Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.
What is geometric progression?When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.
In this question,
The number of rabbits initially=50=a
rabbits after 6 months=100
common ratio=r= 100/50=2
Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.
a₁₁=a₁(r)¹¹⁻¹
=50(2)¹⁰=5120
the 21th term will give us the number of rabbits after 10 years.
a₂₁=a₁(r)²¹⁻¹
=50(2)²⁰=52,428,800
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At Spirit Night slices of pizza cost $2 and pretzels cost $1. The school store sold 150 items and made a total of $250. Write a systems of
equations to represent the situation where x represents the number of slices of pizza sold and y represnts the number o pretzels
Answer:
[tex]x + y = 150[/tex]
[tex]2x + y = 250[/tex]
Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
Trevor used about half of a 5-lb bag of potatoes (2 lb 6 oz). How much did the remaining potatoes weigh?
Answer:
Step-by-step explanation:
f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:
5 lb = 80 oz (since 1 lb = 16 oz)
Remaining potatoes = Total potatoes - Used potatoes
Remaining potatoes = 80 oz - 2 lb 6 oz
Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)
Remaining potatoes = 80 oz - 38 oz
Remaining potatoes = 42 oz
Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
A) 5, 5, 5
B) 5, 1, 5
C) 1, 5, 5
D) 1, 1, 5
The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.
Explain about property of the right triangles?The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A triangle's (of all varieties) cumulative sum of angles is 180°.The length of a triangle's two longest sides added together is longer than for third side.Similar to this, the length of a third side of a triangle's third side is shorter than the difference between its two sides.For the given question:
Triangle with degree angles - 45-45-90
It means two legs are of same length 5 units.
Then, hypotenuse H will be:
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 5√2
Thus, the correct third side of the triangle will be 5√2.
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please help, thank you!
Answer:
To find all values of x for which f(x) = 26, we can set up the equation:
8x + 15/x = 26
Multiplying both sides by x, we get:
8x^2 + 15 = 26x
Bringing all the terms to one side, we get:
8x^2 - 26x + 15 = 0
We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:
8x^2 - 26x + 15 = 0
(4x - 3)(2x - 5) = 0
Setting each factor equal to zero and solving for x, we get:
4x - 3 = 0 OR 2x - 5 = 0
4x = 3 OR 2x = 5
x = 3/4 OR x = 5/2
Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.
As shown in the figure below, Kaitlin is standing 93 feet from the base of a leaning tree. The tree is growing at an angle of
88° with respect to the ground. The angle of elevation from where Kaitlin is standing to the top of the tree is 35°. Find the
length, x, of the tree. Round your answer to the nearest tenth of a foot.
35°
-93 ft-
H
88°
feet
X
5
Answer:The measure of Ф = 75.7° :)
Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф
At first we will find the angle opposite to the side of length 31
∵ 180° - 73° = 107°
hope this helps:)(:
Solve for X
x^2+ y^2=25 and y=x
The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.
Define Equation?
An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.
In the initial equation, we get: by substituting y=x:
[tex]x^2[/tex] +[tex]y^2[/tex]= 25
[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)
2[tex]x^2[/tex] = 25
[tex]x^2[/tex] = 12.5
When the two sides are square, we get:
x = ±[tex]\sqrt{12.5[/tex]
Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]
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Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
3x and 2x are supplementary what is the value of x
Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .
what is angles ?Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.
given
The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:
3x + 2x = 180
Putting similar phrases together on the left side, we get:
5x = 180
When we multiply both sides by 5, we get:
x = 36
Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .
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What is tan(49°)?
O A. 0.75
OB. 0.66
O C. 1.15
OD. 0.82
Answer:
Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:
Step-by-step explanation:
Someone please help me answer this question
The two statements that are both true are as follows: line
AC is perpendicular to line HB and line AC is parallel to FG. That is option A.
What is a perpendicular line?A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.
A line is said to be parallel to each other when they do not intercept as they are both on the same plane.
From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.
Also, line AC is parallel to FG, because they can never intersect till infinity.
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In this unit, you learn about linear functions and graphing lines in the coordinate plane. Linear functions are used in businesses, construction, and planning cities. The slope of a line determines its steepness. Why do you think a horizontal line (flat) has zero slopes, but a vertical line (straight up and down) is considered to have no slope. What's the difference between zero slope and no slope?
Answer:
Step-by-step explanation:
In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
To determine which statements are true, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Using this form, we can rewrite the given equation as:
(x - 1)^2 + y^2 = 3^2 + 1^2 = 10
Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.
To find the radius, we can rearrange the equation as follows:
x^2 - 2x + y^2 = 8
Completing the square for x, we get:
(x - 1)^2 + y^2 = 9
This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Therefore, the three true statements are:
1.The radius of the circle is 3 units.
2.The center of the circle lies on the x-axis.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
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In this figure, 14.2% of the area is painted green. How much of the area is painted green?
Answer:
8.449 square centimeters
Step-by-step explanation:
Area of the figure = area of square + area of triangle
[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]
[tex].142 \times 59.5 = 8.449[/tex]
So 8.449 square centimeters of this figure is green.
Reflect on why you think guitar tabs are easier or harder to read than regular musical notation.
This will have to be in paragraph form. :)
Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.
What is Guitar?Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.
Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.
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What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
Given g(x) = 8x2 − x + 2, find the following.
1) g(0)
2) g(−1)
3) g(r)
4) g(x + h)
Answer:
Step-by-step explanation:
Given g(x) = 8x2 − x + 5, find the following.
(a). g(0) = 5
(b). g(−1) = 14
(c). g(r) = ?
(d). g(x + h) = ?
Which of the following represents the distributive property?
A. a = b then bea
B. a(b+c)=ab+ac
C. if a = band b-c, then a = c
D. If a = b then ac- be
The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac
Which of the expression represents the distributive property?The distributive property is a mathematical property that applies to multiplication and addition or subtraction.
It states that when you multiply a number (or variable) by a sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.
This is represented by the following formula:
a(b + c) = ab + ac
This is represented by Option (B)
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Dan is training for a bike race. He wants to bike 300 miles over the next couples of weeks. Dan biked 29 miles a day for 3 days. Then, he biked 32 miles a day for 4 days. How many more miles does he still have to bike to get to his goal of 300 miles?
A. Sara estimated that Dan would need to bike about 80 more miles to get to his goal of 300 miles. Is this a reasonable estimate? Why or why not?
B. Write an equation for this problem with a letter standing for the unknown quantity.
C. Solve the problem. Show your work.
Answer:
Step-by-step explanation:
a. Sara's estimate is reasonable because:
Dan has biked for 7 days so far, 29 miles for 3 days and 32 miles for 4 days.
If you round 29 and 32 up and down respectively to 30, then Dan will of have ridden about 30 * 7, or 120 miles so far. 300-120 is 80, so that is a good estimate.
b. If x stands for the miles Dan still needs to bike, then:
(29*3) + (32*4) + x = 300
c. 87 + 128 + x = 300
x = 85
PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
what is the solution to this
Answer:
-2
Step-by-step explanation:
A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50 feet. So, it forms a region bounded by the graph of x^2 + y^2 = 50^2 with x ≥ 0 and y ≥ 0. The following equations are models for the floor and ceiling. Floor: z = x+y/ 5 Ceiling: z = 20 + xy /100 Calculate the volume of the room, which is needed to determine the heating and cooling requirements.
Answer:
Step-by-step explanation:
To calculate the volume of the room, we need to integrate the difference between the ceiling and floor functions over the region bounded by the circle. We can use double integrals to do this.
First, let's rewrite the equations for the floor and ceiling in terms of x and y:
Floor: z = (x + y) / 5
Ceiling: z = 20 + xy / 100
The volume of the room can be calculated using the following double integral:
V = ∫∫(20 + xy/100 - (x + y)/5) dA
where the limits of integration are x = 0 to x = 50, and y = 0 to y = √(50^2 - x^2).
We can simplify the integrand by combining like terms:
V = ∫∫(400/100 + xy/100 - (20x + 20y)/100) dA
V = ∫∫(4 + xy/100 - 0.2x - 0.2y) dA
Now we can integrate with respect to y first:
V = ∫0^50 ∫0^√(50^2 - x^2) (4 + xy/100 - 0.2x - 0.2y) dy dx
V = ∫0^50 [(4y + xy^2/200 - 0.2xy - 0.1y^2)|y=0^√(50^2 - x^2)] dx
V = ∫0^50 [(4√(50^2 - x^2) + x(50^2 - x^2)/200 - 0.2x√(50^2 - x^2) - 0.1(50^2 - x^2)^2/200)|x=0^50]
Evaluating this integral, we get:
V ≈ 2,233.5 cubic feet
Therefore, the volume of the room is approximately 2,233.5 cubic feet, which is the amount of space that will need to be heated or cooled.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct option is 1 and 4 of the given inequality –3(2x – 5) < 5(2 – x)
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x
x < 5
Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.
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75909931 rounded to the nearest hundred thousand
Answer:
the answer is supposably 75900000
One year, the population of a city was 137,000. Several years later it was 117,820. Find the percent decrease.
Group of answer choices
14%
15%
16%
19%
Answer:
The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.
Step-by-step explanation:
the area of a rectangle is 14 square units. it has the side length of x and y. given each value for x, find y.
1. x = 4 and 1/5
2. x = 2 and 1/3
3. x = 7/6
Answer:
1. y = 3 1/3
2. y = 6
3. y = 12
Step-by-step explanation:
A = xy => xy = 14 => y = 14/x
1. x = 4 1/5 = 21/5
y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3
2. x = 2 1/3 = 7/3
y = 14/x = 14/(7/3) = (3 x 14)/7 = 6
3. x = 7/6
y = 14/x = 14/(7/6) = (6 x 14)/7 = 12
Polly's sister-in-law is going to have a baby! For the baby shower, Polly decided to sew pillow to give as a gift. She is using a flower-printed rectangular piece of fabric that is 26 inches long and 22 inches wide.
Answer:
The answer is 96
Step-by-step explanation:
2*(26+22)
2*48
96
Dave bought a new game for $28. The tax rate was %7. How much was the tax and the total price?
The tοtal price οf the game including tax is $29.96.
What are the variοus types οf taxes?Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.
Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:
0.07 x $28 = $1.96 in taxes
As a result, the purchase tax is $1.96.
Tο calculate the tοtal price, add the purchase price and the tax:
Purchase price + Tax = Tοtal Price
Tοtal cοst: $28 + $1.96 = $29.96
As a result, the tοtal cοst οf the game, including tax, is $29.96.
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Is ∆PQR a right triangle? Explain
Answer:
Yes, ∆PQR is a right triangle.
Step-by-step explanation:
A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.
PLEASE HELP PICTURE BELOW
Joseph is 1.75 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
34.05 meters. He stands 29.7 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
(Diagram is not to scale.)
Answer:
34.05 m-
2T
1.75 m
29.7 m
Answer:
Step-by-step explanation:
34,05m my love
Answer:
The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.
Step-by-step explanation:
Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.
The two triangles we're interested in are:
Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).
Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).
Since the two triangles are similar, we can set up the following proportion:
h / (29.7 - x) = 1.75 / x
To solve for h, we can cross-multiply and simplify:
h * x = 1.75 * (29.7 - x)
h * x = 52.075 - 1.75x
h = (52.075 - 1.75x) / x
Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:
x = 29.7 - 34.05
x = -4.35
This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.
Substituting x = -4.35 into our equation for h, we get:
h = (52.075 - 1.75(-4.35)) / (-4.35)
h = 15.14