Answer:
So, we divide
1
by
5
6
→
1
÷
5
6
→
1
⋅
6
5
→
6
5
⇒
1
1
5
=
1.2
So, there are
1
1
5
number of
5
6
's in
1
Step-by-step explanation:
the function that gives the deer population \( P(t) \) on the reservation t years from now is:
[tex]\[ \boxed{P(t) = 170 \times (1.30)^t} \][/tex]
To write a function that gives the deer population [tex]\( P(t) \)[/tex] on the reservation t years from now, where the population is increasing at a rate of 30% per year, we'll use the formula for exponential growth:
[tex]\[ P(t) = P_0 \times (1 + r)^t \][/tex]
Where:
- [tex]\( P(t) \)[/tex] is the population after t years,
- [tex]\( P_0 \)[/tex] is the initial population (in this case, 170),
- r is the annual growth rate (in decimal form), and
- t is the number of years.
Given that the population is increasing at a rate of 30% per year, we have [tex]\( r = 0.30 \)[/tex].
Substituting the given values into the formula, we get:
[tex]\[ P(t) = 170 \times (1 + 0.30)^t \][/tex]
Simplifying further:
[tex]\[ P(t) = 170 \times (1.30)^t \][/tex]
Therefore, the function that gives the deer population \( P(t) \) on the reservation t years from now is:
[tex]\[ \boxed{P(t) = 170 \times (1.30)^t} \][/tex]
The complete Question is given below:
There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.
Sarai is mixing a solution. She pours all the liquid from a full small beaker into a larger beaker. The liquid fills the large beaker to 15% of its capacity. If the small beaker holds 300 mL, how much does the large beaker hold?
Answer:
2000 ml
Step-by-step explanation:
Given: Sarai pours all the liquid from a full small beaker into a larger beaker.
The liquid fills the large beaker to 15% of its capacity.
The small beaker holds 300 ml.
Lets assume capacity of large beaker to hold be "x".
As given, Sarai pours all the liquid from a full small beaker into a larger beaker
∴ [tex]15\% \times x= 300\ ml[/tex]
⇒ [tex]0.15x= 300[/tex]
Dividing both side by 0.15
⇒[tex]x= \frac{300}{0.15}[/tex]
∴ [tex]x= 2000\ ml[/tex]
Hence, the large beaker can hold 2000 ml of liquid.
What is the answer
Answer:
A
Step-by-step explanation:
Move the entire triangle left 6 units.
Answer: A
Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 Find f(g(4)). f(g(4)) =
Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
f(x) = x-7
g(x) = x^2
f(4) = 4-7 = -3
g(f(4)) = (-3)^2
(-3)^2 = 9
g(f(4)) is 9
Find f(g(4)).
f(g(4)) = f(g(4)) = 9
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
Composition of the functions is sometimes commutative.
hope this helps!! have an amazing day <3
2021 edg
Which expression represents the phrase the sum of twice a number and 7
Answer:
2n+7
Step-by-step explanation:
A regular pentagon is dilated by a scale factor of 73 to create a new pentagon. How does the perimeter of the new pentagon compare with the original perimeter?
Question:
A regular pentagon is dilated by a scale factor of 7/3 to create a new pentagon. How does the perimeter of the new pentagon compare with the original perimeter?
Answer:
The perimeter of the new pentagon is equal to [tex]\frac{7}{3}[/tex] times the perimeter of the original pentagon
Solution:
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let ,
z is the scale factor
x is the perimeter of the new pentagon
y is the perimeter of the original pentagon
Then,
Scale factor = ratio of perimeters
[tex]z=\frac{x}{y}[/tex]
In this problem we have
[tex]z=\frac{7}{3}[/tex]
Substituting we get,
[tex]\frac{7}{3} = \frac{x}{y}\\\\x = \frac{7}{3}y[/tex]
Which means,
[tex]perimeter\ of\ the\ new\ pentagon = \frac{7}{3} \times \text{ perimeter of the original pentagon}[/tex]
Therefore , the perimeter of the new pentagon is equal to [tex]\frac{7}{3}[/tex] times the perimeter of the original pentagon
The perimeter of a rectangle must be less than 172 feet. If the length is known to be 53 feet, find the range of possible widths for the rectangle. (Note: The formula for the perimeter of a rectangle is P=2l+2w , where l is the length and w is the width).
Express your answer in interval notation. Use decimal form for numerical values.
Answer:
1 - 32.5
Step-by-step explanation:
If the perimider is less then 172, that the limit is 171. 171 - (53)2 = 65. divide that by the two sides that are the width it equals 32.5
Perimeter is the sum of the length of the sides used to make the given figure. The range of the width of the rectangle is (0,33).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given that the perimeter of a rectangle must be less than 172 feet. Also, given that the length of the rectangle is 53 feet. Therefore, we can write inequality of the width of the rectangle as,
2(Length) + 2(Width) < Perimeter
2(53 feet) + 2(Width) < 172 feet
106 feet + 2(Width) < 172 feet
2(Width) < 172 feet - 106 feet
2(Width) < 66 feet
Width < 66feet / 2
Width < 33 feet
Hence, the range of the width of the rectangle is (0,33).
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Given the equation y=-1/3x-7, what are the slope and the y-intercept?
Answer: slope is -1/3 and the y intercept is -7
Step-by-step explanation:
If the function f(x) = (2x - 3)^3is transformed to g(x) = (-2x - 3)^3, which type of transformation occurred?
A. vertical shift
B. horizontal reflection
C. horizontal shift
D.vertical reflection
A snowboard is on sale for $476. If the
original price was $560, what is the
percent discount?
Answer:
15%
Step-by-step explanation:
we call the original price 100% and to find the discount amount :
Multiply 100 by $476 then divide by $560
100 × $476 ÷ $560 = 85
$476 is 85% of the original price therefore the amount of discount as in percentage is 100 - 85 = 15%
A line passes through the origin and through points A(−2, b−14) and B(14−b, 72). What is the greatest possible value of b?
Answer:
The greatest possible value for b is 26.
Step-by-step explanation:
Given that the line passes through the Origin O(0, 0); A(-2, b - 14) &
B(14 - b, 72).
Let us assume the points are in the order: AOB.
Since the line passes through all these points the slope of the line segment AO = The slope of the line segment AB.
Slope of a line with two points: [tex]$ \frac{y_2 - y_1}{x_2 - x_1} $[/tex] where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the points given.
[tex]$ (x_1, y_1) = (0,0) $[/tex]
[tex]$ (x_2, y_2) = (-2, b - 14) $[/tex]
Therefore, the slope of the line segment AO = [tex]$ \frac{b - 14}{-2} $[/tex]
Similarly, for the slope of the line segment OB.
The two points are [tex]$ (x_1, y_1) = (0, 0) $[/tex] and [tex]$ (x_2, y_2) = (14 - b, 72) $[/tex].
The slope is: [tex]$ \frac{72}{14 - b } $[/tex]
Since, the slopes are equal we can equate:
[tex]$ \frac{b - 14}{-2} = \frac{72}{14 - b} $[/tex]
[tex]$ \implies \frac{b - 14}{-2} = \frac{72}{-(b - 14)} $[/tex]
[tex]$ \implies (b - 14)^2 = 72 \times 2 = 144 $[/tex]
[tex]$ \implies (b - 14)^2 = 12^2 $[/tex]
Taking square root on both sides we get:
[tex]$ \implies (b - 14) = \pm 12 $[/tex]
[tex]$ \implies b = 2 \hspace{2mm} or \hspace{2mm} 26 $[/tex]
Therefore, the maximum value of b = 26.
Hence, the answer.
With a simple interest rate of 12%, how much will an investment of $20,000 be worth in 10 years
Answer:
$24,000
Step-by-step explanation:
If each year you get 12% of interest 20,000 dollars x 0.12 = 1 year worth of interest or $2400 then if its over a 10 year span it would be $2,400 x 10 (amount of years) = $24,000
Answer: $44,000
Step-by-step explanation:
1 > 5 (b - 14) + 16 help me please
Answer:
b < 11
Step-by-step explanation:
Given
1 > 5(b - 14) + 16 ← distribute and simplify right side
1 > 5b - 70 + 16
1 > 5b - 54 ( add 54 to both sides )
55 > 5b ( divide both sides by 5 )
11 > b, thus
b < 11
True or false 4.62 < 4.67
True, 4.62 is less than 4.67
identify the terms, coefficients, and constants in the expression.
1. 3 + c + e
2. 5m + 9
3. 3p2 + 7
Answer:
1. 3 is a constant term of the expression.
2. 9 is constant term of the expression.
3.7 is a constant term of the expression.
Step-by-step explanation:
1. 3+c+e
Here 3 is a constant term of the expression.
c and e are the variables.
The coefficient of c is 1.
The coefficient of e is 1.
It is a trinomial expression.
2.
5m +9
9 is constant term of the expression.
m is a variable of the expression.
The coefficient of m is 5.
It is a binomial expression.
3.
3p²+7
7 is a constant term of the expression.
p is the variable.
The coefficient of p² is 3.
It is a binomial expression.
- The lengths (in feet) of the sides of a pentagon can be represented by these
expressions: 6a, a, 4, 8, and 2a. Write a simplified expression for the perimeter
of the pentagon in feet.
Answer:
9a+12
Step-by-step explanation:
The perimeter is the sum of the side lengths, so is ...
6a + a + 4 + 8 + 2a
= a(6 +1 +2) + (4 +8)
= 9a +12
Bonds are a(n) _______________ instrument.
Answer:
indebtedness
Step-by-step explanation:
Find the distance between the points (2,8) and (-1,9)
Use the distance formula: D=sqrt((x2-x1)^2+(y2-y1)^2)
Plug in:
D=sqrt((9-8)^2+(-1-2)^2)
D=sqrt(1^2+(-3)^2)
D=sqrt(1+9)
D=sqrt(10)
So the distance is about 3.16 units
Hope this helped!
PLEASE HELP ! Trying to make honor roll !
Which point represents the solution to the system of equations below?
Answer:
B
Step-by-step explanation:
Because it is higher than the others and also includes the number 2, as it says in the fraction and is located in 1/2
Answer:
Point A
Step-by-step explanation:
You already know y is -2. Just substitute that to the top equation and solve for x. X would be -4.
(-4, -2)
Find the point on the graph and you'll see it falls on point A.
what is 3.40425532 reduced
enter the explicit rule for the geometric sequence.
3/2, 3/4, 3/8, 3/16, 3/32, . . .
an=
PLS HELP! WILL MAKR BRAINLIEST AND GIVE 20 POINTS!!!!
Answer:
See attached table for the answers.
Step-by-step explanation:
Because 1/4 inches is 2 feet, 1 inch is 8 feet, making the conversion factor x8.
Answer:
The scale factor is 1/4 inch to 2 feet but can be simplified to 8 feet per inch.
1. Lobby drawing length is 2 inches.
2. Principal's Office actual length is 10 feet.
3. The library's drawing length is 2.5 inches.
4. The science lab's actual length is 12 feet.
5. The cafeteria's drawing length is 6 inches.
6. The music room's actual length is 32 feet.
8. The gym's actual length is 104 feet.
9. The auditorium's drawing length is 7 inches.
10. The teachers' lounge's actual length is 14 feet.
I hope this helped you. If you would mark brainliest that would be appreciated.
spinner at the right is spun 12 times. It lands on blue 1 time.
What is the experimental probability of the spinner landing on blue?
Answer:
1/12
Step-by-step explanation:
How many times smaller is 2 × 10-3 than 4 × 10-2? PLEASE HELP
A.
20
B.
200
C.
2,000
D.
0.2
Step-by-step explanation:
Let x be the smaller than 4 ×[tex]10^{-2}[/tex].
To find, the number of times smaller is 2 × [tex]10^{-3}[/tex] than 4 × [tex]10^{-2}[/tex] = ?
∴ x = [tex]\dfrac{4\times 10^{-2}}{2\times 10^{-3}}[/tex]
= 2 × [tex]10^{-2}[/tex] × [tex]10^{3}[/tex]
Using the identity,
[tex]a^{m}=\dfrac{1}{a^{-m}}[/tex]
= 2 × [tex]10^{-2+3}[/tex]
Using the identity,
[tex]a^{m} \timesa^{n}=a^{m+n}[/tex]
= 2 × [tex]10^{1}[/tex]
= 2 × 10
= 20
Thus, the required "option A) 20" is correct.
The - - - - - - - - - - - - - - - -,f(x)=x, is formed by the composition of a function and its inverse (2 words)
Answer:
Identity function
What two numbers multiply to -27 and add to 1
Answer:
3 x 9, 1 x 27, 9 x 3
Step-by-step explanation:
you have to multiple 3 x 9 to get to 27. you have to multiple 1 x 27 to get 27. you have to multiple 9 x 3 to get 27.The two numbers that multiply to -27 and add to 1 are 9 and -3.
To find two numbers that multiply to -27 and add to 1, we can use the method of factoring and algebraic manipulation.
Let the two numbers be x and y.
Step 1: Set up the equations based on the given conditions:
xy = -27 (the two numbers multiply to -27)
x + y = 1 (the two numbers add to 1)
Step 2: Solve one of the equations for one variable in terms of the other.
From the second equation, we can express y in terms of x:
y = 1 - x
Step 3: Substitute the value of y into the first equation:
x(1 - x) = -27
Step 4: Expand and rearrange the equation:
x - x^2 = -27
Step 5: Rewrite the equation in standard quadratic form:
x^2 - x - 27 = 0
Step 6: Factor the quadratic equation:
(x - 9)(x + 3) = 0
Step 7: Set each factor equal to zero and solve for x:
x - 9 = 0 --> x = 9
x + 3 = 0 --> x = -3
So, the two numbers are 9 and -3, as 9 * -3 = -27, and 9 + (-3) = 1.
In conclusion, the two numbers that multiply to -27 and add to 1 are 9 and -3. By setting up and solving the system of equations and factoring the quadratic equation, we obtained these two values that satisfy the given conditions.
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RS and ST are 2 sides of a regular 12-sided polygon.
RT is a diagonal of the polygon.
Work out the size of angle STR.
You must show your working.
Answer:
15°
Step-by-step explanation:
The exterior angle at vertex S is 360°/12 = 30°. That angle has a measure that is equal to the sum of the congruent angles at R and T of ΔRST. In other words, ...
∠T = 30°/2 = 15°
The size of angle STR is 15°.
The sides of a regular polygon are congruent.
The size of STR is 15 degrees
The polygon is 12-sided.
This means that:
[tex]\mathbf{n =12}[/tex]
The sum of angles in a regular hexagon is 360.
So, the angle at vertex S is:
[tex]\mathbf{\theta = \frac{360}{n}}[/tex]
This gives
[tex]\mathbf{\theta = \frac{360}{12}}[/tex]
[tex]\mathbf{\theta = 30^o}[/tex]
The external angle of a triangle equals the sum of the opposite internal angles.
This means that:
[tex]\mathbf{\theta = \angle STR + \angle SRT}[/tex]
Where:
[tex]\mathbf{ \angle STR = \angle SRT}[/tex]
So, we have:
[tex]\mathbf{\theta = \angle STR + \angle STR}[/tex]
[tex]\mathbf{\theta = 2\angle STR}[/tex]
Substitute [tex]\mathbf{\theta = 30^o}[/tex]
[tex]\mathbf{30^o = 2\angle STR}[/tex]
Divide both sides by 2
[tex]\mathbf{15^o = \angle STR}[/tex]
Rewrite as:
[tex]\mathbf{\angle STR = 15^o }[/tex]
Hence, the size of STR is 15 degrees
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Luna mixes 2 cup of orange juice with 2 cup of cranberry juice. She gives
cup of the juice to Mags. How much is left in Luna's glass?
in rectangle PQRS, shown below, the diagonal PR is 15 meters. if the sine of angle SPR is 7/10, what is the value of RS?
Answer:sin =perpendicular/hypotenuse
Step-by-step explanation:
Sin angle is given use tan theta or cos theta to find the RS
Add the following numbers and use the checking method (add down and then add up) to make sure your answer is correct. (Copy carefully on scratch paper to work the problem.)
471
+
582
To add 471 and 582, line up the numbers by place value and add each column, carrying over as needed. The sum is 1053. You check by reversing the order of the numbers and adding again; the sum should remain the same.
Explanation:To add the following numbers and use the checking method (add down and then add up), perform the following steps:
Write down the numbers vertically aligned by their place values: 471 + 582 Add the ones place values (1+2) to get 3. Add the tens place values (7+8) to get 15, write down 5 and carry over 1. Add the hundreds place values (4+5) along with the carried over 1 to get 10, write down 0 and carry over 1. Write the carried over 1 in the next left column to get the final sum: 1053 To check, add the sum upwards: 582 + 471 You should arrive at the same sum: 1053.
If you obtain the same result by both adding down and adding up, your answer is verified as correct.
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You start driving north for 7 miles, turn right, and drive east for another 24 miles. At the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]AC = 25\ miles[/tex]
Step-by-step explanation:
Given:
Distance for north side = 7 miles.
Distance for east side = 24 miles.
We need to find the displacement.
Solution:
Figure shows Point A is starting point and AB = 7 miles is North side distance and BC = 24 miles is east side distance and AC is shown as displacement.
Using Pythagoras theorem to find displacement (AC).
[tex](AC)^{2}=(AB)^{2}+(BC)^{2}[/tex]
Substitute AB = 7 and BC = 24 in above equation.
[tex](AC)^{2}=(7)^{2}+(24)^{2}[/tex]
[tex](AC)^{2}=49+576[/tex]
[tex](AC)^{2}=625[/tex]
[tex]AC = \sqrt{625}[/tex]
[tex]AC = 25\ miles[/tex]
Therefore, displacement of the car [tex]AC = 25\ miles[/tex]