Answer:
a) Undefined.
Step-by-step explanation:
[tex]f(x) = \dfrac 3{6x+6} = \dfrac{3}{6(x+1)} = \dfrac{1}{2(x+1)}\\\\\\f(-1) =\dfrac{1}{2(-1+1)}= \dfrac{1}{0}[/tex]
Question 2
suppose there is a city where the mean cost per
month of a one-bedroom apartment is $1,500, with a
standard deviation of $250.
approximately what percentage of one-bedroom
apartments in the city cost between $750 and
$1,000?
Using the normal distribution, it is found that 2.15% of bedroom apartments in the city cost between $750 and $1,000.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 1500, \sigma = 250[/tex]
The proportion of apartments that cost between $750 and $1,000 is given by the p-value of Z when X = 1000 subtracted by the p-value of Z when X = 750, hence:
X = 1000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1000 - 1500}{250}[/tex]
Z = -2
Z = -2 has a p-value of 0.0228.
X = 750:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{750 - 1500}{250}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0228 - 0.0013 = 0.0215.
0.02215 = 2.15% of bedroom apartments in the city cost between $750 and $1,000.
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If the diameter of a youth baseball is 2. 8 inches and the diameter of an adult softball is 3. 8 inches, what is the approximate difference in their volumes? use 3. 14 for pi. round to the nearest tenth. recall the formula sphere volume = four-thirds pi r cubed. 1. 0 cubic inch 17. 2 cubic inches 40. 2 cubic inches 137. 8 cubic inches.
The approximate difference in their volumes is 17.2 cubic inches
How to determine the difference in the volume?The given parameters are:
Diameter, d = 2.8
Diameter, D = 3.8
The radii are the half of the diameter.
So, we have:
r = 1.4
R = 1.9
The volume of the balls is then calculated using:
[tex]V = \frac{4}{3}\pi r^3[/tex]
The difference is then represented as:
[tex]D = \frac{4}{3}\pi (R^3 - r^3)[/tex]
Substitute known values
[tex]D = \frac{4}{3}* 3.14* (1.9^3 - 1.4^3)[/tex]
Evaluate
D = 17.2
Hence, the approximate difference in their volumes is 17.2 cubic inches
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Find the 14 term of the following geometric sequence.
10, 20, 40, 80,
Answer:
81920
Step-by-step explanation:
Finding the common ratio (r) :
20/102Finding the 14th term :
a₁₄ = ar¹⁴⁻¹a₁₄ = ar¹³a₁₄ = (10)(2)¹³a₁₄ = (10)(8192)a₁₄ = 81920Answer:
the 14th term in the sequence would be 81920.
Step-by-step explanation:
because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.
f(x) = x². What is g(x)?
Answer:
We want to get g(x) given that we know f(x) and the graphs for both functions. We will see ...
Step-by-step explanation:
What is 12x³ – 9x² − 4x + 3 in factored form?
Pls hurry
Answer:
[tex]\bold{\green{(4x-3)(3x^{2}-1) }}[/tex]
Step-by-step explanation:
[tex]\sf{12x^{3}-9x^{2}-4x+3 }[/tex][tex]\sf{3x^{2}(4x-3)-1(4x-3) }[/tex][tex]\sf{(4x-3)(3x^{2}-1) }[/tex]Answer:
(3x^2 - 1)(4x - 3)
Step-by-step explanation:
We can use grouping to factor this
12x^3 – 9x^2 − 4x + 3
group into: (12x^3 – 9x^2)(− 4x + 3)
Solve one side at a time:
(12x^3 – 9x^2)
3x^2(4x - 3) factor out a 3x^2
(− 4x + 3)
- 1 (4x - 3) factor out a -1
put the two equations togeth
(3x^2 - 1)(4x + 3)
Construct three parallel lines. Then construct two arbitrary non parallel transversal of the parallel lines. Make sure that the transversals cut the three parallel lines at distinct points mark the points of intersection where the transversals cut the parallel lines. Take a screenshot of your construction, save it, and insert the image below.
The image lines constructed are called parallel lines. They are parallel because they are all equidistant to each other at every point and at no point between any of the lines will there be an intersection of the three lines.
What does it mean for two or more lines to be equidistant from each other?Equidistance is simply another word for equal in distance. That is, parallel lines maintain equal distance from each other at all points along them.
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Find the volume of this rectangular pyramid.
length =5cm
width =6cm
hight =7cm
PLEASE HURRY
help me pls I need to get my grade up before July 11th so help ASAP
Why won't anyone help me :(
The probability will include:
P(A and 1) = 1/24
P(C and 2) = 1/12.
P(B and 3) = 1/12.
P(A and 4) = 1/12
How to calculate the probability?The probability of P(A and 1) will be:
= 1/4 × 1/6
= 1/24
The probability of P(C and 2) will be:
= 1/4 × 2/6
= 1/12
The probability of P(B and 3) will be:
= 2/4 × 1/6
= 1/12
The probability of P(A and 4) will be:
= 1/4 × 2/6
= 1/12
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Vector bought 15.6 pounds of paintballs. Ali together, the balls cost 35.99. About how much did the paintball cost per pound
Answer:
about $2.31 per pound
Step-by-step explanation:
35.99/15.6 = 2.30705128205
2.31
Have a good day! :)
I need help with this
Answer:
The answer is B
Step-by-step explanation:
f(x) = -3x - 5
g(x) = 4x - 2
= -3x - 5 - (4x - 2)
= -7x - 3
Answer:
B. -7x - 3
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x): -3x - 5
g(x): 4x - 2
f(x) - g(x) = (-3x - 5) - (4x - 2)
= -3x - 5 - 4x + 2
= (-3x - 4x) + (- 5 + 2)
= (-7x) + (-3)
[((a ^ 2 - 25b ^ 2) ^ 3 + (25b ^ 2 - 9c ^ 2) ^ 3 + (9c ^ 2 - a ^ 2) ^ 3)/((a - 5b) ^ 3 + (5b - 3c) ^ 3 + (3c - a) ^ 3)]
The factorization is [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
To answer the question, w e need to know what factorization is
What is factorization?Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.
So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have
[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Factorizing out the denominator, we have
= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Cancelling out the denominator, we have
= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
So, the factorization is [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
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Sean counts by 2s from 15 to 35. which number does Sean count?
HELP ME ASAP!!!
The number that Sean counts is 27.
What number does Sean count?
When Sean counts by 2s from 15 to 35, he would be counting odd numbers. An odd number is a number that cannot be perfectly divided by 2. There would always be a remainder.
Here are the options:
13
27
16
22
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From his eye, which stands 1.63 meters above the ground, Isaac measures the angle
of elevation to the top of a prominent skyscraper to be 17°. If he is standing at a
horizontal distance of 294 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary.
The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of the skyscraper, hence:
tan(17) = h/294
h = 89.88 meter
Total height = 89.88 + 1.63 = 91.51 meter
The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter
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Find the indicated measures for each circle 0
Answer:
there are no indicate measure bro in circle
Step-by-step explanation:
Why was federal ruling system implemented in Nepal?Give any four reasons
pls help me im confused!
angle #1 = x = ?
angle #2 = X + 30 = ?
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The measure of ∠1 is 30°, while the measure of ∠2 is 60°.
What are Complementary Angles?When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
Since the two angles together form a 90° angle. The angles are complementary to each other, therefore, we can write,
∠1 + ∠2 = 90°
x + x + 30 = 90°
2x = 60°
x = 30°
Thus, the measure of the angles can be written as,
∠1 = x = 30°
∠2 = x+30° = 60°
Hence, the measure of ∠1 is 30°, while the measure of ∠2 is 60°.
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Use the digits 1-9 without repeating, to create two prisms with the same volume
Two prisms with the same volume are rectangular prisms of the dimensions 1 by 4 by 9 and 2 by 3 by 6
How to create the prisms?To do this, we start by determining the type of prism to create.
Assume that we want to create a rectangular prism.
The volume of a rectangular prism is:
Volume = Length * Width * Height
Using the digits 1 - 9, we have:
Prism 1
Length = 1
Width = 4
Height = 9
The volume is
Volume = 1 * 4 * 9 = 36
This means that the second prism must have a volume of 36.
Using the digits 1 - 9, we have:
Prism 2
Length = 2
Width = 3
Height = 6
The volume is
Volume = 2 * 3 * 6 = 36
Notice that the digits are not repeated.
Hence, two prisms with the same volume are rectangular prisms of the dimensions 1 by 4 by 9 and 2 by 3 by 6
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the hcf of 12x^2-4xy+15x-5y
Answer:
-1
Step-by-step explanation:
We have 2 letters, x and y. what letter is in all of them? none of them. that means the HCF can't contain a letter. let's take away the letters, we have 12, -4, 15, -5. Since -5 is a prime number. the answer is -1
order from the least to the greatest 5 -13 _19 -8 _14 -12
Select the correct answer for the blank: if everything else stays the same, the required sample size ____ as the confidence level decreases to reach the same margin of error. answer: question 1 options: increases decreases remains the same
The complete statement is "if everything else stays the same, the required sample size decreases as the confidence level decreases to reach the same margin of error." This is further explained below.
What is the margin of error?Generally, the margin of error is simply defined as a measure of how far your findings depart from the population average.
In conclusion, As confidence levels decline, the needed sample size reduces to provide the same margin of error, assuming all other variables remain constant.
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Solve the system of equations.
8x – y = 8
8x2 – y = 8
(0, 8) and (0, –8)
(1, 0) and (0, –8)
(2, 8) and (1, 0)
(3, 16) and (2, 24)
Answer:
(1, 0 ) and (0, - 8 )
Step-by-step explanation:
8x - y = 8 → (1)
8x² - y = 8 → (2)
since both equations are equal to 8 then equate the left sides
8x² - y = 8x - y ( subtract 8x - y from both sides )
8x² - 8x = 0 ← factor out 8x from each term
8x(x - 1) = 0
equate each factor to zero and solve for x
8x = 0 ⇒ x = 0
x - 1 = 0 ⇒ x = 1
substitute these values into (1) and solve for y
x = 0 : 8(0) - y = 8 ⇒ y = - 8 ⇒ (0, - 8 )
x = 1 : 8(1) - y = 8 ⇒ y = 0 ⇒ (1, 0 )
Which number line represents the solution set for the inequality –4(x 3) ≤ –2 – 2x?
The solution to the inequality expression is x ≥ - 5
Inequality expressionsInequality are expressions not separated by an equal sign. Given the inequality;
–4(x + 3) ≤ –2 – 2x
Expand
-4x - 12 ≤ -2 - 2x
Collect the like terms
-4x + 2x ≤ -2 + 12
-2x ≤ 10
Divide both sides by -2
-2x/-2 ≤ 10/-2
x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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Answer:
First line
Explanation: Edge2023
Two similar triangles are shown below
Which two sets of angles are corresponding angles?
Answer:
I cant help unfortunately
Step-by-step explanation:
can you help me in the comprehension of the story uncle Marcos ?
My exam is in 4 hours btw
Payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. The table shows his data.
A 2-row table with 9 columns. The first row is labeled number of hours with entries 1, 2, 3, 4, 5, 6, 7, 8. The second row is labeled number of errors with entries 36, 34, 30, 31, 23, 16, 11, 5.
Which is the approximate slope of the line of best fit for the data?
Using a calculator, it is found that the approximate slope of the line of best fit for the data is of -4.54762.
How to find the slope of the line of best fit?
The slope is found inserting the points (x,y) in a calculator. In this problem, the points are as follows:
(1, 36), (2,34), (3,30), (4,31), (5,23), (6,16), (7,11), (8,5).
Hence, using the calculator, the slope is of -4.54762.
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Malaki constructed \overline{CG}
CG
start overline, C, G, end overline parallel to \overline{AB}
AB
start overline, A, B, end overline through point CCC.
Which of the following statements best justifies why \overleftrightarrow{CG}
CG
C, G, with, \overleftrightarrow, on top is parallel to \overleftrightarrow{AB}
AB
A, B, with, \overleftrightarrow, on top?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Lines perpendicular to the same transversal are parallel.
(Choice B)
B
Lines with supplementary same-side angles are parallel.
(Choice C)
C
Lines with congruent alternate interior angles are parallel.
(Choice D)
D
Lines with congruent corresponding angles are parallel.
Answer: Lines with congruent corresponding angles are parallel.
CG is parallel to AB because Lines with congruent corresponding angles are parallel.
How to define transverse lines?From the given image, we see that there is a transverse line cutting across lines AB and CG.
Now, from transverse line theorem we know that If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.
Thus, we can conclude that CG is parallel to AB because Lines with congruent corresponding angles are parallel.
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Mr. Rodrigo pours himself a glass of orange juice every morning. Yesterday he drank 5/6 of his glass. Today he drank 7/12 of his glass. On which day did drink more
Find the slope and y-intercept for the following graph of a linear equation
Answer:
Slope: [tex]\frac{4}{1}[/tex]
Y - intercept: -1
Step-by-step explanation:
We can see from the graph that the slope is [tex]\frac{4}{1}[/tex].
We can also identify the y - intercept as -1.
Therefore, the linear equation would be y = [tex]\frac{4}{1}[/tex]x -1
Hope this helps:) Goodluck!
How many solutions are there for the system of nonlinear equations represented by this graph?
The total solution for the system of nonlinear equations represented by this graph is 2 solutions
Graphs and FunctionsQuadratic function have a leading degree of 2. The graph of a quadratic function is parabolic in nature.
Since the given graph consists of a parabola, hence the total solution for the system of nonlinear equations represented by this graph is 2 solutions
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what is the answer to 8^6÷8
Answer:
32768
Step-by-step explanation:
8^6 is 262144
then divide 262144 by 8
so 262144 / 8 = 32768
Hope This Helped
(Refer to the attached image)
Answer:
missing side: 133 cm
Explanation:
Provided 2 length sides and one angle also need to find one missing side.
So, use cosine rule:
⇒ a² = b² + c² - 2bc cos(A)
Insert values
⇒ g² = 166² + 147² - 2(166)(147) cos(50)
⇒ g² = 17794.3935
⇒ g = √17794.3935
⇒ g = 133.3956
⇒ g = 133 (rounded to nearest whole number)