|p_hat - p| < 0.05) = 0.8327
Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
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There are 80 people in a choir.
Half the people in the choir are women.
The number of men in the choir is one quarter of the number of women.
The rest of the people in the choir are children.
the number of children in the choir: the number of men in the choir = n: 1
Work out the value of n.
You must show how you get your answer.
Answer:
3
Step-by-step explanation:
Number of people in the choir = 80
Number of women = half of 80 = 40
Number of men in the choir is ¼ of the women = 40/4 = 10
Number of men plus women = 10 +40 = 50
Number of children = 80 - 50 = 30
Ratio of children to men = n:1 = 30:10
Divide both sides by 10
30:10 = 3:1
n = 3
8. describe the center and spread of the chi-square distributions. 9. what is the chi-square test statistic? is it on the formula sheet? what does it measure? 10. how many degrees of freedom does the chi-square distribution have? 11. what is the rule of thumb for all expected counts in a chi-square goodness of fit test?
8. Spread = SD = sqrt(2*df)
9. The difference between the observed and expected frequencies of the outcomes of a set of events or variables.
10. Degrees of 1 freedom does the chi-square distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
8. Describe the center and spread of the chi-square distributions.
Shape - skewed right because can't be zero
µ = df = tipping point
mode = df - 2 = peak
spread = SD = sqrt(2*df)
9. Chi-square test is a non-parametric test (a non-parametric statistical test is a test whose model does not specify conditions about the parameter of the population from which the sample is drawn.). It is used for identifying the relationship between a categorical variable and denoted by χ2.
10. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
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The diameter of a softball is 3.8 inches. Estimate the volume within the softball. Round answers to the nearest
whole number and leave in the answer.
a. Volume: 73
b. Volume: 14
c. Volume: 9
d. Volume: 58
The volume of the ball is 9π (optionC)
What is volume of a sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.
The ball takes the shape of the sphere. The volume of a sphere is therefore calculated as ;
V = 4/3 πr³
r = d/2 = 3.8/2 = 1.9
V = 4/3 × π × 1.9³
V = 27.44 π/3
V = 9π ( nearest whole number)
therefore the volume of the ball is 9π (nearest whole number)
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GM is tangent to circle O at point G, and GS
is a secant line. If mGS = 84°, find
m/SGM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.
What is secant line?Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.
the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:
m∠MGS = 90°
Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.
m∠SGM = 1/2 (mSE - mGE)
where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.
mSE = 2mGS
mSE = 2(84°) = 168°
m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°
Therefοre, m∠SGM = 84°.
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d. if a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an mba degree (to decimals)?
0.4
The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.
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Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
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What is the product of (3x+2) and (x - 7) ?
in a gambling game a person draws a single card from an ordinary 52-card playing deck. a person is paid $19 for drawing a jack or a queen and $5 for drawing a king or an ace. a person who draws any other card pays $2. if a person plays this game, what is the expected gain? (round your answer to the nearest cent.)
the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.
There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.
The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:
Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)
Expected gain = 38/13 - 10/13 - 18/13
Expected gain = 10/13 ≈ 0.77
Therefore, the expected gain is $0.77, rounded to the nearest cent.
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Priya has a recipe for banana bread. She uses 7 1/2 cups of flour to make 3 loaves of banana bread. Andre will follow the same recipe. He will make b loaves of banana bread using f cups of flour. Which of these equations represents the relationship between b and f?
Answer:
Step-by-step explanation:
asdf
if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
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