The main threat to concluding that the tutor was effective in helping students understand confounding and obscuring variables is the issue of 'practice effects'.
Practice effects occur when exposure to specific materials or questions during a study can artificially inflate performance on subsequent measures, such as an exam.
In this case, if the practice questions from the tutor were exactly the same as those on the exam.
Then the students who interacted with the tutor may have had an advantage on the exam .
Due to familiarity with the questions rather than a true understanding of the material.
The use of the same practice questions in the tutor and on the exam .
It represents a potential confounding variable that could affect the interpretation of the results.
It is possible that the tutor may have been effective.
But it is also possible that the practice effect of the repeated questions contributed to the observed improvement in performance.
Future research could use different practice questions in the tutor and on the exam.
Use a different exam altogether to assess performance.
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what is 88 closer to 64 or 125
Answer:
64
Step-by-step explanation:
Answer:
64...i think
Step-by-step explanation:
125 - 88=37
88-64=24
PLS MARK BRAINLIEST
La familia de una de tus compañeras, que disponía de un terreno con 7 lotes colindantes, y se vieron en la necesidad de venderlos. Establecieron un precio por metro cuadrado de 800 pesos y tienen que calcular el costo, con base en los metros cuadrados que tiene cada lote. Determina el área de cada terreno, así como su precio
The area and cost of each of the lots is given below
What is the area?The area and cost of each of the lots is calculated below
To calculate the rectangle trapezoid, it will be:
B = 140m
h = 50m
b = 70m
Note that Area of Lot 1 : A =(B+b)h/2
Hence Height will be:
A= (140m+ 70m) 50m/2
A = 5250 m²
Cost: C = 5250m² *800 pesos = $4,200,000
Lot 2 is another rectangle trapezoid:
B = 150m
b = 80m
h = 50m
Area: A= (150m+ 80m)50m/2
A = 5750 m²
Cost: C = 5750m² x 800 pesos = $4,600,000
So, for Lot 3 which is a rectangle:
b = 70m
to = 50m
Area: A =a x b
W=50m x 70m
A = 3500 m²
Cost: C = 3500m² x 800 pesos = $2,800,000
Lot 4 is a right triangle:
b = 70m
h = 50m
Area: A =b x h/2
A= (50m x 70m)/2
A = 1750 m²
Cost: C = 1750 m² x 800 pesos = $1,400,000
So for Lot 5 that is a rhomboid:
b = 150 base meters
h=50m
Area: A=b x h
A= (150m x 50m
H = 7500 m²
Cost: C = 7500m² x 800 pesos = $6,000,000
So, for Lot 6 that is an isosceles triangle:
b = 140m
h= 50m
Area: A =b x h/2
A= (140m x 50m)/2
A = 3500 m²
Lastly, the Cost: C = 3500m² x 800 pesos = $2,800,000
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See transcribed text below
The family of one of your colleagues, who had a piece of land with 7 adjoining lots, and they found themselves in need of selling them. They established a price per square meter of 800 pesos and they have to calculate the cost, based on the square meters that each lot has. Before continuing, review the terrain sketch and answer the questions
What is the area and cost of each of the lots?
please help...................
Which coordinates below form a rectangle that is a translation of the rectangle
shown above?
A(0, 3), (0, 9), (5, 3), (5,9)
B(0, 0), (0, 3), (5, 0), (5, 3)
C(0, 0), (4,0), (0, 4)
D(7, 0), (7, 3), (12, 0), (12, 3)
The point R(-2, 9) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point, R′?
The coordinates of the resulting point, R′ are R' = (-9, -2)
What are the coordinates of the resulting point, R′?From the question, we have the following parameters that can be used in our computation:
The point R(-2, 9) is rotated 90° clockwise around the origin.
This means thar
R = (-2, 9)
Rotation rule = 90° clockwise around the origin.
The rotation rule of 90° clockwise around the origin is
(x,y) becomes (y,-x)
So, we have
R' = (y, -x)
Substitute the known values in the above equation, so, we have the following representation
R' = (-9, -2)
Hence, the coordinates of the resulting point, R′ are R' = (-9, -2)
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3
33 points
Given the bbjective Function:
Revenue =75x + 85y
and the critical points:
(0,0) (180, 120) (300,0)
Which critical point will yield a maximum revenue?
the (0,0)
the (180, 120)
the (300,0)
Cannot be determined with this information
Can be more than 1 answer
The critical point (180, 120) will yield a maximum revenue of 23,700. So, the correct answer is the (180, 120).
To determine which critical point will yield a maximum revenue, we need to evaluate the objective function at each point and compare the results.
Objective Function: Revenue = 75x + 85y
1. Point (0,0):
Revenue = 75(0) + 85(0) = 0
2. Point (180, 120):
Revenue = 75(180) + 85(120) = 13500 + 10200 = 23700
3. Point (300,0):
Revenue = 75(300) + 85(0) = 22500 + 0 = 22500
Comparing the revenues at each point:
(0,0) - Revenue = 0
(180, 120) - Revenue = 23700
(300,0) - Revenue = 22500
The critical point (180, 120) will yield a maximum revenue of 23,700. So, the correct answer is the (180, 120).
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The owner of a company asks a manager, "How many hours does an employee work each week?" a. Is this a statistical question? Explain. The question a statistical question because there. Question 2 b. The manager records the number of hours worked each week by several employees. Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data. Hours worked 40 39 40 39 47 38 41 37 40 41 40 43 40 41 40 38 40 42 40 42 Most of the data are clustered around. There is a peak at and a gap between. Question 3 c. Use the distribution of the data to answer the question. Most employees work about hours each week
This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.
a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.
b. Here's a dot plot of the data provided:
37: •
38: ••
39: ••
40: ••••••••
41: •••
42: ••
43: •
47: •
The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.
c. Based on the distribution of the data, most employees work about 40 hours each week.
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can someone help? asking for a friend (literally) I’d really appreciate it!
The graphs of the sinusoidal function for the question 1 to 4 created with MS Excel are attached
5. The function is; y = cos(θ) + 2
6. The function is; y = sin(2·θ) - 4
What is a sinusoidal function?A sinusoidal function is a smooth periodic or repetitive function based on the sine or cosine of an angle.
The equations for the graphs in the sinusoidal function indicates that we get;
The period = 2·π/B
The horizontal shift = -C/B
The vertical shift = D
Where;
B = The coefficient of the angle, θ
C = The constant within the parenthesis
D = The constant term outside the sine or cosine function parenthesis
1. y = 2·sin(2·θ + 1)
The function indicates that the amplitude is 2, the period is 2·π/2 = π, the vertical shift is 0, and the horizontal shift is -1/2
Please find attached the graph of the function, created with MS Excel
2. y = -cos(θ) - 2
The amplitude is 1
The period is 2·π
The horizontal shift is 0
The vertical shift is -2
Please find attached the graph of the function y = -cos(θ) - 2, created with ms Excel
3. y = 4·cos(3·θ -2)
The amplitude is 4
The period is 2·π/3
The horizontal shift is 0
The vertical shift is -2
Please find attached the graph of the function y = 4·cos(3·θ -2), created with MS Excel
4. y = 3·sin(6·θ) - 1
The amplitude is 3
The period is π/3
The horizontal shift is 0
The vertical shift is -1
Please find attached the graph of the function y = 3·sin(6·θ) - 1, created with MS Excel
5. The points on the graph are;
Peak; (0, 3)
The next adjacent trough; (180, 1)
The adjacent peak; (360, 3)
Therefore;
The amplitude is 1
The period is 360°
The horizontal shift is 2
The vertical shift is 0
The peak point at θ = 0, indicates;
The function is; y = cos(θ) + 2
6. The points on the graph are;
Peak; (45, -3)
The next adjacent trough; (135, -5)
The adjacent peak; (225, -3)
Therefore;
The amplitude is 1
The period is 180 = π radians
The horizontal shift is 0
The vertical shift is -4
The function is; y = sin(2·θ) - 4
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Find the surface area of the net below in square centimeter 12,9,9
A study was conducted by the Director of Parking and Transportation at a large university. One variable under study is the method of transportation to campus used by off-campus students. The choices for students on the survey were drive alone, carpool, public transportation, walk, or a paid driving service. Which type of variable is this?
The type of variable being studied in this case is a categorical variable, specifically a nominal variable.
What s the type of variable in the question?Categorical variables are variables that can be classified or grouped. The categories in this example are the various modes of transportation utilized by off-campus students (drive alone, carpool, public transportation, walk, or a paid driving service).
Nominal variables are categorical variables with no intrinsic order or numerical value. Because the various modes of transportation in this study have no numerical value or inherent order, they are classified as nominal variables.
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Need help with these questions!! Person who answers will be marked brainliest
Answer:
1.5 for both
Step-by-step explanation:
Taking each number and multiplying it by 1.5 will get you the dilated coordinates
Determine whether each situation can have only one value for the variable or more than one value for the variable.
select only one or more than one for each situation.
the total cost to buy t movie tickets for $8.50 each
o only one
more than one
the number of ounces of tomato juice, j, in 2 quarts
o only one
o more than one
the number of pizzas to order, p, if each person eats 2 slices
only one
more than one
the greatest number of $6 notebooks, n, ed can buy with $36
only one
0. more than one
the area, a, of a wall with a length of 5 meters and a height of 3 meters
o only one
o more than one
The total cost to buy t movie tickets for $8.50 each is o only one, the number of ounces of tomato juice, j, in 2 quarts o only one, the number of pizzas to order, p, if each person eats 2 slices more than one, the greatest number of $6 notebooks, n, ed can buy with $36 only one, and the area, a, of a wall with a length of 5 meters and a height of 3 meters o only one.
1. The total cost to buy t movie tickets for $8.50 each:
- Only one value for the variable
The cost to buy a specific number of movie tickets at a fixed price will have only one total cost value.
2. The number of ounces of tomato juice, j, in 2 quarts:
- Only one value for the variable
There are 32 ounces in a quart, so 2 quarts will always have 64 ounces.
3. The number of pizzas to order, p, if each person eats 2 slices:
- More than one value for the variable
The number of pizzas needed depends on the number of people attending, which can vary, leading to different values for p.
4. The greatest number of $6 notebooks, n, Ed can buy with $36:
- Only one value for the variable
Since each notebook costs $6, Ed can buy exactly 6 notebooks with $36 (36/6 = 6).
5. The area, a, of a wall with a length of 5 meters and a height of 3 meters:
- Only one value for the variable
The area of a rectangle is calculated by multiplying its length and height. In this case, the area will always be 15 square meters (5m x 3m = 15m²).
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given m||n, find the value of x
Answer:
Step-by-step explanation:
The value of x is 19 if the lines l and m are parallel.
The lines l and m are parallel
The corresponding angles are equal
We have to find the value of x
6x-9 = 5x+10
Let us take all the variable terms on one side
6x-5x=10+9
x=19
Hence, the value of x is 19 if the lines l and m are parallel.
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The table shows the number of turkey and ham sandwiches sold by Derby’s Deli for several days in one week Sandwiches Sold at Derby’s Deli Day Turkey Ham Monday 7 9 Tuesday 13 11 Wednesday 8 8 Thursday 15 6 Friday 12 16 What is the difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold?
The difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold is 3.
First, let's find the median number of turkey and ham sandwiches sold.
To find the median:
1. Arrange the data in ascending order.
2. If there's an odd number of data points, the median is the middle value. If there's an even number of data points, the median is the average of the two middle values.
Turkey sandwiches sold: 7, 8, 12, 13, 15
Ham sandwiches sold: 6, 8, 9, 11, 16
Now let's find the medians:
Turkey median: There are 5 data points, which is odd, so the median is the middle value, 12.
Ham median: There are 5 data points, which is odd, so the median is the middle value, 9.
Finally, let's find the difference between the medians:
Difference = Turkey median - Ham median
Difference = 12 - 9
Difference = 3
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consider the first month's sales data for the south region.
select the correct answer from each drop-down menu.
for the south region, the proportion of sales from current stores is approximately______ %.
a.63
b.37
c.58
d.24
because this proportion is_________
a. relatively close to
b. significantly different from
the sales director's statistical model, the data is______
a. inconsistent
b. consistent
with the model.
Answer is:
For the south region, the proportion of sales from current stores is approximately 58 %.
because this proportion is relatively close to the sales director's statistical model, the data is consistent with the model.
The given information states that the proportion of sales from current stores in the South region is approximately 58%. This value falls within the range of the sales director's statistical model, which could be an estimated value or a range of values based on past data or other sources. Since the proportion of sales falls within the expected range, the data is consistent with the model. This means that the actual value observed is not significantly different from the expected value, and there is no evidence to suggest that the model needs to be revised or updated.
Therefore, the answer to the second drop-down menu is "consistent". If the actual proportion of sales from current stores in the South region was significantly different from the expected value in the sales director's statistical model, then the answer would be "inconsistent". However, since the observed proportion is relatively close to the expected value, the data is consistent with the model.
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Which shapes contain at least one obtuse angle?
Select each correct answer.
Responses are the pictures
Answer:
Shape 1 and Shape 3
Step-by-step explanation:
An obtuse angle is an angle that is greater than 90° but less than 180°.
We can see that the first shape has 2 angles that are greater than 90°, making this a correct choice.
The second shape has 4 boxes, meaning the angles are exactly 90°, making this incorrect.
The third shape has 6 angles that are greater than 90°, making this another correct choice.
The last shape has all 3 angles under 90°, making this also incorrect.
So, the 1st and 3rd shapes are correct.
Hope this helps! :)
Victoria drove 76 miles, burning 4 gallons of gasoline. She knows the total number of miles she can drive is proportional to the number of gallons of gas she burns and wants to create an equation that can be used to predict the number of miles she can drive for any number of gallons of gas used. Drag the correct values to create an equation which will accurately represent the total number of miles, m, Victoria should expect to be able to drive if she uses g gallons of gasoline
The equation that represents the total number of miles, m, Victoria should expect to be able to drive if she uses g gallons of gasoline is m = (19g).
We can determine the proportionality constant by dividing the total number of miles driven (76) by the number of gallons of gasoline burned (4), which gives us 19 miles per gallon (76/4 = 19).
We can then use this proportionality constant to create the equation m = (19g), where m represents the total number of miles Victoria should expect to be able to drive if she uses g gallons of gasoline. This equation tells us that for every additional gallon of gasoline burned, Victoria should expect to be able to drive an additional 19 miles.
For example, if Victoria were to burn 6 gallons of gasoline, she should expect to be able to drive 114 miles (6 x 19 = 114). This equation assumes that Victoria's car has a constant fuel efficiency of 19 miles per gallon.
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Tables
Contingency Tables
10. In recent years, concerns have been expressed about adverse health effects from amalgam
dental restorations, which contain mercury. The table shows results from a study in which
some patients were treated with amalgam restorations and others were treated with composite
restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value
needed to test for independence between the type of restoration and sensory disorders.
Adverse health
condition reported
No adverse health
condition reported
01136
Amalgam
36
231
Composite
28
239
(1 poin
The critical value needed to test for independence between the type of restoration and sensory disorders is 6. 635.
How to find the critical value ?To evaluate the correlation between sensory impairments and restoration type, a chi-square test of independence can be used. To determine the critical value for this statistical test, consult the chi-square distribution table at a 0.01 significance level.
The degrees of freedom for a chi-square test of independence :
Degrees of Freedom ( df ) = ( Number of Rows - 1 ) x ( Number of Columns - 1 )
The number of rows from the table = 2
Number of columns is also = 2
The df is therefore:
df = (2 - 1) x (2 - 1) = 1 x 1 = 1
The critical value for χ² with 1 degree of freedom at a 0. 01 significance level can be founding using the Chi - Square table to be approximately 6.635.
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Full question is:
In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which contain mercury. The table shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value needed to test for independence between the type of restoration and sensory disorders.
And 7/8 hours Greg reads 2/3 chapters. What is the unit rate in chapters per hour? Write your answer in simplest form
The unit rate for chapters per hour is calculated as 16/21
How to find the unit rateIn order to find the unit rate for the number of chapters Gregory reads in an hour, we must firstly divide the total amount of chapters read by the amount of hours devoted to the activity:
= 2/3 chapters ÷ 7/8 hours
= 2/3 chapters × 8/7 hours
= 16/21 chapters per hour
Consequently, the unit rate for chapters per hour is calculated as 16/21, which already exists in its most simplified form.
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What is the surface area of this right triangular prism?
The surface area of the triangular prism is 720in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as
SA = 2B +ph
where p is the perimeter of the base and h is the height of the prism.
Base area = 1/2 bh
= 1/2 × 24 × 5
= 12 × 5
= 60 in²
Perimeter of the base = 24 +13 +13
= 50 in²
the height of the prism = 12 in
therefore SA = 2 × 60+ 12 × 50
= 120 + 600
= 720 in²
Therefore the surface area of the prism is 720 in²
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If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)? (1 point)
41
35
11
−35
As per the given information in the question, we can compute that the correct option is C) 11.
According to the question:
[tex]f(x)=x^{2} -6x-4[/tex]
[tex]g(x)=5x+3[/tex]
Therefore,
[tex](f+g)(x)= f(x)+g(x) \\
=x^{2} -6x-4+5x+3 \\
=x^2-x-1[/tex]
Now, to find (f+g)(-3):
substituting x=-3 in the above equation
we get,
[tex](f+g)(-3)= (-3)^2-(-3)-1 \\
= 9+3-1 \\
=11[/tex]
Hence (f+g)(-3)=11
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Include all given digits mercury venus earth mars jupiter saturn uranus neptune distance from the sun (au) 0. 39 0. 72 1 1. 52 na 19. 18 30. 06 orbital period (years) 0. 242 0. 0616 1 1. 88 na 84. 0 165
The values of distance and orbital periods of planets Mercury is 0.39AU and 0.242yrs,Venus 0.72AU distance and 0.616yrs,Earth 1AU distance and 1yrs,Mars 1.52AUdistance and 1.88,Jupiter 5.2AUdistance and 1.88 ,Saturn N/Adistance and NA years as infromation is not provided,Uranus 19.18AUdistance and 84yrs,Neptune 30.06AUdistance and165yrs.
Based on the given information, here are some key facts about the planets in our solar system:
- Mercury is the closest planet to the Sun, with a distance from the Sun of 0.39 astronomical units (AU). It has an orbital period of 0.242 years.
- Venus is the second planet from the Sun, with a distance of 0.72 AU. Its orbital period is 0.616 years.
- Earth is the third planet from the Sun, with a distance of 1 AU. Its orbital period is 1 year.
- Mars is the fourth planet from the Sun, with a distance of 1.52 AU. Its orbital period is 1.88 years.
- Jupiter is the fifth planet from the Sun, with a distance of 5.2 AU. Its orbital period is 11.86 years.
- Saturn is the sixth planet from the Sun, with a distance of N/A AU. Its orbital period is N/A.
- Uranus is the seventh planet from the Sun, with a distance of 19.18 AU. Its orbital period is 84 years.
- Neptune is the eighth planet from the Sun, with a distance of 30.06 AU. Its orbital period is 165 years.
Therefore the the distance and orbital periods are in increasing arrangement mercury, venus, earth, mars, jupiter, saturn ,uranus, neptune distance from the sun.
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A recent survey of fortune 500 firms found that on average, they contribute $332.54 per month for each salaried employee's health insurance. if you are told that almost all salaried employees at fortune 500 firms receive a health insurance contribution between $220.61 and $444.47, and assuming a bell-shaped distribution, what must the standard deviation for this data be
The standard deviation for the data must be approximately $111.93.
How to calculate the standard deviationSince we are given a range of values that encompasses about 95% of the data, we can assume that this range is within two standard deviations of the mean.
Thus, we can set up the following equation:
2σ = $444.47 - $220.61
Simplifying this equation, we get:
2σ = $223.86
σ = $111.93
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State the number of complex zeros and the possible rational zeros for the function
show your work
The function f(x) = x² + 12x - 3 has two distinct real roots and no rational or complex roots. The possible rational roots are ±1 and ±3, but they are not actual roots of the equation.
To find the number of complex zeros and possible rational zeros of the function f(x) = x² + 12x - 3 = 0, we can use the same methods as in the previous question.
According to the rational root theorem, any rational root of the polynomial must be of the form p/q, where p is a factor of the constant term (-3) and q is a factor of the leading coefficient (1). The possible rational roots are therefore ±1, ±3.
To determine if there are any complex roots, we can use the quadratic formula. The solutions to the equation f(x) = 0 are given by
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the coefficients of the polynomial, we get
x = (-12 ± √(12² - 4(1)(-3))) / 2(1)
x = (-12 ± √(156)) / 2
x = -6 ± 3√(13)
Since the discriminant (b² - 4ac) is positive, the square root is real, and the roots are two distinct real numbers. Therefore, there are no complex roots.
The possible rational roots we found earlier, ±1 and ±3, are not actual roots of the equation, since plugging them into the equation does not give us zero. Therefore, there are no rational roots either.
In conclusion, the equation f(x) = x² + 12x - 3 = 0 has two distinct real roots and no complex or rational roots.
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--The given question is incomplete, the complete question is given
" State the number of complex zeros and the possible rational zeros for the function f(x) = x² + 12x -3 = 0
show your work"--
If y, p and q vary jointly and p is 14 when y and q are equal to 2, determine q when p and y are equal to 7
In the given question, if y, p and q vary jointly and p is 14 when y and q are equal to 2 and p and y are equal to 7, we get q is equal to 14 using the joint variation formula.
To solve this problem, we need to use the formula for joint variation, which states that y, p, and q vary jointly if there exists a constant k such that ypk = kq.
In this case, we know that when y=2 and q=2, p=14. So we can set up the equation: 2*14*k = 2kq
Simplifying this, we get: 28k = 2kq
Dividing both sides by 2k, we get: 14 = q
So when p=7 and y=7, we can use the same equation: 7*14*k = 7kq
Simplifying this, we get: 98k = 7kq
Dividing both sides by 7k, we get: q = 14
Therefore, when p and y are equal to 7, q is equal to 14.
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Mabel saved up her money and bought a model train. Each of the 8 cars on the train was the same length. When Mabel put all the cars together, the train was 3 feet long. How long was each car?
Each car on Mabel's train is a little less than half a foot long i.e., 3/8 feet long, or 0.375 feet long. This is solved by using simple mathematical operations.
To find the length of each car on Mabel's train, we can use the formula:
Total length of train = length of one car × number of cars
We are given that Mabel's train has 8 cars and is 3 feet long, so we can substitute those values into the formula and solve for the length of one car:
3 = x × 8
where x is the length of one car.
To solve for x, we can divide both sides by 8:
3/8 = x
Therefore, each car on Mabel's train is 3/8 feet long, or 0.375 feet long.
In other words, each car is a little less than half a foot long.
To help visualize this, imagine dividing the 3-foot length of the train into 8 equal parts. Each part would be 3/8 feet long, which is the length of one car. So when Mabel puts all 8 cars together, they form a train that is 3 feet long.
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Simplify 3y(y^2-3y+2)
Step-by-step explanation:
if this factorisation because I think you alr simplified, but here's the answer for factorisation anyways.
you can text me below in the comments section if that's not you want, I will try to answer if I can!!!
Answer:
3y(y - 2)(y - 1)
Step-by-step explanation:
Simplify by factoring
3y(y² - 3y + 2)
= 3y(y - 2)(y - 1)
Sylvia’s car trunk measures 4.25 ft wide by 4 ft deep and 4 1 thirdft high. she has cubic boxes 16 inches wide and smaller rectangular boxes 3 inches wide by 6 inches long and 4 inches high. she has to get as many of the large boxes into her trunk as she can, and after that, she can fill the space up with the smaller boxes. how many large and small boxes can she fit into her trunk?
Sylvia can fit 9 large cubic boxes and 240 small rectangular boxes into her car trunk.
How many boxes can fit in Sylvia's car trunk?We first need to convert all measurements to the same unit. Since the large cubic boxes are given in inches, we need to convert the dimensions of the trunk to inches as well.
The trunk measures 51 inches wide (4.25 ft x 12 in/ft), 48 inches deep (4 ft x 12 in/ft), and 53.33 inches high (4*1/3 ft x 12 in/ft).
Next, we need to determine how many large boxes can fit in the trunk. Since each large box is 16 inches wide,
we can fit 3 boxes across the width of the trunk:
(51 inches ÷ 16 inches = 3.19)
Similarly, we can fit 3 boxes deep and 3 boxes high.
Therefore, the maximum number of large boxes Sylvia can fit in her trunk is:
27 (3 x 3 x 3 = 27)
After fitting as many large boxes as possible, we can calculate the remaining volume of the trunk and use this to determine how many small boxes can fit.
The remaining volume is approximately 59,712 cubic inches (51 in x 48 in x 20 in).
Dividing this by the volume of each small box:
(3 in x 6 in x 4 in = 72 cubic inches)
We can fit 829 small boxes in the remaining space.
Therefore, Sylvia can fit a total of 27 large boxes and 829 small boxes in her trunk.
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Nine hundred thirty six student's, 65% of the entire student body, attended the football game. find the size of the student body.
The size of the student body is approximately 1440 students.
To determine the size of the student body, we'll use the given information that 936 students represent 65% of the total number of students. We can set up a proportion to solve for the unknown total (let's call it "x"):
(65% of x) = 936
To express the percentage as a decimal, divide 65 by 100, which equals 0.65:
0.65 * x = 936
Next, to find the value of x, divide both sides of the equation by 0.65:
x = 936 / 0.65
x ≈ 1440
So, the size of the student body is approximately 1440 students. In this problem, we used the concept of percentage to find out the total number of students in the student body, knowing that 936 students (65%) attended the football game.
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Use the differential dz to approximate the change that will be
observed in z = f (x, y) = 5/x^2 + y^2 as x changes from −1 to
−0.93 and y changes from 2 to 1.94.
To approximate the change in z = f(x, y) as x changes from −1 to −0.93 and y changes from 2 to 1.94, we can use the differential dz.
First, we need to find the partial derivatives of f with respect to x and y:
∂f/∂x = -10/x³(y²)
∂f/∂y = -10(x²)/y³
Then, we can use the following formula:
dz ≈ ∂f/∂x * Δx + ∂f/∂y * Δy
where Δx and Δy are the changes in x and y, respectively.
Substituting in the given values, we have:
Δx = -0.93 - (-1) = 0.07
Δy = 1.94 - 2 = -0.06
Using the partial derivatives we calculated earlier, we get:
dz ≈ (-10/-1.037³(2²)) * 0.07 + (-10((-1)²)/1.94³) * (-0.06)
dz ≈ -0.031
Therefore, the approximate change observed in z as x changes from −1 to −0.93 and y changes from 2 to 1.94 is -0.031.
To approximate the change in z using the differential dz, we first need to find the partial derivatives of z with respect to x and y. Given z = f(x, y) = 5/(x² + y²):
∂z/∂x = -10x/(x² + y²)²
∂z/∂y = -10y/(x² + y²)²
Now, we need to find the differential dz:
dz = (∂z/∂x)dx + (∂z/∂y)dy
Since x changes from -1 to -0.93, dx = -0.93 - (-1) = 0.07. Similarly, y changes from 2 to 1.94, so dy = 1.94 - 2 = -0.06.
Now, plug in the initial values of x and y (-1, 2):
∂z/∂x = -10(-1)/((-1)² + 2²)² = -10/25
∂z/∂y = -10(2)/((-1)² + 2²)² = -40/25
Now, plug in dx and dy into the dz equation:
dz = (-10/25)(0.07) + (-40/25)(-0.06) = 0.28 - 0.096 = 0.184
So, the approximate change in z when x changes from -1 to -0.93 and y changes from 2 to 1.94 is 0.184.
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