No calculator Explanation please. Will choose brainliest. Pre-Calc. Lim as x approaches 9
Answers
The limit of the expression is determined as 0.
What is the limit of the expression?The limit of the expression is calculated as follows;
The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)
For the given limit in the expression, we have x maps to 9 or x tends to 9.
When x tends to 9, we will have;
x ---->9 = (9 - 9 ) / (√9 - 3)
= (0)/(-3 - 3)
note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.
= 0/-6
= 0
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[tex]\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ [/tex]
Now , by using Identity:-
a² - b² = ( a+b ) ( a-b )[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ [/tex]
Related Questions
Which table represents a linear function? A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 2, 4, 8. A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 0, 1, 3, 6. A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 0, 1, 0, 1. A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 3, 5, 7.
Answers
Answer:
A linear function is a function that produces a straight line when it is graphed. The equation of a linear function is of the form y = mx + b, where m is the slope and b is the y-intercept.
Looking at the four tables, we can calculate the slopes of the lines that would be produced by each table. The slope is given by the change in y divided by the change in x.
For the first table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.
For the second table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.
For the third table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.
For the fourth table, the change in y is 2, and the change in x is 1. Therefore, the slope is 2/1 = 2.
Only the first three tables have the same slope, which is 1. Therefore, only the first three tables represent a linear function.
This is because the second column has a constant rate of change (or slope) between any two consecutive values of x. The slope of the function can be calculated as:
slope = (change in y) / (change in x)
If we take any two consecutive values of x from the last table (e.g. x=0 and x=1), we can calculate the slope as:
slope = (y1 - y0) / (x1 - x0) = (3 - 1) / (1 - 0) = 2/1 = 2
If we do this for any other pair of consecutive values of x in the table, we will get the same slope of 2. This indicates that the function is a linear function with a constant slope of 2.
this coordinate plane showes the value of of point w. what is the value of the x-coordinate of point W?
Answers
The value of the x-coordinate of point W is -3.5.
Coordinate geometry is the study of geometry using the points in space.
From the graph, the location of the point W is (-3.5, 1.5).
In the coordinate plane, the x-coordinate is always given first, followed by the y-coordinate, in the form (x, y). Therefore, point W is located at -3.5 on the x-axis and 1.5 on the y-axis.
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The complete question is given below.
A recipe calls for 3 tablespoons of pineapple juice. A can of pineapple juice is 12 fluid oz. How many teaspoons of juice are in the can
Answers
The teaspoons of juice that are in the can is 4
How many teaspoons of juice are in the canFrom the question, we have the following parameters that can be used in our computation:
A recipe calls for 3 tablespoons of pineapple juice. A can of pineapple juice is 12 fluid oz.Using the above as a guide, we have the following:
Teaspoons = Pineapple/Recipe
Substitute the known values in the above equation, so, we have the following representation
Teaspoons = 12/3
Evaluate
Teaspoons = 4
Hence, the number of teaspoons is 4
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Explain how you would solve this figure below
Answers
Answer:
Step-by-step explanation:
Connect N and L to create a triangle. Connect P and L so that you also form a rectangle. Connect P and H to create a semicircle. Finally, connect H and K to create another rectangle, and another triangle. Use rectangle area formula, triangle area formula, and semicircle area formula to solve for the area.
What’s the value of the expression when x=5, 4x-8
Answers
Answer:
12
Step-by-step explanation:
4(5)-8
20-8
12
Solve for
. Make sure to show your work.
Answers
The value of {g} on solving the given expression is 84.
The given expression is -
(16/4)(3x7) = g
We can solve for {g} as -
g = 16/4 x (3 x 7)
g = 4 x 21
g = 84
Therefore, the value of {g} on solving the given expression is 84.
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{Complete ques is -
Solve for g . Make sure to show your work.
(16/4)(3x7)=g}
Please help with this if you don’t know don’t answer
Answers
a) The amount at the end of 1 year is given as follows: $10,170.
b) The amount at the end of 2 years is given as follows: $11,492.10.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 9000, r = 0.13, n = 1.
Hence the equation for the balance at the end of t years is given as follows:
[tex]A(t) = 9000(1.13)^t[/tex]
After one year, the balance is given as follows:
[tex]A(1) = 9000(1.13)^1 = 10170[/tex]
After two years, the balance is given as follows:
[tex]A(2) = 9000(1.13)^2 = 11492.1[/tex]
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Find each angle measure
Answers
Answer:
12. m∠C = 100° and m∠F = 100°
13. m∠S = 89° and m∠U = 89°
Step-by-step explanation:
Question 12
The two triangles ΔABC and ΔDEF have two of their angles equal:
m ∠A = m ∠D
m∠B = m∠E
Therefore the third angles must be equal:
m∠C = m∠F
m∠C = (4x²)° and m∠F = (3x² + 25)°
Setting these two right side expressions in parentheses equal to each other gives
4x² = 3x² + 25
4x² - 3x² = 25
x² = 25
x = ±√25 = ±5
Ignoring the negative value we get
x = 5
Therefore
m∠C = (4x²)° = (4 · 5²)° = (4 · 25)° = 100°
Since, m∠F = m∠C ,
m∠F = 100°
But we can double check
m∠F = (3x² + 25)° = (3 · 5² + 25)° = (3 · 25 + 25) = (75 + 25)° = 100°
Question 13
This is similar to question 12
The quadrilateral RSTU is divided into two triangles ΔRST and Δ RUT
We are given
m∠RTS = m∠TRU
m∠TRS = m∠RTU
Therefore the third angle of ΔRST must be equal to the third angle of Δ RUT
In other words,
m∠S= m∠U
Plugging in the expressions for each of these angles we get
(5x - 11)° = (4x + 9)°
Set the expressions inside parens equal to each other and solve for x:
5x - 11 = 4x + 9
5x - 4x - 11 = 9 (subtract 4x from both sides)
x - 11 = 9
x = 11 + 9 (add 11 both sides)
x = 20
m∠S= (4x + 9)° = (4 · 20 + 9)° = (80 + 9)° = 89°
Therefore m∠RUT is also 89°
but we can double-check
m∠U= (5x - 11)° = (5 · 20 - 11)° = (100 - 11)° = 89°
Which of the following applications represents exponential growth?
A In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8%.
B John kicked a ball from the top of the bleachers at 20 feet in the air at a velocity of 10 feet per second.
C At an amusement park, Skylar gets a $20 prepaid charge card, and she spends $1.75 for each ride.
D The population a tree frogs in an environment is 12,345 the population decreases by 3% each week.
Answers
In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8% is an example of exponential growth. Then the correct option is A.
Option A depicts exponential development among the applications provided. A tiny town's population is expanding at a 0.8% yearly rate. Because of the increasing population, the rate of rise will be higher each year as the population expands. As a result, an exponential function may be used to depict population expansion.
Option B is not an illustration of exponential development because it depicts projectile motion with a constant velocity.
Skylar spends a certain amount for each ride, therefore Option C depicts linear expenditure and is not an illustration of exponential growth.
Option D depicts exponential decline, in which the number of tree frogs falls by 3% per week. This indicates exponential decay rather than exponential growth since the amount is declining at a rate proportionate to its present value.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
9,16,23,...
Find the 46th term.
Answers
The 46th term of the sequence is 324.
We have,
To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.
Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference
of 7.
To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:
a(n) = a(1) + (n - 1) d
where a(1) is the first term, d is the common difference, and n is the term number we want to find.
Using the given information, we have:
a(1) = 9
d = 7
n = 46
Plugging these values into the formula, we get:
a (46) = 9 + (46 - 1)7
a (46) = 9 + 45 (7)
a(46) = 9 + 315
a(46) = 324
Therefore,
The 46th term of the sequence is 324.
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Homework
2. The numbers of pets that several children have
are 2, 1, 2, 3, 4, 3, 10, 0, 1, and Q. Make a box plot
of the data and find the range and interquartile
range. Decide which measure better describes
the data set and explain your reasoning.
0 1 2 3 4 5 6 7 8 9 10 11 12
=
B
range=
interquartile range.
Answers
The Median of the distribution above is 2.5.
What is the data set?The order the values of the numbers from smallest to largest are:
0, 1, 1, 2, 2, 3, 3, 4, 10, Q
To find the median of the data set, that is the middle value when the data is ordered, one need to average of the two middle values, and the middle values are 2 and 3:
Hence:
Median = (2 + 3)/2
= 2.5
The interquartile range IQR is seen as the range in values that is obtained from the first quartile Q1 to the third quartile Q3 and it can be gotten from the IQR by removing Q1 from Q3.
IQR = Q3 - Q1
Note that the first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half. So the value are:
Q1 = 1
Q3 = 4
IQR = Q3 - Q1
= 4 - 1
= 3
To get the range, it will be:
10 - 0
= 10
To explain, note that the range and IQR tells different areas of the data set. The range tells us the way that the data spread out and the IQR measures the spread of the middle 50% of the above data.
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Please I need the answers asap
Answers
The missing test scores were both 8.3. The standard deviation for the test scores was 21.66. The difference between the harmonic mean and the geometric mean of the 12 students was 3.26.
The sum of the scores of the 10 students is 63. The average score of the 10 students is
(63 + x + x) / 12 = 8.3
Solving for x, we get
x = 8.3 * 12 - 63 - 13.8 - 10.4
x = 100.6 - 63 - 13.8 - 10.4
x = 13.4
Therefore, each missing script has a score of 13.4.
To find the standard deviation, we first need to find the variance
Find the mean
(2.7 + 6.3 + 4.1 + 6.4 + 3.5 + 4.7 + 13.8 + 79 + 12.1 + 10.4 + 13.4 + 13.4) / 12 = 11.0
Subtract the mean from each score and square the result
(2.7 - 11)², (6.3 - 11)², (4.1 - 11)², (6.4 - 11)², (3.5 - 11)², (4.7 - 11)², (13.8 - 11)², (79 - 11)², (12.1 - 11)², (10.4 - 11)², (13.4 - 11)², (13.4 - 11)²
Add up the squared differences
5697.36
Divide by the number of scores minus one, to get the variance
5697.36 / 11 = 517.03
Take the square root of the variance to get the standard deviation
√(517.03) = 22.76
Therefore, the standard deviation for the test scores is 22.76.
The harmonic mean is calculated by dividing the number of scores by the sum of the reciprocals of the scores, and then taking the reciprocal of the result
12 / (1/2.7 + 1/6.3 + 1/4.1 + 1/6.4 + 1/3.5 + 1/4.7 + 1/13.8 + 1/79 + 1/12.1 + 1/10.4 + 1/13.4 + 1/13.4) = 5.04
The geometric mean is calculated by taking the product of all the scores, and then taking the nth root of the product, where n is the number of scores
(2.7 * 6.3 * 4.1 * 6.4 * 3.5 * 4.7 * 13.8 * 79 * 12.1 * 10.4 * 13.4 * 13.4)^(1/12) = 8.30
Therefore, the difference between the harmonic mean and the geometric mean is
5.04 - 8.30 = -3.26
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Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
pt. 2:
Do the following segment lengths form a triangle? If so, is the triangle acute, obtuse, or right?
pls help!!
Answers
The answers are explained in the solution.
Given are right triangles, we need to find the missing lengths,
Here we will use Pythagoras theorem,
Hypotenuse² = base² + perpendicular²
1) x² = 5²+2²
x = √25+4
x = √29
2) 6² = x²+4²
x = √36-16
x = √26
3) 25² = x² + √24²
x = √625-576
x = √49
x = 7
Only the 3rd is following the rule of Pythagorean triplet.
Part 2 = The Triangle Inequality :-
The Triangle Inequality (theorem) says that in any triangle, the sum of any two sides must be greater than the third side.
a) 2, 4, 8
2+4 = 6 < 8 [not a triangle]
b) 5, 6, 7
5+6 = 11 > 7
6+7 = 13 > 5
7+5 = 12 > 6
Therefore, it is forming a triangle,
7² = 49
5²+6² = 36+25 = 61
∵ 7² < 5²+6²
Therefore, the triangle is an acute triangle.
c) 6, 8, 15
6 + 8 = 14 < 15 [not a triangle]
d) 9, 12, 15
9 + 12 = 21 > 15
12 + 15 = 27 > 9
15 + 9 = 24 > 12
Therefore, it is forming a triangle,
15² = 225
9²+12² = 81 + 144 = 225
∵ 15² = 9²+12²
Therefore, the triangle is a right triangle.
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What number is not part of the solution set to the inequality below?
w−10≤16
A) 11
B) 15
C) 26
D) 27?
Answers
The number which is not the part of the solution set to the inequality below is 27.
Given inequality is,
w - 10 ≤ 16
WE have to find the solution for the inequality.
Adding both side of the inequality with 10,
w - 10 + 10 ≤ 16 + 10
w ≤ 26
So the solution of the inequality consists of all the points which are less than or equal to 26.
So it contains 11, 15 and 26.
It does not contain 27.
Hence the solution does not contain 27.
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John drove from here to San Antonio which is 180 miles away in 3 hours. Which rate is equivalent to
the rate at which John drove to San Antonio?
Answers
The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour
Which rate is equivalent to the rate at which John drove to San Antonio?From the question, we have the following parameters that can be used in our computation:
John drove from here to San Antonio which is 180 miles away in 3 hours.
This means that
Distance = 180 miles
Time = 3 hours
Using the above as a guide, we have the following:
Speed = Distance/Time
Substitute the known values in the above equation, so, we have the following representation
Speed = 180/3
Evaluate
Speed = 60
Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour
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help please i don’t understand this and need to finish this asap
Answers
a. WXYZ is a kite
b.In the kite mWQZ = 90° because XZ bisects WY
c. WY = 24 mm because WQ = QY
What is a kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and perpendicular diagonals.
a. From the figure, we see that WXYZ is a kite
b. To determine mWQZ, we use the property of a kite which says that the diagonals of a kite intersect at right angles. Since XZ and WX are the diagonals of the kite, they thus intersect at right angles.
Since a right angle is 90° and the angle of intersection is mWQZ, thus mWQZ = 90°
So, mWQZ = 90° because XZ bisects WY
c. To determine WY, we know that WY is the shorter diagonal of the kite. Since one of the properties of a kite says that the longer diagonal bisects the shorter diagonal. So, XZ bisects WY. So, WY = WQ + QY. Since XZ bisects WY, WQ = QY.
So, WY = WQ + QY
= QY + QY
= 2QY
= 2(12 mm)
= 24 mm
So, WY = 24 mm because WQ = QY
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For what value of 2 will the function f(x), be continuous at x=0?
(See Image) Thanks
Answers
(i) [tex]\lim_{x \to \pi/3}[/tex] f(x) = 1 + √3.
(ii) [tex]\lim_{x \to \frac{\pi}{4}} f(x)[/tex] does not exist.
For λ = 2.5, the function f(x) will be continuous at x = 0.
Given the function is,
f(x) = 1.5, when x = 0
= 1 -2 sin x, when x < π/4
= 1 + 2 sin x, when x > π/4
= 1 + (sin λx/sin 5x)
Now,
[tex]\lim_{x \to \pi/3}[/tex] f(x) = [tex]\lim_{x \to \pi/3}[/tex] (1 + 2 sin x) [Since, π/3 > π/4]
= 1 + 2 sin (π/3)
= 1 + 2√3/2 = 1 + √3
Hence, [tex]\lim_{x \to \pi/3}[/tex] f(x) = 1 + √3.
Now left hand limit is,
[tex]\lim_{x \to \frac{\pi^+}{4}}[/tex] f(x) = [tex]\lim_{x \to \frac{\pi^+}{4}}[/tex] (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2
and right hand limit is,
[tex]\lim_{x \to \frac{\pi^-}{4}}[/tex] f(x) = [tex]\lim_{x \to \frac{\pi^-}{4}}[/tex] (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2
Since left hand limit and right hand limit are not equal so value of [tex]\lim_{x \to \frac{\pi}{4}} f(x)[/tex] does not exist.
[tex]\lim_{x \to 0}[/tex] f(x) = [tex]\lim_{x \to 0}[/tex] (1 + (sin λx/sin 5x)) = 1 + [tex]\lim_{x \to 0}[/tex] ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5
Since f(x) is continuous at x = 0.
So, [tex]\lim_{x \to 0}[/tex] f(x) = f(0)
1 + λ/5 = 1.5
λ/5 = 1.5 - 1 = 0.5
λ = 2.5
Hence the value of λ will be 2.5.
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A computer system purchased by Jones Company cost $49,500. Using the MACRS method, calculate the accumulated depreciation at the end of year 3. (Use Table 17-1 and Table 17-2. Round all dollar amounts to the nearest cent.)
Answers
Answer:
To calculate the accumulated depreciation using the MACRS method, you will need to use Table 17-1 and Table 17-2 from your textbook. Here are the steps:
1. Determine the depreciation rate for the computer system based on its class life. According to Table 17-1, the class life for computers is 5 years. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method (which is used in the first year) is 40%. Therefore, the depreciation rate for the computer system in year 1 is 40%.
2. Calculate the depreciation for year 1 using the depreciation rate and the cost of the asset. The depreciation for year 1 is the cost of the asset multiplied by the depreciation rate, which gives us:
Depreciation for year 1 = $49,500 x 40% = $19,800
3. Determine the depreciation rate for year 2. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 2 is 32%. Therefore, the depreciation rate for the computer system in year 2 is 32%.
4. Calculate the depreciation for year 2 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 1 is the cost of the asset minus the depreciation for year 1, which gives us:
Remaining book value after year 1 = $49,500 - $19,800 = $29,700
Depreciation for year 2 = $29,700 x 32% = $9,504
5. Determine the depreciation rate for year 3. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 3 is 19.2%. Therefore, the depreciation rate for the computer system in year 3 is 19.2%.
6. Calculate the depreciation for year 3 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 2 is the cost of the asset minus the depreciation for year 1 and year 2, which gives us:
Remaining book value after year 2 = $29,700 - $9,504 = $20,196
Depreciation for year 3 = $20,196 x 19.2% = $3,880.35
Need help quick! ?(will give brainliest)
Answers
Considering that the surface area and the volume of the cylinders are equal, the surface areas are given as follows:
108π ft².
250π ft².
Here, we have,
the surface area and the volume of a cylinder:
For a cylinder of radius r and height h, the surface area is given by:
S = 2πr(h + r).
The volume is given by:
V = πr²h.
For item 14, the parameters are given as follows:
r = 6 ft, h = x ft.
Hence we solve for x equaling the surface area and the volume as follows:
V = S
36πx = 12π(x + 6)
3x = x + 6
2x = 6.
x = 3.
Hence the surface area is:
S = 12π(3 + 6) = 108π ft².
For item 15, the parameters are given as follows:
r = 10 ft, h = x ft.
Hence we solve for x equaling the surface area and the volume as follows:
V = S
100πx = 20π(x + 10)
5x = x + 10
4x = 10.
x = 2.5.
Hence the surface area is:
S = 20π(2.5 + 10) = 250π ft².
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Which of the following situations can be modeled with an exponential function? The number of fish in a tank increases by five per month. The number of people in a city increases by 100 every year. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year. The value of a phone drops $100 per year.
Answers
Answer:
C. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year.
Step-by-step explanation:
An exponential function models situations in which a quantity grows or decays by a constant percentage or factor over equal intervals of time.
Let's analyze each situation:
A. The number of fish in a tank increases by five per month.
This situation represents a constant increase (addition) of fish every month. It can be modeled by a linear function, not an exponential function.
B. The number of people in a city increases by 100 every year.
This situation also represents a constant increase (addition) in the number of people per year. It can be modeled by a linear function, not an exponential function.
C. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year.
This situation represents a constant percentage decrease (multiplication) in the value of the car each year. It can be modeled by an exponential function (e.g., V(t) = V_0 * (1 - 0.08)^t, where V(t) is the value of the car after t years and V_0 is the initial value of the car).
D. The value of a phone drops $100 per year.
This situation represents a constant decrease (subtraction) in the value of the phone per year. It can be modeled by a linear function, not an exponential function.
Parte III. Resuelve
1. La compañía de teléfonos Boom Mobile brinda un servicio de llamadas con un costo fijo de
$17 al mes, más un costo variable de $0.12 por minuto de llamada.
a. Presenta un modelo lineal, determinando el costo total C por servicio de llamadas en
el mes.
b. ¿Qué representa la pendiente en el modelo lineal?
c. ¿Cuál es el costo total para un cliente que realizó en total 739 minutos durante el mes
de mayo?
I
Answers
T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.
Given that,
T-Mobile charges a base fee of $15 per month plus $0.05 for each minute you are on the phone for any long-distance call, while Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls.
We have to find how long would you need to call for them to charge the same amount.
We can write the equation as
15+0.05x=0.10x
0.05x-0.10x=-15
-0.05x=-15
0.05x=15
x=15/0.05
x=300 minutes
Therefore, 300 minutes long would you need to call for them to charge the same amount.
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complete question:
For any long-distance call T-Mobile charges a base rate of $15 per month plus $0.05 a minute
that you are on the phone, while Verizon charges a base rate of only $10 per month, but charges
$0.10 per minute for long distance calls. Write the equation that represents the total cost for one month of long distance calls for each company, where y is total cost and x is the amount of minutes used:
T-Mobile:
Verizon:
Using an algebraic method, determine how many minutes the two plans will cost the same.
What is the surface area of the rectangle pyramid below 13 13 13
Answers
Answer:
Step-by-step explanation:
Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:
First, we need to calculate the area of the rectangular base, which is simply length x width:
Area of rectangular base = 13 x 13 = 169 square units
Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.
To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:
a² + b² = c²
where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.
13² + 13² = c²
338 = c²
c ≈ 18.38
Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:
Area of isosceles triangle = (1/2) x base x height
Area of isosceles triangle = (1/2) x 13 x 18.38
Area of isosceles triangle ≈ 119.14 square units
To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:
Area of right triangle = (1/2) x base x height
Area of right triangle = (1/2) x 13 x 18.38
Area of right triangle ≈ 119.14 square units
Since there are two of each type of triangular face, the total surface area of the pyramid is:
Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle
Surface area = 169 + 2 x 119.14 + 2 x 119.14
Surface area = 546.28 square units
Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.
I am a parallelogram. Two of my sides are parallel to the bottom of the paper. The endpoints of the bottom side are at (2, 5) and (9, 5). The slope of the line segments that form my two sides is 0.75, and the length of each side is 5 units. What are my other two vertices?
Answers
According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).
How to find the vertices of the parallelogram?To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,
m = slope(x1, y1) = point on the lineFor the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:
y - 5 = 0.75(x - 2)Simplifying, we get:
y = 0.75x + 3.5To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:
y = 0.75(7) + 3.5 = 8Therefore, the vertex at the top right of the parallelogram is (7, 8).
For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:
y - 5 = -0.75(x - 9)Simplifying, we get:
y = -0.75x + 11.25To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:
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Let /_D be an acute angle. Use a calculator to approximate the measure of /_D to the nearest tenth of a degree. sin D = 0.75
Answers
The measure of angle D is 48.59 degrees where angle D is acute.
For finding the measure of angle when a trigonometric ratio is given, we use inverse trigonometric functions.
For sine there lies arcsin, for cos, there lies arccos and so on.
Thus, sinD=0.75
∠D = sin⁻¹(0.75)
∠D = 48.59
But since ∠D is acute, thus we have ∠D = 48.59
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The following are the ages of 12 history teachers In a school district 29,30,32,32,39,41,46,49,50,51,52,53 minimum lower quartile median upper quartile maximum and interquartile range
Answers
The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
How does interquartile range work?Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.
According to the given information:To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.
Step 1: Find the median (Q2)
When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:
Median (Q2) = (41 + 46)/2 = 43.5
Step 2: Find the lower quartile (Q1)
The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:
Q1 = (32 + 32)/2 = 32
Step 3: Find the upper quartile (Q3)
The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:
Q3 = (50 + 51)/2 = 50.5
Now we have all the information we need to construct the five-number summary and interquartile range:
Minimum: 29
Lower quartile (Q1): 32
Median (Q2): 43.5
Upper quartile (Q3): 50.5
Maximum: 53
Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5
the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
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A Fair Isaac Corporation (FICO) score is used by credit agencies such as banks to determine whether to lend
money and the interest rate to charge. Its value ranges from 300 to 850 and if you have a score over 700,
you are considered to be a "quality" credit risk. The mean credit score of average income earners in
California is estimated by Fair Isaac to be 591. A recent survey of 21 high income earners in California had a
mean FICO score of 7-584 and a standard deviation of 8-20. Use a 0.025 significance level to test the claim
that the mean FICO score of high income earners in California is less than 591, the mean score of average
income earners in California.
Claim: Select an answer which corresponds to Select an answer
Opposite: Select an answer
which corresponds to Select an answer
The test is: Select an answer
The test statistic is:
(to 3 decimals)
Identify the range of the p-value: [Select an answer
Based on this we: Fail to reject the null hypothesis
Conclusion There does
appear to be enough evidence to support the claim that the mean
FICO score of high income earners in California is less than 591, the mean score of average income earners
in California.
Answers
We can conclude here that we have sufficient evidence that the mean score is not equal to 571.
How to explain the hypothesisThe test statistic here is computed as:
= (589 - 571) / 46/✓26
= 1.9953
Now the p-value for n-1 = 25 degrees of freedom here is computed from the t-distribution tables as:
p = 2P( t25 > 1.9953 ) = 2*0.0285 = 0.0570
0.05 < P-value < 0.1
As the p-value here is 0.0570 < 0.1 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here.
Therefore we can conclude here that we have sufficient evidence that the mean score is not equal to 571.
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Martha’s clubhouse is shaped like
a square pyramid with four congruent equilateral triangles for its sides. All of the edges are 6 feet
long. What is the total surface area of the clubhouse including the floor? Round your answer to the nearest hundredth.
A=
Answers
The total surface area of the clubhouse including the floor is approximately 95.98 square feet.
We have,
The surface area of a square pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.
Since the base is a square, its area is 6^2 = 36 square feet.
Each triangular face is an equilateral triangle with a side length of 6 feet, so its area can be found using the formula.
A = (√(3)/4) x s²,
where s is the length of a side.
The area of each triangular face.
A = (√(3)/4) x 6² = 9 √(3) square feet.
The total surface area is then:
A = 4 x 9 √(3) + 36
A = 36 √(3) + 36 ≈ 95.98 square feet
(rounded to the nearest hundredth)
Therefore,
The total surface area of the clubhouse including the floor is approximately 95.98 square feet.
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Solve for x value:
7+ √(-36-5x)5 = 250
x =
Answers
7 + √(-36 - 5x) * 5 = 250
Let's start by isolating the square root term by subtracting 7 from both sides:
√(-36 - 5x) * 5 = 243
Now we can isolate the square root term by dividing both sides by 5:
√(-36 - 5x) = 243/5
Squaring both sides, we get:
-36 - 5x = (243/5)^2
Simplifying the right side, we get:
-36 - 5x = 11808/25
Adding 36 to both sides, we get:
-5x = 11808/25 + 36
Simplifying the right side, we get:
-5x = 11808/25 + 900/25
Combining the fractions on the right side, we get:
-5x = 12708/25
Dividing both sides by -5, we get:
x = -12708/125
So the value of x that solves the equation is x = -101.664.
Good luck!
A number cube of questionable fairness is rolled 100 times. The probability distribution shows the results. What is P(3≤x≤5) ? Enter your answer, as a decimal, in the box.
Answers
P(3≤x≤5) = P(x=3) + P(x=4) + P(x=5)
From the probability distribution, we can see that:
P(x=3) = 0.22
P(x=4) = 0.31
P(x=5) = 0.16
Plugging these values into the formula, we get:
P(3≤x≤5) = 0.22 + 0.31 + 0.16 = 0.69
Therefore, the probability of rolling a 3, 4, or 5 on the number cube is 0.69.
Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the
widths (mm) of skulls from 150 A.D. Construct a 99% confidence interval estimate of the mean skull width.
128.1 138.2 125.7 132.3 143.2 134.7 138.8 129.3
mm<
(Round to two decimal places as needed.)
Answers
The 99% confidence interval estimate of the mean skull width is given as follows:
(126.8 mm, 140.76 mm).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The sample in this problem is given as follows:
128.1, 138.2, 125.7, 132.3, 143.2, 134.7, 138.8, 129.3.
Inserting these values into a calculator, the parameters are given as follows:
[tex]\overline{x} = 133.78, s = 5.64, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 8 - 1 = 7 df, is t = 3.5.
The lower bound of the interval is given as follows:
133.78 - 3.5 x 5.64/sqrt(8) = 126.8 mm.
The upper bound of the interval is given as follows:
133.78 + 3.5 x 5.64/sqrt(8) = 140.76 mm.
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