Answer:
64 and 65
Step-by-step explanation:
Let the two lockers be x and (x+1) since they are consecutive
The sum is 129 so,
x + (x+1) = 129
2x + 1 = 129
2x = 128
x = 64
x + 1 = 65
The locker numbers are 64 and 65
Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $40,000 on a clear day and $14,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 60% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 14% that it will be sunny and 26% that it will be cloudy.
Answer:
$6240
Step-by-step explanation:
given likelihoods:
sunny day = 14% = 0.14
cloudy day = 26% = 0.26
rainy day = 60% = 0.60
profits:
profit on a sunny day = $40,000
profit on a cloudy day = $14,000
Loss on a rainy day = -$5,000
expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)
expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)
=6240
labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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number 33!!!! this is a test !!!
33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)
How to calculate the volume of a triangular prism?To calculate the volume of a triangular prism, the formula that should be used is given as follows;
Volume= BH
where;
B= area of base = 1/2 × base×height
= 1/2×4×3
= 6
H= 6
Volume= 6×6= 36.
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HELP I DONT NOW WHICH ONE IT IS?
The correct statement is the first one:
f(0) = 2
g(-2) = 0
Which statement is true about the two graphs?Here we can see the graph of two quadratic equations.
The orange one is g(x), and we can see that it has the vertex at (-2, 0).
And the blue one is f(x), we can see that the vertex is at (2, 0)
From, that, we coclude that:
g(-2) = 0
f(2) = 0
We also can see that the two have the sa,me y-intercept (0, 2), so:
f(0) = g(0) = 2
Then the correct statement is the first one:
f(0) = 2
g(-2) = 0
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16
Find x.
25
X
X
x = [?]√]
The value of x in the right triangle using pthagorean theorem is 3√41.
What is the value of x?The figure in the image is that of a right triangle with of its interior angle at 90 degrees.
Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the figure:
Hypotenuse c = 25
Leg a = 16
Leb b = x
Plug these values into the above formula and solve for x:
c² = a² + b²
25² = 16² + x²
625 = 256 + x²
x² = 625 - 256
x² = 369
Take the square root( we use the positive value because its dimension ).
x = √369
x = 3√41
Therefore, the value of x is 3√41.
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What is the inverse of the following conditional statement? "If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle." If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle. If the polygon is a triangle, then the sum of the interior angles of the polygon is not more than 180°. If the sum of the interior angles of a polygon is equal to 180°, then the polygon is a triangle. If the polygon is not a triangle, then the sum of the interior angles of the polygon is more than 180°.
The inverse of the original statement is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
The inverse of the conditional statement "If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle" is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
To find the inverse, we need to negate both the hypothesis and the conclusion of the original statement.
The hypothesis of the original statement is "the sum of the interior angles of a polygon is more than 180°". To negate this, we say "the sum of the interior angles of a polygon is not more than 180°".
The conclusion of the original statement is "the polygon is not a triangle". To negate this, we say "the polygon is a triangle".
In summary, the inverse of the original statement is "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
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Question 2 (1 point)
Which one of the following is true of the mean?
1) one of the less common averages
2) equals some whole number
observations must be ordered from least to most before calculating the
3)
mean
4) equals the sum of all observations divided by the number of observations
The correct statement about the mean is:
The mean equals the sum of all observations divided by the number of observations.
The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.
To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.
The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.
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The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
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Consider the transformation.
2 trapezoids have identical angle measures but different side lengths. The first trapezoid has side lengths of 4, 2, 6, 2 and the second trapezoid has side lengths of 8, 4, 12, 4.
Which statement about the transformation is true?
The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.
The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.
First Trapezoid:
Side lengths: 4, 2, 6, 2
Second Trapezoid:
Side lengths: 8, 4, 12, 4
To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.
Comparing the corresponding sides:
4 / 8 = 2 / 4 = 6 / 12 = 2 / 4
We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:
The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.
A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.
This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.
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4. Brooke earns a salary of $38 000 per year as a cook and works part-time in a department
store.
Her part-time job pays $10.25 per hour and she usually works 12 hours per week.
a) Determine her monthly income.
b) She is looking at renting a new apartment. The rent is $975 per month and includes
utilities. If she takes this apartment, will it fall within the guidelines for housing?
a) Brooke's monthly income is $3,166.67 from her full-time job as a cook, and an additional $532.59 from her part-time job, resulting in a total monthly income of $3,699.26.
b) Yes, the rent of $975 per month for the new apartment falls within the housing guideline of spending 30% or less of her monthly income on housing.
a) To determine Brooke's monthly income, we need to calculate her earnings from both her full-time and part-time jobs.
Full-time job income: Brooke earns $38,000 per year as a cook.
To find her monthly income from this job, we divide her annual salary by 12:
Monthly income from full-time job = $38,000 / 12 = $3,166.67
Part-time job income: Brooke earns $10.25 per hour and works 12 hours per week.
To find her weekly income from this job, we multiply her hourly rate by the number of hours she works:
Weekly income from part-time job = $10.25/hour x 12 hours/week = $123
To find her monthly income, we multiply her weekly income by the average number of weeks in a month (approximately 4.33):
Monthly income from part-time job = $123/week x 4.33 weeks/month = $532.59 (rounded to the nearest cent)
To calculate Brooke's total monthly income, we add her full-time and part-time job incomes:
Total monthly income = $3,166.67 + $532.59 = $3,699.26 (rounded to the nearest cent)
b) The rent for the new apartment is $975 per month, including utilities. To determine if it falls within the housing guidelines, we need to compare it to a percentage of Brooke's monthly income.
Typically, a common guideline is to spend no more than 30% of your monthly income on housing.
Percentage of monthly income for housing = 30% of total monthly income
= 30/100 x $3,699.26
= $1,109.78 (rounded to the nearest cent)
Since the rent of $975 is lower than the guideline of $1,109.78, if Brooke takes this apartment, it will fall within the housing guidelines.
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In circle M below, diameter AC, chords AB and BC, and radius MB
are drawn.
Which statement is not true?
(1) AABC is a right triangle. (3) mBC = m/BMC
(2) AABM is isosceles.
(4) mAB = mLACB
The statement which is not true include the following: (2) AABM is isosceles.
What is an isosceles triangle?In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length and two (2) equal angles.
By critically observing circle M shown above, we can reasonably infer and logically deduce the following true statements:
ΔABC is a right triangle.
BM = MC (radius of circle M).
mBC = m∠BMC
mAB = 1/2m∠ACB (intersecting secant theorem).
In this context, we can logically conclude that triangle ABM does not represent an isosceles triangle because it does not have two (2) sides that are equal in length.
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What is the distance from A to B?
10
108642
A(-8, -3)
-2
-6
-8
-10
B6, 6)
2 4 6 8 10
A 21 units
B. 15 units
C. 225 units
D. 3 units
The distance from point A to point B is approximately 16.64 units. None of the given options (A, B, C, D) match this value exactly, so there seems to be an error in the options provided.
To find the distance from point A to point B, we can use the distance formula in Euclidean geometry. The distance formula between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, point A is (-8, -3) and point B is (6, 6). Plugging these values into the distance formula, we have:
distance = sqrt((6 - (-8))^2 + (6 - (-3))^2)
= sqrt((6 + 8)^2 + (6 + 3)^2)
= sqrt(14^2 + 9^2)
= sqrt(196 + 81)
= sqrt(277)
≈ 16.64
Thus, the distance between points A and B is roughly 16.64 units. Since none of the available options (A, B, C, or D) exactly match this value, there appears to be a problem with the options.
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The ratio of the length to the width of a rectangle is 3:2. If the perimeter of the rectangle is 40, what is the length of the rectangle?
Answer:
Step-by-step explanation:
Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:
P = 2(3x + 2x)
40 = 2(5x)
Now, let's solve for x:
40 = 10x
x = 40/10
x = 4
Now that we have the value of x, we can find the length of the rectangle:
Length = 3x = 3(4) = 12
Therefore, the length of the rectangle is 12.
Given the sequence 9/8, 3/4, 1/2,...,8/81 is the geometric sequence. Find the common ratio and the number of all terms of this sequence.
Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
As we know that,
Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.
So, r= (n+1)th term / nth term
where r ⇒ common ratio
(n+1)th term⇒ succeeding term
nth term⇒ preceding term
According to the given question, r = (9/8) / (3/4)
r = (2/3)
We also know,
Any term of a G.P. [nth term] can be obtained by the formula:
Tₙ= a[tex]r^{n-1}[/tex]
where, Tₙ= nth term
a= first term of G.P.
r=common ratio
Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.
Tₙ= a[tex]r^{n-1}[/tex]
⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])
⇒ (64/729)= ([tex]2/3^{n-1}[/tex])
⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])
⇒ n-1 = 6
⇒ n = 7
∴ The total number of terms in G.P. is 7.
Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.
Explanation:The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.
So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.
To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.
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1cm on a picture of a swimming pool represents 1200cm of the actual swimming pool. The length of the pictured swimming pool is 4.5cm and the width is 3cm. What is the perimeter of the actual swimming pool? Express your answer in meters.
Answer:
180 meters
Step-by-step explanation:
To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.
Length of actual swimming pool = 4.5 cm × 1200 cm = 5400 cmWidth of actual swimming pool = 3 cm × 1200 cm = 3600 cmPerimeter of actual swimming pool = (5400 cm + 3600 cm) × 2 = 18000 cm.Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:
100cm = 1mNow we can divide 18000 by 100:
18000 cm ÷ 100 = 180 m
Therefore, the perimeter of the actual swimming pool is 180 m.
A parabola can be drawn given a focus of ... 100pts
Answer:
[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]
[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]
Step-by-step explanation:
The given directrix of the parabola is x = -2, which is a vertical line.
The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.
The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.
The standard form of a horizontal parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the focus is (-4, -7), then:
[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]
As the directrix is x = -2, then:
[tex]h - p=-2[/tex]
To find the value of h, sum the equations involved h and p to eliminate p:
[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]
To find the value of p, substitute the found value of h into one of the equations:
[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]
Therefore, the values of h, k and p are:
h = -3k = -7p = -1The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.
The parabola has a vertex at (-3, y), has p-value of 1 and it equation is
(x + 3)² = 4y.
What is the equation of the parabola?To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:
(x - h)² = 4p(y - k)
where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given:
Focus: (-4, -7)
Directrix: x = -2
1. Finding the vertex:
Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.
Therefore, the vertex of the parabola is (-3, y).
2. Finding the p-value:
The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.
Therefore, the value of "p" is 1.
3. Writing the equation of the parabola:
Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:
(x - h)² = 4p(y - k)
(x - (-3))² = 4(1)(y - y)
Simplifying, we get:
(x + 3)² = 4(y - y)
(x + 3)² = 4y
So, the equation of the parabola is (x + 3)² = 4y.
The vertex of the parabola is (-3, y) and the p-value is 1.
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debbie wants tp compare the simple interest to compound interest on 60,000 investment
Answer:
this question is incomplete
Suppose that ƒ is a function given as f(x) = 4x² + 5x + 3.
Simplify the expression f(x + h).
f(x + h)
Simplify the difference quotient,
ƒ(x + h) − ƒ(x)
h
=
Submit Question
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(x+h)-f(x)
f'(x) =lim
h→0
h
ƒ(x + h) − f(x)
h
=
Answer:
f(x +h) = 4x² +4h² +8xh +5x +5h +3
(f(x+h) -f(x))/h = 4h +8x +5
f'(x) = 8x +5
Step-by-step explanation:
For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.
F(x+h)Put (x+h) where h is in the function, and simplify:
f(x+h) = 4(x+h)² +5(x+h) +3
= 4(x² +2xh +h²) +5x +5h +3
f(x +h) = 4x² +4h² +8xh +5x +5h +3
Difference quotientThe difference quotient is ...
(f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h
= (4h² +8xh +5h)/h
(f(x+h) -f(x))/h = 4h +8x +5
LimitWhen h=0, the value of this is ...
f'(x) = 4·0 +8x +5
f'(x) = 8x +5
__
Additional comment
Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.
<95141404393>
Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.
The values in the table represent a function.
x
-6
7
4
3
-5
f(x)
8
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
(3) is
f(x)=-5 when x is
Done
The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (-6, 8).
f(x) = -5 when x is 4.
In function notation, we represent the input value as 'x' and the corresponding output value as 'f(x)'.
Looking at the first row of the table, we see that when x is -6, the corresponding value of f(x) is 8.
Therefore, we can write this ordered pair as (-6, 8) in function notation.
Similarly, we can determine that f(x) = -5 when x is 4 by examining the second row of the table.
The value of f(x) is -5 when x is 4, so we can express it as f(4) = -5.
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Where will the hand of a clock stop if it
(a) starts at 12 and makes 1/2 of a revolution,clockwise?
(b) starts at 2 and makes 1/2 of a revolution,clockwise?
(c) starts at 5 and 1/4 of a revolution,clockwise?
(d) starts at 5 and makes 3/4 of a revolution,clockwise?
(a) Starting at 12 and making 1/2 revolution clockwise, the hand stops at 6.
(b) Starting at 2 and making 1/2 revolution clockwise, the hand stops at 8.
(c) Starting at 5 and making 1/4 revolution clockwise, the hand stops at 8.
(d) Starting at 5 and making 3/4 revolution clockwise, the hand stops at 11.
To determine where the hand of a clock will stop, we need to consider the fractions of a revolution made by the hand starting from different positions.
(a) If the hand starts at 12 and makes 1/2 of a revolution clockwise, it will stop at 6.
This is because a half revolution corresponds to the hand moving from 12 to 6 on the clock face.
(b) If the hand starts at 2 and makes 1/2 of a revolution clockwise, it will stop at 8.
Again, a half revolution corresponds to the hand moving from 2 to 8 on the clock face.
(c) If the hand starts at 5 and makes 1/4 of a revolution clockwise, it will stop at 8.
A quarter revolution corresponds to the hand moving from 5 to 8 on the clock face.
(d) If the hand starts at 5 and makes 3/4 of a revolution clockwise, it will stop at 11.
A three-quarter revolution corresponds to the hand moving from 5 to 11 on the clock face.
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The following data represents the number of days absent and the final grade for a sample of college students in a
Math 241 course.
r=
Number of Days Absent
Final Grade in Course
y =
O
1
y =
2
X+
3
4
89.2 83.5 84.8 82.6 76.9
5
82.3
where the number of days absent is the explanatory variable and the final grade is the response variable.
Determine the linear correlation coefficient. (Round to decimal places)
c.) Determine the equation of the regression line. (Round values to four decimal places)
6
7
b.) Does the linear correlation coefficient suggest a strong positive, strong negative, weak positive, or weak negative
linear correlation?
81.2 79.3 73.5
8
d.) Use the regression line to calculate the best predicted final grade for a student who misses 5 days of
class. (Round to one decimal place)
a) The least squares regression line for the given data is y = -3.5358x + 87.2857.
b) The slope of -3.5358 indicates that for each additional day absent, the final grade is expected to decrease by approximately 3.5358 points on average.
c) The y-intercept of 87.2857 represents the estimated final grade when the number of absences is zero, implying that a student who did not miss any classes is expected to have a final grade of approximately 87.2857.
a) To find the least squares regression line, we need to determine the equation of the line in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's calculate the necessary sums:
∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
∑y = 89.2 + 86.4 + 83.5 + 81.1 + 78.2 + 73.9 + 64.3 + 71.8 + 65.5 + 66.2 = 759.9
∑xy = (0 * 89.2) + (1 * 86.4) + (2 * 83.5) + (3 * 81.1) + (4 * 78.2) + (5 * 73.9) + (6 * 64.3) + (7 * 71.8) + (8 * 65.5) + (9 * 66.2) = 5079.6
∑[tex]x^2[/tex] = [tex](0^2) + (1^2) + (2^2) + (3^2) + (4^2) + (5^2) + (6^2) + (7^2) + (8^2) + (9^2)[/tex] = 285
[tex]\sum y^2 = (89.2^2) + (86.4^2) + (83.5^2) + (81.1^2) + (78.2^2) + (73.9^2) + (64.3^2) + (71.8^2) + (65.5^2) + (66.2^2) = 59718.63[/tex]
Using the formulas for the slope (m) and y-intercept (b):
m = (n∑xy - (∑x)(∑y)) / (n∑x^2 - (∑x)^2)
b = (∑y - m(∑x)) / n
Substituting the calculated values:
m = (10 * 5079.6 - (45 * 759.9)) / (10 * 285 - (45)^2)
b = (759.9 - m(45)) / 10
Calculating the values:
m ≈ -3.5358
b ≈ 87.2857
Therefore, the least squares regression line is y = -3.5358x + 87.2857.
b) The slope (-3.5358) represents the change in the final grade (y) for each additional day absent (x). This means that on average, for each additional day a student is absent, their final grade is expected to decrease by approximately 3.5358 points.
c) The y-intercept (87.2857) represents the estimated final grade when the number of absences (x) is zero. In other words, it is the predicted final grade for a student who did not miss any classes.
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Question
The following data represents the number of days absent, x, and the final grade, y, for a sample of college students at a community college.
No.of absences, x | 0 1 2 3 4 5 6 7 8 9
Final Grade, y | 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
a) Find the least squares regression line treating the number of absences as the explanatory variable and the final grade as the response variable.
b) Interpret the slope using complete sentences.
c) Interpret the y intercept using complete sentences.
Find the area of the shaded region
Answer:
17.5
Step-by-step explanation:
The triangle is an equilateral triangle since all sides are equal
Area of a equilateral triangle is:
[tex]ar(triangle) = \frac{a^2\sqrt{3} x}{4}[/tex]
[tex]=\frac{5^2\sqrt{3} }{4} \\\\=\frac{25\sqrt{3} }{4} \\[/tex]
the sde of the square = diameterof the circle(d)
d = 6
r = d/2 = 3
ar(circle) = πr²
= π * 3²
= 9π
= 9*22/7
= 198/7
ar(shaded region) = ar(circle)-ar(triangle)
[tex]= \frac{198}{7} - \frac{25\sqrt{3} }{4}[/tex]
= 17.5
9.
Find the volume of the cylinder. All measurements are in
centimeters. Keep your answer exact.
5
Answer:
The volume of the cylinder is 628.318530718
Step-by-step explanation:
The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.
The radius is 5, and the height is 8. Plug these values into the equation and solve:
[tex]v =\pi *5^2*8[/tex]
[tex]v = 628.318530718[/tex]
So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32
Answer:
200π or 628
Step-by-step explanation:
Note: your picture is not clear so I am assuming the height to be 8.
r = 5
h = 8
Volume = πr²h
= π * 5² * 8
= (25*8) π
= 200π
= 200*3.14
= 628
please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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a house is covers by a rectangle of ground 15.7m by 12.3m on the plan of the house the length of the rectangle is 78.5cm what is the scale of the plan in form 1:n ? find width if the house on the plan
The width of the house on the plan is 0.615 meters.
To find the scale of the plan in the form 1:n, we can compare the measurements on the plan to the actual measurements of the house.
Length of the rectangle on the plan = 78.5 cm
Actual length of the house = 15.7 m
We need to convert the actual length of the house to the same unit as the length on the plan, which is centimeters.
1 meter = 100 centimeters
So, the actual length of the house in centimeters = 15.7 m [tex]\times[/tex] 100 cm/m = 1570 cm
Now, we can find the scale of the plan by dividing the length on the plan by the actual length of the house:
Scale = Length on the plan / Actual length of the house
= 78.5 cm / 1570 cm
Simplifying this fraction, we get:
Scale = 1/20
Therefore, the scale of the plan is 1:20.
To find the width of the house on the plan, we can use the same scale.
Width of the house in actual measurements = 12.3 m.
Width of the house on the plan = (Width of the house in actual measurements) / Scale
= 12.3 m / 20
= 0.615 m.
So, the width of the house on the plan is 0.615 meters.
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please answer i am stuck
please help!!!!!!!!!!!!!!!!!!!!!!
The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.
The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.
The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.
What are systematic, random and cluster samples ?A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.
A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.
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if 3+5 equals 8 then what does 5+3 equal?
Answer:
8
Step-by-step explanation:
In a sample of 5,000 students , the mean GPA is 2.80 and the standard deviation is 0.35. Assume the distribution to be normal.
How many students score below 2.60?
In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.
To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.
First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.
Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.
To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.
Since the number of students must be a whole number, we round down to 1428 students.
Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.
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