Answer:
f(16)=162
Step-by-step explanation:
-In a geometric sequence, the quotient between any tow consecutive numbers is called the common ratio,r:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
Given that f(3)=32 and f(9)=72, we can find the common ratio as below:
[tex]r=\frac{a_n}{a_{n-1}}\\\\\therefore \frac{f(9)}{f(3)}=r^6\\\\\frac{72}{32}=r^6\\\\r^6=2.25\\\\r=2.25^{1/6}[/tex]
#We substitute and use the same formula to find the nth term:
[tex]a_n=ar^{n-1}[/tex]
let f(3) be a(the first term):
[tex]a_n=ar^{n-1}\\\\a_{16}=32(2.25^{1/6})^{16-3-1}\\\\a_{16}=32(2.25^{1/6})^{12}\\\\\\=162[/tex]
Hence, f(16)=162
* WILL GIVE BRAINLIEST *
Caleb started with 50 bacteria for his science experiment, and the number of bacteria doubled in one day. Jenna also started with 50 bacteria for her experiment, and after one day the number of bacteria was equal to 50 to the second power. How many bacteria did Caleb and Jenna each have in their experiments?
Answer:
100+50²=2600
Step-by-step explanation:
because 50x2=100 and 50² is 2500. Add those and you get 2600.
The number of bacteria Caleb and Jenna each have in their experiments is 2600.
Given that, Caleb started with 50 bacteria for his science experiment, and the number of bacteria doubled in one day.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The number of bacteria doubled
= 2×25=50
The number of bacteria was equal to 50 to the second power
= 50²
= 2500
So total = 2500+100=2600
Therefore, the number of bacteria Caleb and Jenna each have in their experiments is 2600.
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George can run 10 laps around the track in 25 minutes. Write an equation to represent the relationship between x laps and y minutes
Question 4 options:
y = x + 5/2
y = 5/2x
y = x + 2/5
y = 2/5X
Answer: The answer is D: y=2/5x
Step-by-step explanation:
Let y represent the number of laps George runs, and x the number of minutes it takes him to run those laps. We know that it it takes George 25 minutes to run 10 laps; therefore, the number of laps George runs per minute is 10/25 which is equal to 2/5.
(Make sure you keep your promise(s) lol.)
Which equation represents a circle with a center at (2,-8) and a radius of 11?
(x – 8)2 + (y + 2)2 = 11
(x - 2)2 + (y + 8)2 = 121
(x + 2)2 + (y - 3)2 = 11
(X + 8)2 + (y - 2)2 = 121
Answer:
2 Nd one
Step-by-step explanation:
Got it right
Answer:
B. (x – 2)² + (y + 8)² = 121
Step-by-step explanation:
Mr. Thomas cooked 36 hamburgers and hot dogs at a cookout. He cooked twice as many hot dogs as hamburgers. How many hamburgers and hot dogs were cooked?
(Use Substitution)
A. (24 hamburgers, 12 hot dogs)
B. (12 hamburgers, 24 hot dogs)
C. (6 hamburgers, 12 hot dogs)
D. (12 hamburgers, 6 hot dogs)
Answer:
b
Step-by-step explanation:
You would have twice as many hot dogs and 24 is two times 12 and if you add them you get 36.
Natalie budgets $146 for yoga training. She buys a yoga mat for $10 and pays $9 per yoga class. Which inequality represents the number of classes, c, that Natalie can take and stay within her budget?
A. 146 ≤ 9c + 10
B. 146 ≥ 9c + 10
C. 146 ≤ 10c + 9
D. 146 ≥ 10c + 9
if i can get brainliest that would be great
Answer: The answer is B. Because she can't go over 146. $10 is a one time fee and she pays $9 per classes.
Answer:
a
Step-by-step explanation:
you must subtract ten from each side to get 136 is less than or equal to 9c then divide by nine to get c=15.111111
What is the range of the data below?
60
70
80
90
100
oooo
Help!
Answer:
40
Step-by-step explanation:
100-60=40
Answer:
40
Step-by-step explanation:
Range is the difference between the highest value, and the lowest value
1) Ramesh is buying a new bike helmet. The price of the helmet is $60 and there is a 5% sales
tax. Ramesh wants to know the total price of the bike helmet including sales tax.
Which box?
Answer:
$63.00
Step-by-step explanation:
$60 * 5% or $60 * 0.05 = $3.00
$60 + $3 = $63.00
Answer:
its the third box
Step-by-step explanation:
i got it right
The product of two numbers is 161. The difference between the two is 16. What are the two numbers?
Answer:
23 and 7
Step-by-step explanation:
Multiply 23 and 7 to get 161. Subtract 7 from 23 and get 16
Answer: 23 and 7
Step-by-step explanation: When you multiply 23 x 7, you will get the answer 161.
Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars.
0.8d
d – 0.2
d – 0.2d
1 – 0.2d
The correct expression that represents a 20% discount off the original price d is 0.8d or d – 0.2d. The other options do not correctly represent a percentage discount from the original price.
Explanation:The expression that represents a 20% discount off the price of an item that originally cost d dollars would be calculated by first determining what 20% of the original price is, and then subtracting that value from the original price. So if the original price is d, then 20% of d is 0.2d. Subtracting that from d would give us the discounted price. Therefore, the correct expression that represents a 20% discount would be d – 0.2d, which simplifies to 0.8d.
d – 0.2 is not a percentage of d, but rather a fixed amount subtracted from d, and 1 – 0.2d is not meaningful in the context of pricing and discounts. So the expressions that represent a 20% discount off the price are:
Yes: 0.8dNo: d – 0.2Yes: d – 0.2dNo: 1 – 0.2dThe correct answers are the expressions: 0.8d and d – 0.2d.
In the circle below, UW is a diameter and UX is tangent at U. Suppose m UV=128
Answer:
Step-by-step explanation:
The value of the angle ∠VUW is 26° and ∠VUX will be 116°.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
Given the circle
Since ∠UOV is 128°
So,
∠UOW = 180 - ∠UOV
∠UOW = 180 - 128 = 52°
Now,
∠VUW = 1/2 ∠UOW
∠VUW = (1/2)52 = 26°
Now ∠VUX = ∠VUW + 90°
∠VUX = 26 + 90 = 116°
Hence "The value of the angle ∠VUW is 26° and ∠VUX will be 116°".
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Which formula is used to calculate the standard deviation of sample data?
s = StartRoot StartFraction (x 1 minus x overbar) squared + (x 2 minus x overbar) squared + ellipsis + (x n minus x overbar) squared Over n minus 1 EndFraction EndRoot.
sigma squared = StartFraction (x 1 minus mu) squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction
Sigma = StartRoot StartFraction (x 1 minus mu) squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction EndRoot
x = StartFraction (x 1 minus x overbar) squared + (x 2 minus x overbar) squared + ellipsis + (x n minus x overbar) squared Over n minus 1 EndFraction
Answer:
the first one
Step-by-step explanation:
i just got it right on edge
The standard deviation of sample data is "[tex]s = \sqrt{\frac{(x_1 -\bar{x})^2+ (x_2-\bar{x})^2 + ..... + (x_n -\bar{x})^2}{ n- 1}}[/tex]"
The standard deviation of the sample data:Random variables, samples, statistical populations, information sets, or probabilistic distributions are equal to the square root of its variance.
It's much less resilient in reality than the average absolute deviation, but it makes algebraic expressions easier.
A sampling divided by the size of the data set is less than one, n - 1. To get the standard deviation, take the square root of the variance. The standard deviation is obtained by taking the square root of the standard deviation.
Therefore, the standard deviation of sample data is "[tex]s = \sqrt{\frac{(x_1 -\bar{x})^2+ (x_2-\bar{x})^2 + ..... + (x_n -\bar{x})^2}{ n- 1}}[/tex]"
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Use Vieta's Theorem to solve the problems. The difference of the two solutions of x2+19x+c=0 is 15. Find c.
Answer:
c = 34
Step-by-step explanation:
x = [-19 +/- sqrt(19² - 4(1)(c)]/2
x = [-19 +/- sqrt(361 - 4c)]/2
The difference of the roots would be:
sqrt(361 - 4c) = 15
361 - 4c = 15²
361 - 225 = 4c
4c = 136
c = 34
You spin the spinner for candy land. There are 4 colors on the spinner that have equal likelihoods of occurring. These colors are red, blue, green, and yellow. What's the chance of spinning green? Record your answer as a simplified fraction using "/" as your fraction key.
Answer:
1/4
Step-by-step explanation:
If you have four colors on the spinner and you want to land on the green spot and there is 1/4 chances
Simplify and solve for x. 5(x+20)= 7x+30
Answer:
x = 35
Step-by-step explanation:
Solve for x:
5 (x + 20) = 7 x + 30
Expand out terms of the left hand side:
5 x + 100 = 7 x + 30
Subtract 7 x from both sides:
(5 x - 7 x) + 100 = (7 x - 7 x) + 30
5 x - 7 x = -2 x:
-2 x + 100 = (7 x - 7 x) + 30
7 x - 7 x = 0:
100 - 2 x = 30
Subtract 100 from both sides:
(100 - 100) - 2 x = 30 - 100
100 - 100 = 0:
-2 x = 30 - 100
30 - 100 = -70:
-2 x = -70
Divide both sides of -2 x = -70 by -2:
(-2 x)/(-2) = (-70)/(-2)
(-2)/(-2) = 1:
x = (-70)/(-2)
The gcd of -70 and -2 is -2, so (-70)/(-2) = (-2×35)/(-2×1) = (-2)/(-2)×35 = 35:
Answer: x = 35
Answer:
x = 35
Step-by-step explanation:
5(x+20)= 7x+30
5x + 100 = 7x + 30
-30 -30
5x + 70 = 7x
-5x -5x
70 = 2x
/2 /2
35 = x
admission to the fair is $5.25 for adults and $3.75 for children. A group spends $29.25 for admission. How many of each kind of ticket did they buy?
Answer:
Two adults and five children
Step-by-step explanation:
(3.75×5)+(5.25×2) = 29.25
18.75 + 10.5 = 29.25
(:
Factor completely please
Answer:
Step-by-step explanation:
hello :
1-x² = (1-x)(1+x) by identity : a²-b²=(a-b)(a+b)
Find the area of the isosceles triangle.
13 cm side
10 cm base
The area of the given isosceles triangle with 13 cm and 10 cm base will be 60 square cm.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
An isosceles triangle is a triangle in which two sides are the same.
The given isosceles triangle has been drawn below,
The area of a triangle is given as (1/2) × base × height.
Height = √(13² - 5²) = 12
Area = (1/2) × 10 × 12 = 60 square cm.
Hence "The area of the given isosceles triangle with 13 cm and 10 cm base will be 60 square cm".
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To find the area of an isosceles triangle with given side lengths, use the Pythagorean theorem to find the height. Then, apply the formula for the area of a triangle using the base and the calculated height. The area of the given isosceles triangle is 60 square centimeters.
To find the area of an isosceles triangle with a base of 10 cm and two equal sides of 13 cm, we first need to determine the height of the triangle. We can use the Pythagorean theorem to find the height (h).
Since the base splits the isosceles triangle into two right triangles, each having a base of 5 cm (half of 10 cm) and a hypotenuse of 13 cm:
Using the Pythagorean theorem:
→ Hypotenuse (hyp) = 13 cm
→ Base/2 (base) = 5 cm
→ Height (h) = ?
→ hyp² = base² + h²
→ 13² = 5² + h²
→ 169 = 25 + h²
→ h² = 169 - 25
→ h² = 144
→ h = √144
→ h = 12 cm
Now that we know the height, we can use the formula for the area of a triangle:
→ Area = 1/2 × base × height
→ Area = 1/2 × 10 cm × 12 cm
→ Area = 5 × 12
→ Area = 60 square centimeters
What is true about the transformation that was
performed? Check all that apply
g(x) has an axis of symmetry atx=3
g(x) is shifted down 5 units from the graph of fix).
g(x) is shifted right 3 units from the graph of f(x).
g(x) is shifted up 4 units from the graph of f(x).
g(x) is narrower than fu).
Answer:
the answer is A C and D if you’re using edu.
Step-by-step explanation:
Answer:
A,C,DStep-by-step explanation:
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = 1/3x -3
Step-by-step explanation:
Some help please?
What are the factors of the product represented below?
Answer:
A. (x+4) (2x+3)
Step-by-step explanation:
Find the median of the data.
12, 33, 18, 28, 29, 12, 17, 4, 2
The median is
Answer:
The median is 29
Step-by-step explanation:
So you have to cross out 12 then 2 then 33 then 4 then 18 then 17 then 28 then 12 and the last number that's standing is 29.
What is the value of x?
Answer:
Step-by-step explanation:
since we can see that the lines are parallel
and we can see that the both are interior angles and when we sum up both angles we get 180
2x - 5 + 45 = 180
2x + 40 =180
2x = 180 - 40
2x =140
x = 140/2
x = 70
Solve each equation. Be sure to check your solution.
0.3a = 51
Answer:
a = 170
Step-by-step explanation:
0.3a = 51
a = 51 : 0.3
a = 51 : 3/10
a = 51 x 10/3
a = 510/3
a = 170
0.3x170 =
= 3/10x170
= 510/10
= 51
Answer:
a= 170
Step-by-step explanation:
[tex]0.3a = 51 \: [/tex]
[tex]a = \frac{51}{0.3} = 170 \: [/tex]
To verify:
LHS = 0.3 a = 0.3× 170= 51 = RHS
A triangle undergoes a sequence of transformations. First, the triangle is dilated by a scale factor of 1/3 about the origin. Then the triangle is reflected over the x-axis. Finally, the triangle is translated left 3 units and up 2 units. How does the image triangle compare to the pre-image triangle?
The image triangle compare to the pre-image triangle will be similar due to dilation.
Step-by-step explanation:
As given in the question ,the sequence of transformation undergone by a triangle are :-
First, the triangle is dilated by a scale factor of 1/3 about the origin.Secondly, the triangle is reflected over the x-axis the triangle is translated left 3 units and up 2 units.
Due to the process of dilation, the two triangles will be similar. Another important factor is that the scale factor is less than one and is a reduction, thus, the image will be smaller than the pre-image but the triangle will be similar
The transformations mentioned in the above statement altered the position and scale of the triangle, but the angle measures of both the triangle remains the same.
Thus we can say that
The image triangle compare to the pre-image triangle will be similar due to dilation.
Answer:
Sample Response: Because there was a dilation, the two triangles will be similar. The scale factor was less than one, so the image will be smaller than the pre-image.
Step-by-step explanation:
edge ;)
Evaluate each finite series for the specified number of terms...
40+20+10+...; n=10
(Please show work)
Answer:
the sum of the first 10 terms is: 79.921875
Step-by-step explanation:
Notice that this is a geometric series, of the sequence that has "40" as the first term, and the following ones are obtained by multiplying by the common ratio "1/2".
So the common ratio [tex]r=\frac{1}{2}[/tex], and the first term [tex]a_1=40[/tex], then, recalling the formula for the partial sum of n terms of a geometric sequence:
[tex]S_n=\frac{a_1\,(1-r^n)}{1-r}[/tex]
we can find the sum of this sequence's first 10 terms (n=10):
[tex]S_n=\frac{a_1\,(1-r^n)}{1-r} \\S_{10}=\frac{40\,(1-(\frac{1}{2}) ^{10})}{1-\frac{1}{2} } \\S_{10}=79.921875[/tex]
What is the ratio of a:c?
Step-by-step explanation:
The answer is 2 : 3 because the value of a is 2 and c is 3
Translate the sentence into an equation.
Four times the sum of a number and 2 equals 5.
Use the variable x for the unknown number.
Find the area of these composite shapes
Answer:
37.5 cm 2
Step-by-step explanation:
The area of the first figure, the rectangle is 30cm2. The base which is 5cm, times the height which is 6cm equals 30cm2. The triangle's area is 7.5cm2 because the height which is 3cm times the base which is 5cm equals 15cm. Because it's a triangle tho, we have to find half of it which 7.5cm2. 30cm2+7.5cm2 equals 37.5cm2.
A company that makes mirrors sends their slightly flawed products to a discount store. This week, the company sent four mirrors to the discount store. Each mirror is approximately rectangular, with both lengths the same and both widths the same.
Mirror 1
length: 16 inches
width: 18 inches
diagonal: 25 inches
Mirror 2
length: 16 inches
width: 18 inches
diagonal: 26 inches
Mirror 3
length: 16 inches
width: 18 inches
diagonal: 23 feet
Mirror 4
length: 16 inches
width: 18 inches
diagonal: 24 inches
Based on these dimensions, which mirror is the closest to rectangular?
Mirror 1
Mirror 2
Mirror 3
Mirror 4
Answer:
mirror 4
Step-by-step explanation:i just did the quiz and got it right
Answer:D
Step-by-step explanation:
In the accompanying diagram, AEFB, AD II EC , DF || CB, mDAE = 34 and m DFE = 57. Find
m < ECB.
Answer:
1. Solve small triangle
2. 180-90-57=33
3.solve medium triangle
4. E=33
5.C=90
6.180-90-33=57
7.B=57
8. solve big triangle
9.A=34
10.F=57
11.D=90