Answers
Answer:
The derivative does not exist at the extremum (-2, 0).
Step-by-step explanation:
Given function:
[tex]f(x)=(x+2)^{\frac{2}{3}}[/tex]
To differentiate the given function, use the chain rule and the power rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule of Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\textsf{Let}\;u &= x+2& \implies f(u) &= u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}{x}}&=1 &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{(\frac{2}{3}-1)}=\dfrac{2}{3}u^{-\frac{1}{3}}\end{aligned}[/tex]
Apply the chain rule:
[tex]\implies f'(x) = \dfrac{\text{d}y}{\text{d}{u}} \cdot \dfrac{\text{d}u}{\text{d}{x}}[/tex]
[tex]\implies f'(x) = \dfrac{2}{3}u^{-\frac{1}{3}} \cdot1[/tex]
[tex]\implies f'(x) = \dfrac{2}{3}u^{-\frac{1}{3}}[/tex]
Substitute back in u = x + 2:
[tex]\implies f'(x) = \dfrac{2}{3}(x+2)^{-\frac{1}{3}}[/tex]
[tex]\implies f'(x) = \dfrac{2}{3(x+2)^{\frac{1}{3}}}[/tex]
An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (-2, 0).
To determine the value of the derivative at (-2, 0), substitute x = -2 into the differentiated function.
[tex]\begin{aligned}\implies f'(-2) &= \dfrac{2}{3(-2+2)^{\frac{1}{3}}}\\\\ &= \dfrac{2}{3(0)^{\frac{1}{3}}}\\\\&=\dfrac{2}{0} \;\;\;\leftarrow \textsf{unde\:\!fined}\end{aligned}[/tex]
As the denominator of the differentiated function at x = -2 is zero, the value of the derivative at (-2, 0) is undefined. Therefore, the derivative does not exist at the extremum (-2, 0).
Related Questions
THERE ARE 2 PARTS PLEASE ANSWER BOTH RIGHT TY HELPP!! There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat.
Part A. What is the theoretical probability of drawing a purple card from the hat?
Part B.
In a trial, a card is drawn from the hat and then replaced 1,080 times. A purple card is drawn 324 times. How much greater is the experimental probability than the theoretical probability?
Enter the correct answers in the boxes.
A. The theoretical probability of drawing a purple card from the hat is ______.
B. The experimental probability of drawing a purple card is ____%
greater than the theoretical probability.
Answers
Part A. The probability pf drawing a purple card out of the hat is 28%.
Part B. The experimental probability is 2% greater than the theoretical probability.
Define probability?The probability that a specific event will occur is known as probability. The ratio of favourable outcomes to all other possible outcomes serves as a stand-in for the likelihood that an event will occur.
In numerous disciplines, including mathematics, statistics, physics, economics, and computer science, uncertain events are described and understood using probability theory. It is used to analyse risks, make decisions, and forecast events.
Now in the given question,
Total cards in the hat = 12 + 17 + 14 + 7 = 50 cards
Total purple cards in the hat = 14
Probability of getting a purple card from the hat = 14/50
= 0.28
= 28%
Now similarly for the experiment,
Probability = 324/1080
= 0.3
= 30%
Therefore, the experimental probability is 30% - 28% = 2% greater than the theoretical probability.
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I'm not sure where I'm going wrong here and need a detailed explanation with a full answer please.
Answers
Answer:
g(x) = 1/2|x - 1| + 2
Step-by-step explanation:
You were almost there, you just got the slope wrong.
original vertex (h, k): (0, 0)
transformed vertex (h', k'): (1, 2)
original slope: 1
transformed slope: m = (3-2)/(3-1) = 1/2 pick any 2 points to find the slope
equation for the transformed function shown in the graph:
g(x) = 1/2|x - h'| + k'
g(x) = 1/2|x - 1| + 2
The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
Answers
a) The domain of the function is [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.
b) The trip had a duration of 5.1875 hours.
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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Find the missing length indicated
Answers
The value of x is 5
Define the term Similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.
Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.
from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB
By using Thales's theorem, the ratio of the sides of triangles are;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5
Define the term Similar triangles?Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.
If matching sides are proportional and corresponding angles are congruent, two triangles are similar.
Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB
The ratio of triangle sides can be calculated using Thales' theory, and it is;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Answers
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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59, 60, 61, 62, 63, 64, 65, and 66 Find the values of x for which the series converges. Find the sum of the series for those values of x. 59. § (-5)".z" n=1 Answer + 00 60. Σ(α + 2)" n=1 61. (x - 2)" 3" n=0 Answer + 62. (-4)" (x - 5) n=0 00 63. 2" ch NO Answer
Answers
The values of x for which the series converges is x ∈ (-1/5, 1/5). The sum of the series for those values of x is (-5x)/(1 + 5x).
The series is [tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex].
We can write this series as [tex]\Sigma^{\infty}_{n=1}(-5x)^n[/tex].
This is a infinite geometric series with first term a = -5x and common ration r = -5x.
It is convergent when
|r| < 1
|-5x| < 1
|-5| |x| < 1
5|x| < 1
Divide by 5 on both side, we get
|x| < 1/5
The series is convergent when x ∈ (-1/5, 1/5).
Sum of the series is
Sₙ = a/1 - n
Sₙ = (-5x)/{1 - (-5x)}
Sₙ = (-5x)/(1 + 5x)
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The complete question is:
Find the values of x for which the series converges. Find the sum of the series for those values of x.
[tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex]
10 POINTS NEED HELP ASAP!!!! PLEASE HELP ME FIND THE AREA AND THE PERIMETER!!
Answers
The area of the composite shape using the area formula for the different shapes is 460.48ft².
What are composite shapes?The area of composite shapes refers to the space occupied by any composite shape. A composite shape is a shape that is made by connecting a few polygons to form the required shape.
These figures or shapes can be built from a wide range of shapes, such as triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.
Now in the question,
First let us find the area of the semi-circle.
Area of semi-circle = πr²/2
= [3.14 × (16/2) ²]/2
= (3.14 × 8²)/2
= 200.96/2
= 100.48ft²
Now coming to the rectangle,
area of the rectangle = l × b
= 20 × 15
= 300ft²
Now for calculating the area of the triangle,
area = 1/2 × b × h
= 1/2 × 12 × 10
= 60ft²
Therefore, the area of the total figure = 100.48 + 300 + 60 = 460.48ft².
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g suppose x and y are two random variables. you don't know their distribution, but someone tells you e[x]
Answers
When x and y are independent variables with x having uniform distribution (0,1) and y having exponential distribution respectively, then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3, and e (x2 e24) is -1/3 22etyx u (0,1) > Independent y exp (1) > Independent
The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process.
E (x) = 0+1/2 = 1/2
v (x) = [1 – 0]2 / 12 = 1/12
E x2 = v (x) + [Ex]2
= 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3
E (y) = 1 v(y)=1
E y2= 1+1= 2
Eety = ∫0etye-ydy
Eety = ∫0e-y (1 – t)dy
a : E (x+y) = E (x) + E(y)
E (x+y) = 1/2+1 = 3/2
b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2
c: E (x+y)2 = E (x2 - 2xy+ y2)
= 1/3 - 2 x 1/2 + 2
= 1/3 + 1 = 4/3
d. E x2e24
= 1/3 x -1 = - 1/3
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The following joint probability density function for the random variables Y1 and Y2, which represent the proportions of two components in a somaple from a mixture of insecticide.
f(y1,y2) = { 2, 0 <= y1 <= 1, 0 <= y2 <= 1, 0 <= y1+y2 <=1
{ 0, elsewhere
For the chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).
Answers
The joint probability density function for the random variables Y1 and Y2 E(Y1+Y2) and V(Y1+Y2) is 41/144.
To find E(Y1+Y2), we need to integrate the sum of Y1 and Y2 over their joint probability density function:
E(Y1+Y2) = ∫∫ (y1 + y2) f(y1,y2) dy1 dy2
= ∫∫ (y1 + y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 <=1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex](y1 + y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (2y1 + 1) (1-y1)² dy1
= 5/12
To find V(Y1+Y2), we can use the formula V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]².
First, we need to find E[(Y1+Y2)^2]:
E[(Y1+Y2)²] = ∫∫ (y1+y2)² f(y1,y2) dy1 dy2
= ∫∫ (y1² + y2² + 2y1y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 = 1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex] (y1² + y2² + 2y1y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (1/3)y1³ + (1/2)y1² + (1/2)y1
(1/3)y1 + (1/4) dy1
= 7/12
Next, we need to find [E(Y1+Y2)]²:
[E(Y1+Y2)]² = (5/12)² = 25/144
Therefore, V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]² = (7/12) - (25/144) = 41/144.
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PLEASE HELPPPPP 30 POINTSSSS!
Answers
Answer:
the answer will be 117
Step-by-step explanation:
you need to multiply
School administrators asked a group of students and teachers which of two
school logo ideas, logo A or logo B, they prefer. This table shows the results.
Students
Teachers
Total
Logo A
14
14
28
Logo B
86
11
97
Total
100
25
125
Are being a student and preferring logo B independent events? Why or why
not?
A. Yes, they are independent, because P(student) = 0.8 and
P(student logo B) = 0.89.
B. No, they are not independent, because P(student) = 0.8 and
P(student logo B) 0.78.
C. No, they are not independent, because P(student) = 0.8 and
P(student logo B) * 0.89.
D. Yes, they are independent, because P(student) = 0.8 and
P(student logo B) 0.78...
Answers
B, No, they are not independent events because the probability of a student preferring logo B (0.78) is different from the overall probability of preferring logo B (0.89), which includes both students and teachers.
How to find independent events?To determine whether being a student and preferring logo B are independent events, we need to compare the probability of a student preferring logo B (P(student logo B)) with the overall probability of preferring logo B (P(logo B)).
P(student logo B) = 0.78 (from the table)
P(logo B) = (86 + 11) / 125 = 0.89
If the two probabilities are equal, then the events are independent. However, in this case, P(student logo B) is not equal to P(logo B), indicating that being a student and preferring logo B are dependent events. Therefore, being a student and preferring logo B are dependent events.
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which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2
Answers
When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.
Dilation:
Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.
According to the Question:
How to determine the scale factor
In figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
K = 1.5/0.6
Dividing the equation:
k = 2.5
Hence, the true statement is (d) The scale factor is 2.5.
Complete Question:
The first figure is dilated to form the second figure. Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
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Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 JQK
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
Answers
The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.
The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.
Actual count of K = 12 - 2 = 10
Total count of 6 and K = 7 + 10 = 17
The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:
Experimental probability = (frequency of K or 6) / (total number of draws)
Experimental probability = 17 / 100
Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
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Express using algebra:
Z increased by 16%
Answers
Answer:
Let's start by expressing "Z increased by 16%" using algebra.
Let Z be the original value of some quantity.
To increase Z by 16%, we need to add 16% of Z to Z:
Z + 0.16Z
Simplifying this expression by factoring out Z, we get:
Z(1 + 0.16)
Combining like terms, we have:
Z(1.16)
Therefore, "Z increased by 16%" can be expressed algebraically as:
Z increased by 16% = Z(1.16)
Answer:
z(1.16)
Step-by-step explanation:
4^(-x)=1/256
I believe it is x=4, but I need how to work it out pls thxxx
Answers
Answer:
x = 4
Step-by-step explanation:
using the rule of exponents
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then
[tex]4^{-x}[/tex] = [tex]\frac{1}{4^{x} }[/tex]
and 256 = [tex]4^{4}[/tex]
then
[tex]\frac{1}{4^{x} }[/tex] = [tex]\frac{1}{4^{4} }[/tex]
so
[tex]4^{x}[/tex] = [tex]4^{4}[/tex]
since bases on both sides are equal, bot 4 then equate exponents
x = 4
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, compute the system's impulse response h[n] without using z-transforms.
Answers
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, the impulse response of the system: h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
To compute the impulse response h[n] of a linear time-invariant (LTI) system given its input-output relationship, we can use the convolution sum:
y[n] = x[n] * h[n]
y[n] = (1/2)*(x[n] + 2x[n-1] + 3x[n-2])
y[n] = (1/2)*(δ[n] + 2δ[n-1] + 3δ[n-2])
y[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
Thus, the impulse response of the system is:
h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2],where δ[n] is the impulse signal.
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Find an equation of the plane that passes through the given point and contains the specified line. (-1, 0, 1); x = 5t, y=1+t, z= -t
Answers
The equation of the plane passing through the point (-1,0,1) and containing the lines x = 5t, y=1+t, z= -t is y + z = 1 .
We substitute , t=0 in the given line equations ,
we get; x=0 , y = 1 and z = 0 ;
So, the plane contain the line , Thus plane will also pass through (0,1,0);
Now, we have that plane passes through (-1,0,1) and (0,1,0), direction ratios of line joining these 2 points are ;
⇒ DR₁ = (-1-0 , 0-1 , 1-0) = (-1,-1,1);
So , the line can be written as x/5 = (y-1)/1 = z/-1 = t;
So, the direction ratio of this line will be :
⇒ DR₂ = (5 , 1 , -1);
The Direction Ratio of normal to the plane is = DR₁ × DR₂;
= (-1,-1,1) × (5,1,-1);
= [tex]\left|\begin{array}{ccc}i&j&k\\-1&-1&1\\5&1&-1\end{array}\right|[/tex]
On solving ,
We get;
= 4j + 4k = (0,4,4) ;
We know that for a normal with direction ratios (a,b,c), equation of plane is written as ax + by + cz = d;
We got direction ratio for plane normal = (0,4,4);
So, equation of plane is 0x+ 4y + 4z = d;
the plane passes through the point (-1,0,1) ;
⇒ 4(0) + 4(1) = d ⇒ d = 4;
we get the equation of plane is 4y + 4z = 4;
⇒ y + z = 1.
Therefore, the equation of the required plane is y + z = 1.
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given natural numbers a and b not both equal to 0, we know that there exist integers k and l with ak bl
Answers
The equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l).
The equation ak + bl = 0 is a linear equation in two variables and is solved using the method of elimination. The equation can be written in the form ax + by = c, where a, b, c are constants. To solve this equation, both sides of the equation should be divided by the coefficient of one of the variables (a or b). This will result in a equation of the form x + qy = r, where q and r are constants. Then, the equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l). The two variables can then be calculated using the point of intersection by substituting the x and y values into the two equations. In this way, the two variables k and l can be found such that ak + bl = 0.
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What are the integers k and l such that ak + bl = 0?
5) What is the probability of picking a vowel, replacing it
and then picking a consonant from the word "SLEEP"?
Answers
The probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is approximately 0.096 or 9.6%.
What is probability?Probability is usually expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain.
According to question:There are two vowels (E) and three consonants (S, L, P) in the word "SLEEP".
The probability of picking a vowel on the first draw is 2/5, because there are two vowels out of five letters total.
Since we replace the vowel we picked, the probability of picking another vowel on the second draw is also 2/5.
The probability of picking a consonant on the third draw is 3/5, because there are three consonants left out of five letters total.
Therefore, the probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is:
(2/5) x (2/5) x (3/5) = 12/125 or approximately 0.096 or 9.6%.
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.59°C and 0.88°C.
Answers
The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.
What is mean?The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.
In this question, using the formula,
z-score = (x – μ) / σ
where:
x: individual data value
μ: population mean
σ: population standard deviation
for x=0.59
μ= 0
σ= 1
z-score= 0.59
Probability=0.7224
for x=0.88
z-score= 0.88
Probability=0.8106
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Mrs. Cabana has 8 pets total. Three of the pets are chameleons and the rest are fish. Select all the answers that are a ratio relationship for Mrs. Cabana's pets.
Question 1 options:
Multi choice
3/5
3 to 11
3:8
5 to 8
8:1
Answers
Answer: numbers 1,3 and 4
Step-by-step explanation:
can anyone help with this triangle question
Answers
The triangle's other leg, side B, measures 12 cm in length.
Are there 180 right triangles in all?When one of the interior angles is 90 degrees, or a right angle, the triangle is said to be a right triangle. The three internal angles of a triangle add up to 180 degrees in a right triangle because one angle must always be 90 degrees and the other two must always total to 90 degrees (they are complementary).
We can observe that the given triangle is a right triangle because angle A's measure is 90 degrees. The hypotenuse, which is represented by the letter "c," is the side that is opposite the right angle. The legs are the other two sides, and they are indicated by "a" and "b".
We are told that the hypotenuse (side c) is 13 cm long and that one leg (side a) is 5 cm long. The length of the other leg must be determined (side b).
The Pythagorean theorem, which asserts that in a right triangle, can be used.
a² + b² = c²
Inputting the values provided yields:
5² + b² = 13²
25 + b² = 169
b² = 144
b = 12
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Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
Answers
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
Mr. and Mrs. Davenport have 3 kids, ages 3, 6, and 13. Their financial matters for 2019 are as follows:Adjusted Gross Income: $65,000Un-reimbursed Medical Expenses: $5,250How much would the Davenports' medical expenses contribute to their total itemized deductions?
Answers
The Davenports' medical expenses contribute to their total itemized deductions are $375 (7.5% for 2019).
The costs you incurred for state and local income or sales taxes, real estate taxes, personal property taxes, mortgage interest, and disaster losses are all included in itemised deductions. You can also count charitable donations and a portion of your out-of-pocket medical and dental costs.
Currently for the 2019 (due 2020), you can deduct medical expenses that exceed 7.5% of your AGI, but back then in 2019, the threshold was 7.5%, not 10%.
So the Davenports can only deduct
$5,250 - ($65,000 x 7.5%) = $375
if they decided to itemize their deductions.
The threshold will increase back to 10% starting 2020 (due 2021) tax returns.
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Samir's statement shows a previous balance of $5,336.22, a payment of $607, and a
new transaction totaling $186. What is his new balance if his APR is 29.0%? Round
answer to hundredths place if answer does not have a hundredths place this use
zeros so it does. Do not include the units. Be sure to attach work for credit
Your Answer:
Answers
Samir's new balance is $5,044.17.
To calculate Samir's new balance, add the previous balance, subtract the payment, add the new transaction, and multiply by the interest rate for one period. The following formula can be used to calculate the interest for a single period:
balance * APR / 12 = interest
where APR stands for annual percentage rate and 12 represents the number of months in a year.
When we apply this formula to Samir's balance and APR, we get:
5336.22 * 0.29 / 12 = 128.95 in interest
As a result, the total new balance is:
5336.22 - 607 + 186 + 128.95 = 5044.17
We get the following when we round to the nearest hundredth:
$5,044.17
As a result, Samir now has a balance of $5,044.17.
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On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.
1. On which day will 640 people see the video? Explain or show your reasoning.
2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?
Answers
On the 7th day after the videο was pοsted, 640 peοple will see the videο.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.
1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:
[tex]V = 5 x 2^n[/tex]
where n is the number οf days after the videο was pοsted.
Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:
[tex]640 = 5 x 2^n[/tex]
[tex]2^n = 128[/tex]
n = lοg2(128) = 7
2. Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:
[tex]20,000 = 5 x 2^n[/tex]
2^n = 4,000
n = lοg2(4,000) ≈ 11.29
Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues
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Find the Z-score for each of the following IQ scores
90 160(Einstein's IQ)
Answers
Answer:
z=3.75
Step-by-step explanation:
A company has a fixed cost of $1277 each day to run their factory and a variable cost of $1.93 for each widget they produce. How many widgets can they produce for $2127?
Answers
The company can produce approximately 425 widgets for $2127.
What is cost function ?
The key concept used here is the concept of cost functions, which is an important concept in economics and business. A cost function is a mathematical function that expresses the total cost of production as a function of the level of output produced. In this case, the cost function is a linear function of the form C = a + bx, where C is the total cost, a is the fixed cost, b is the variable cost per unit, and x is the level of output.
Finding the number of widgets the company can produce given a fixed cost and a variable cost per widget :
To solve this problem, we can set up an equation that relates the total cost to the number of widgets produced.
Let x be the number of widgets produced.
The total cost C is given by:
C = fixed cost + variable cost
C = 1277 + 1.93x
We want to find the number of widgets produced for a total cost of $2127. So we can set up an equation:
2127 = 1277 + 1.93x
Subtracting 1277 from both sides gives:
850 = 1.93x
Dividing both sides by 1.93 gives:
x ≈ 439.9
Since we can't produce a fractional number of widgets, we need to round down to the nearest integer. Therefore, the company can produce approximately 425 widgets for $2127.
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Individuals who identify as male and female were surveyed regarding their diets.
Vegetarian
Pescatarian
Total
89
101
190
Male
Female
Total
Meat-eater
35
37
72
12
23
35
24
14
38
Vegan
18
27
45
What is the probability that a randomly selected person is a meat-eater? Round your
answer to the hundredths place.
Answers
Answer:
To find the probability that a randomly selected person is a meat-eater, we need to add up the number of meat-eaters and divide by the total number of individuals surveyed. From the given table, we can see that there are 72 meat-eaters out of a total of 190 individuals surveyed:
Total meat-eater = 72
Total surveyed = 190
So the probability of selecting a meat-eater is:
P(meat-eater) = Total meat-eater / Total surveyed
P(meat-eater) = 72 / 190
P(meat-eater) = 0.38 (rounded to the hundredths place)
Therefore, the probability that a randomly selected person is a meat-eater is 0.38 or 38%.
Christine has a six-sided dice numbered from 1 to 6. She rolled it a total of 50 times. It landed on an odd number 21 times. a) Work out the relative frequency of the dice landing on an odd number. Give your answer as a decimal. b) If the dice were fair, what would the theoretical probablity of it landing on an odd number be? Give your answer as a decimal. c) Is the dice definitely biased or definetely not biased, or is it impossible to tell? Write a sentence to explain your answer.
Answers
A) Relative frequency is number of times an event happened over total number of events:
Answer is 21/50 = 0.42
B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50
C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.
