Answer: 12.496
Step-by-step explanation:
The formula to find the sum of geometric progression is given by :-
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Given : The first term : [tex]a_1=10[/tex]
Common ratio = [tex]r=\dfrac{1}{5}=0.2[/tex]
Then , the sum of first five terms of a geometric series is given by :-
[tex]S_5=\dfrac{10(1-(0.2)^5)}{1-0.2}=12.496[/tex]
Hence, the sum of the first five terms of given geometric series =12.496
Use the horizontal line test to identify the relation whose inverse is not a function.
The graph 3 whose inverse is not a function.
What is an inverse of a function?The inverse function agrees with the resultant, operates and reaches back to the original function. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.
Horizontal Line Test :-
Let f be a function. If any horizontal line intersects the graph of f more than once, then f does not have an inverse. If no horizontal line intersects the graph of f more than once, then f does have an inverse.
So, according to the definition, the only graph which follows the rule of horizontal lines test is the graph 3.
Hence, the graph 3 whose inverse is not a function.
Learn more about inverse of a function, click;
https://brainly.com/question/17872426
#SPJ2
By using the horizontal line test, a relation whose inverse is not a function is: D. relation D.
In Mathematics and Euclidean Geometry, the horizontal line test states that if the graph of a function (f) is intersected by any horizontal line more than once, then, the function (f) does not have an inverse.
Conversely, if the graph of a function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.
By critically observing the graph of the given relation shown in the image attached below, we can logically deduce that it does not have an inverse because it didn't pass the horizontal line test.
Determine whether the sequence shown are arithmetic or geometric 1,8,15,22,29
A blimp is 1300 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 71.9° and 27.1°, how far apart are the two stadiums to the nearest meter?
Answer:
Step-by-step explanation:
tanα=height/distance
tanα=h/d
d=h/tanα so
d1=h/tanα and d2=h/tanß
Then the distance between them is:
d=h/tanß-h/tanα, we know that h=1300, α=(90°-71.9°=18,1°), and ß=90°-27.1°=62.9°) so
d=(3100*tan62.9)-(3100*tan18.1) meters
d≈2116 (to nearest meter)
The GCD(a, b) = 6, the LCM(a, b)=180. Find the least possible value of a+b.
Which is the best approximation for the value of √140?
A.11
B.12
C.70
D.72
Answer:
12
Step-by-step explanation:
because if you put it all together it will equal 12
A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters? 290
Find 93 • 87 using mental math.
To estimate 93 × 87 using mental math, round 87 to 90, multiply by 93 to get 8370, and subtract 3 × 93 (279) for an estimate of 8091.
To find 93 × 87 using mental math, we can employ a strategy that simplifies the multiplication process. One way is to round one of the numbers to the nearest multiple of ten, perform the multiplication, and then adjust the result accordingly. Here, we can round 87 up to 90 and multiply 93 by 90. This is easier because 90 is a multiple of 10.
93 × 90 = (93 × 9) × 10 = 837 × 10 = 8370
Since we rounded 87 to 90, we overestimated by 3 per unit of 93. Hence, we need to subtract 3 times 93 from 8370.
3 × 93 = 279
Thus, 8370 - 279 = 8091.
If (-3)^-5 =1/x, what is the value of x?
Fiona decides to join a gym for a minimum of one month to train for a triathlon. The gym charges a joining fee of $100 and a monthly fee of $38. If x represents the number of months that Fiona is a member of the gym, the equation below can be used to determine C, her total membership fee for that duration of time: 100 + 38x = C Fiona has allocated a maximum of $328 to spend on her gym membership. Which number line shows the possible number of months that Fiona can be a member of the gym?
Answer:
x = 6
Step-by-step explanation:
Given : Fiona decides to join a gym :
A joining fee of $100
A monthly fee of $38
x represents the number of months.
Fiona has allocated a maximum of $328 to spend on her gym membership
Her total membership fee for that duration of time: 100 + 38x = C
Solution :
It is given that Fiona has allocated a maximum of $328 to spend
So, C = $328
Putting this value in equation 100 + 38x = C
⇒[tex]100+38x=328[/tex]
⇒[tex]38x=328-100[/tex]
⇒[tex]38x=228[/tex]
⇒[tex]x=\frac{228}{38}[/tex]
⇒[tex]x=6[/tex]
Thus, x = 6 is number line that shows the possible number of months that Fiona can be a member of the gym.
Expressing parametric equations that don't have an x or y equation
The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).
The equation of the parabola is y =
x2 +
x +
.
The equation of the parabola with a vertex at (-2, -20) and a y-intercept at (0, -12) is y = 2x^2 + 8x - 12.
Explanation:To find the equation of the parabola, we can use the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola, and 'a' is a coefficient that determines the parabola's width and direction. Since we have the vertex (-2, -20) and the y-intercept (0, -12), we can plug in these values to solve for 'a':
y = a(x - (-2))^2 - 20
Using the y-intercept:
-12 = a(0 - (-2))^2 - 20
-12 = 4a - 20
8 = 4a
a = 2
The equation of the parabola is therefore:
y = 2(x + 2)^2 - 20
Expanding the equation:
y = 2(x^2 + 4x + 4) - 20
y = 2x^2 + 8x + 8 - 20
y = 2x^2 + 8x - 12
The final quadratic equation of the parabola is:
y = 2x^2 + 8x - 12
Please help! Given b = 4 and h = 1, what is the equation of the graph if the parent function is y = sqrt x?
A. y = sqrt (4x - 4)
B. y = sqrt (4x + 4)
C. y = - sqrt (4x - 4)
D. y = - sqrt (4x + 4)
To solve this problem, we make use of the formula:
y = a sqrt (b (x – h)) + k ---> 1
Since we are given the parent function:
y = sqrt (x) ---> 2
Then this automatically means that:
a = 1 and k = 0
So going back to equation 1 at a = 1 and k = 0:
y = 1 sqrt (b (x – h))
Since it is given that, b = 4 and h = 1, therefore:
y = sqrt (4 (x – 1))
y = sqrt (4 x – 4)
Answer:
A. y = sqrt (4 x – 4)
Explain in terms of the unit circle and geometry why the trig identity cos2 x + sin2 x = 1 holds true for all values of x.
PLEASE I NEED HELP ASAP
We can imagine the given equation cos2 x + sin2 x = 1 to be in the form of the hypotenuse equation.
Where cos x and sin x is the base and height of the triangle and 1 is the hypotenuse.
Since 1 is the hypotenuse, it also indicates to the radius of the circle. Supposing that the center of the circle is at the origin, then at all values of x (at all values of the angle), the radius of the circle will always be the same which is equal to 1.
Therefore the equation cos2 x + sin2 x = 1 holds to be true for all values of x for a unit circle.
Trey's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Trey $4.80 per pound, and type B coffee costs $5.85 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $603.45 . How many pounds of type A coffee were used?
Let x = the number of pounds of Type A coffee.
We know that this month's blend used 3 times as many pounds of type B coffee as type A coffee.
Total pounds of coffee = x + 3x
The total cost is:
(cost for Type A)(x) + (cost for Type B)(3x) = $603.45
$4.80x + $5.85(3x) = $603.45
$4.80x + $17.55x = $603.45
$22.35x = $603.45
x = 603.45/22.35 = 27 pounds
Simplify the expression. Type your answer in the blank.
-
Mr. James has cylindrical beakers that measure 4 inches in diameter and are 9 inches high. What is the volume contained within the beakers? Use 3.14 for pi. Round your answer to the nearest hundredth. 56.52 cubic inches 100.34 cubic inches 113.04 cubic inches 226.08 cubic inches
The answer is C, or 113.04 cubic inches.
Whats the perimeter of a rectangle with length 12 m and width 5m
The surface area of a sphere
324 square centimeters. What is volume in cubic centimeters, of the sphere? Express your answer in terms of pi
The surface area of the sphere is SA = 324π cm².
Calculate the surface area of the sphere by using the formula: SA = 4πr².
To find the value of r, substitute SA = 324π in the above formula.
324π = 4πr²
81 = r²
r = ± 9.
The measurements of the sphere cannot be expressed in negative sign.
The radius of the sphere is r = 9 cm.
Calculate the surface area of the sphere by using the formula: V = (4/3)πr³.
Substitute r = 9 in the above formula
V = (4/3)π 9³ = 972π cm³.
3+-1/1/3 the first half is 3+-1 the second half is 1/3
where is the best place to learn spanish for free and become fluent on line
Answer:
DUOLINGOOOO
Step-by-step explanation:
keeps you persistent through notifications so turn it on
How do you write 56% as a fraction in simplest form?
We can write 56% as a fraction to the simplest form as [tex]\mathbf{= \dfrac{14}{25} }[/tex]
A fraction is a numeric value divided into two parts, the upper part(numerator) and the lower part(denominator) which are separated by a division line.
From the given information:
56% can be written in fraction as [tex]\mathbf{\dfrac{56}{100}}[/tex]
Now, to its simplest form means to divide the numerator and the denominator to their lowest term. By doing so, we have:
[tex]\mathbf{\dfrac{56}{100}}[/tex]
Divided by (2)
[tex]\mathbf{= \dfrac{28}{50} }[/tex]
Divided by (2)
[tex]\mathbf{= \dfrac{14}{25} }[/tex]
Therefore, we can conclude that 56% as a fraction to the simplest form is [tex]\mathbf{= \dfrac{14}{25} }[/tex] since no other number can go in both the numerator and the denominator.
Learn more about fraction here:
https://brainly.com/question/6201432?referrer=searchResults
How many possible 10-digit phone numbers with the area code 617 are there? (any decimal digit can be the digit of a phone number. For instance the number 617−000−0000 is a possible phone number)
Answer:
10,000,000
This is the answer because you have to do 10^7 because 3 of ten dights are filled so you have seven dights remaining. And yeah, i already checked it in my homework thingy fir RSM cuz I had the same problem. So yeah. I hope everyone who sees this has a lovely and beautiful day.
Quote of the day is: Everyone Suffers. Thats the truth. You have you pain and I have mine. But in your life, you pain will come to an end. Don't waste good opportunities and don't be afraid to hide yourself of how you look, or act, or your race and sexuality. Think of it like this, if your pain is a dark tunnel, you are so close to the end you can almost touch the light, so keep moving!
-Me
Hope everyone has a great day and an amazing life ahead
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=−16 t 2 +25t+8 h=−16t2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Geometry Question Please Help!!!!
Neptune has 8 known moons. This is 2 more than 1/3 of the number of known moons on Saturn. How many moons is Saturn known to have?
Through setting up and solving the equation 1/3 * x + 2 = 8, where x represents the number of Saturn's moons, it was determined that Saturn is known to have 18 moons.
Explanation:The student's question pertains to a comparison of the moons of Neptune and Saturn, using mathematical operations to deduce the number of known moons of Saturn. First, we're told that Neptune has 8 known moons, which is said to be 2 more than 1/3 of the number of known moons on Saturn. We are seeking to solve for the number of moons that Saturn has.
To find out, we set up an equation where 1/3 of the number of moons of Saturn plus 2 equals the number of Neptune's moons: 1/3 * x + 2 = 8, where x represents the number of Saturn's moons. Solving for x, we subtract 2 from both sides to get 1/3 * x = 6. We then multiply both sides by 3 to isolate x and find that x = 18.
Therefore, Saturn is known to have 18 moons according to the given information.
Which of the following types of functions cannot have "all real numbers" as either its domain or its range? Exponential function Quadratic function Linear function Inverse Variation function
: adam and melissa went fly-fishing and caught a total of 32 salmon. melissa caught three times as many salmon as adam. how many salmon did adam catch?
This prism has a volume of 112 cm3. What would the volume of the prism be if each dimension was doubled?
(Scale factor is 2)
224 cm3
896 cm3
448 cm3
336 cm3
If each dimension was doubled, the volume of the prism would be: B. 896 cm³.
What is a scale factor?In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
Scale factor of volume = (Scale factor of dimensions)³
Scale factor of volume = (2)³
Scale factor of volume = 8
Therefore, the new volume is given by;
New volume of prism = 112 × 8
New volume of prism = 896 cm³.
Read more on scale factor here: brainly.com/question/29967135
#SPJ2
The growth of a new strain of bacteria is represented by 7=79.31(1.48)^x,where x represents the number of days and y represents the number of bacteria. which is the best prediction for the number of bacteria on day 6
A.833
B.117
C.704
D.647
Answer:
A. 833
Step-by-step explanation:
Given:
The growth of a new strain of bacteria is represented by [tex]y = 79.31(1.48)^x[/tex], where "x" represents the number of days and "y" represents the number of bacteria.
We need to find the number of bacteria on day 6.
So, here x = 6, we need to plug in x = 6 in the given function and find the answer.
[tex]y = 79.31(1.48)^6[tex]
Simplify the above expression, we get
y = 833.49
The bacteria cannot be in decimal form, let's round off the answer to nearest whole number.
y = 833
Therefore, answer is A. 833
what is the inverse funtion f(x)=4x+8?