Final answer:
The smallest number in the domain of the composite function f^o g, is -8.
Explanation:
To find the smallest number that is in the domain of the composite function fo g, we need to consider the domains of the individual functions f(x) and g(x). First, since f(x) = √7x, f is only defined for x ≥ 0, as the square root function requires non-negative input. Secondly, g(x) = x+8 is defined for all real numbers, as it's a linear function.
However, the composite function f(g(x)) will also require that the output of g(x) be non-negative, because this output becomes the input for f(x). Thus, we need to find the smallest x such that g(x) is non-negative, which occurs when x+8 ≥ 0. Solving for x gives us x ≥ -8.
Hence, the smallest x in the domain of fo g is -8.
What is the correct way to write 6.3 × 10^8 in standard notation? (25 Points)
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
When a point in quadrant 2 is rotated 180 degrees counterclockwise, it will land in quadrant 4.
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
Begin in quadrant 2 (Q2).Rotating 180 degrees counterclockwise leads to the point's final position in quadrant 4 (Q4).Explain why two similar right triangles will have the same cosine ratios.
Find the sum of the first 15 terms of the series 4+16+64+256+...
The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.What is the value of x?
A movie theater sold 422 tickets on Friday. On Saturday, they sold 518 tickets. What was the approximate percentage that ticket sales increased on Saturday?
Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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The demand function for an auto parts manufacturing company is given by f(x) = 100000 - 2500x , where x represents price and f(x) represents quantity. f^-1 (x) = _______. In the inverse function, the variable X represents _____
Answer:
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
The variable X represents the quantity.
Step-by-step explanation:
We are given that
The demand function for an auto parts manufacturing company is fiven by
f(x)=100000-25 x
Where x=Represents price
f(x)= Represents quantity
We have to find inverse function [tex]f^{-1}(X)[/tex]
Let f(x)=X
[tex]X=100000-2500 x[/tex]
[tex]2500x=100000-X[/tex]
[tex]x=\frac{100000-X}{2500}[/tex]
Substituting the value of x then we get
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Therefore, the inverse function
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Where X= Represents the quantity
[tex]f^{-1}(X)[/tex]=Represents price
You invest $3,756.00 and buy 100 shares of a company's stock. Their value increases by 12%. How much is each share worth?
Answer:
Each share worth is $42.0672 .
Step-by-step explanation:
As given
You invest $3,756.00 and buy 100 shares of a company's stock.
Their value increases by 12%.
12% is written in the decimal form
[tex]= \frac{12}{100}[/tex]
= 0.12
Share value increase = 0.12 × Investment cost
= 0.12 × 3756
= $450.72
Total value of shares becomes after increases of 12% = Share value increase + Investment cost .
Total value of shares becomes after increases of 12% = $3756+ $450.72
= $4206.72
[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]
[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]
Each shares worth = $42.0672
Therefore the each share worth is $42.0672 .
The circle shown below has ab and bc as its tangents: ab and bc are two tangents to a circle which intersect outside the circle at a point
b. if the measure of arc ac is 160°, what is the measure of angle abc? 80° 40° 60° 20°
Answer:
Answer: 20°
Step-by-step explanation:
help factoring trinomial
need 2 numbers when added = 5 and when multiplied = -24
answer is D
-3+8 = 5
-3*8 = -24
I need help with this problem and a few others
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.
Explanation:In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the
perimeter
of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.
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Factor the polynomial below.
30x^2 + 15x^2 +10x
What is 8q+3(10q^2+2)+8
A cylinder is a type of prism.
true
false
What are the solutions of the equation z2-12z+36=0
The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.
BE is [tex]7.73[/tex]
What is Square?
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
What is equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.
We have to find BE.
Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]
The angle EAB is [tex]90+60 = 150[/tex]°
Using the law of the cosines, we get
[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]
[tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]
⇒[tex]BE=7.73[/tex]
Hence, we can conclude that BE is [tex]7.73[/tex]
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SOMEONE PLEASE HELP!!!!
Which area formula or formulas show(s) a joint variation?
I A=s^2
II A=pir^2
III A=l*w
Select one:
a. III only
b. II and III
c. II only
d. I, II, and III
Answer:
Step-by-step explanation:
NEED HELP ASAP PLEASE!!!
The triangle JKL shown on the coordinate grid below is reflected once to map onto triangle J'K'L': Triangle JKL is drawn on a 4 quadrant coordinate grid with vertices J is at 8, 1. K is at 5, 7. L is at 3, 4. If vertex L' is at (−3, 4), what are the coordinates of vertex J'?
Answer:
The vertex J' is at (-8,1).
Step-by-step explanation:
If is given that the triangle JKL reflected once to map onto triangle J'K'L'.
The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).
[tex]L(3,4)\rightarrow L'(-3,4)[/tex]
It is in the form of
[tex](x,y)\rightarrow (-x,y)[/tex]
Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.
The vertices of image are,
[tex]K(5,7)\rightarrow K'(-5,7)[/tex]
[tex]J(8,1)\rightarrow J'(-8,1)[/tex]
Therefore the vertex J' is at (-8,1).
Relations and functions need help please.
A delivery truck uses $375 in gasoline during a 3 week period. if the truck is driven 5 days per week, how much is spent on gas each day?
Final answer:
Approximately $17.86 is spent on gas each day.
Explanation:
To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.
First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.
Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86
Therefore, approximately $17.86 is spent on gas each day.
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18.
Answers: symmetrical, uniform, skewed to the left, skewed to the right.
if f(x) = (x+1)^-1 and g(x) = x-2, what is the domain of f(x) divided by g(x)
a rectangle has sides 2x + 3 and x - 4. what is the perimeter of the rectangle
Find the area of a regular hexagon with a 48-inch perimeter.
48√3 in2
96√3 in2
192√3 in2
in2 means inches squared
Women athletes at the university of colorado, boulder, have a long-term graduation rate of 67% (source: the chronicle of higher education). over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university of colorado, boulder, is not less than 67%? use a 5% level of significance. find the p-value of the test statistic (round to the nearest ten thousandths).
The solution would be like this for this specific problem:
H0: p = p0, or
H0: p ≥ p0, or
H0: p ≤ p0
find the test statistic z = (pHat - p0) / sqrt(p0 * (1-p0) / n)
where pHat = X / n
The p-value of the test is
the area under the normal curve that is in agreement with the alternate
hypothesis.
H1: p ≠ p0; p-value is the area in the tails greater than |z|
H1: p < p0; p-value is the area to the left of z
H1: p > p0; p-value is the area to the right of z
Hypothesis equation:
H0: p ≥ 0.67 vs. H1: p < 0.67
The test statistic is:
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 )
z = -1.538681
The p-value = P( Z < z
)
= P( Z < -1.538681 )
= 0.0619
which of the following could be the equation of the graph shown below
Answer:
-4x+2y+-6 and y=3x-2
which angles are corresponding angles? check all that aply