Question 1 Part A: (4 Points): A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, and n days.
Complete the inequality below by dragging and dropping the answers on the left into the given boxes
Answers
Answer:
0 ≤ n ≤ 5
Step-by-step explanation:
We have the function for growth as
[tex]g(n) = 10(1.02)^n[/tex]
We also know that after a specific n days, the flower has grown to 11.04 inches
Since g(n) represents the height of the flower, we can substitute 11.04 for g(n) and solve for n
∴We get
[tex]11.04 = 10(1.02)^n[/tex]
Switching sides we get
[tex]10(1.02)^n = 11.04[/tex]
Divide both sides by 10 to get
[tex]1.02^n = 1.104[/tex]
Take log on both sides
[tex]\log(1.02^n) = \log(1.104)[/tex]
[tex]\log(x^a) = a \log(x)[/tex]
So
[tex]\log(1.02^n) = n \log(1.02)[/tex]
Therefore
[tex]n \log(1.02) = \log(1.104)[/tex]
[tex]n = \dfrac{\log(1.104)}{\log(1.02)}[/tex]
Using a calculator this works out to
[tex]n = 4.9963[/tex]
Therefore it takes at least these many days for the flower to reach 11.04 inches
Rounding number of days to 5, we get the right side of the inequality as n ≤ 5
n cannot be negative so it starts of with a value of 0 so on the right side of the inequality we get n ≥ 0 which can be rewritten as 0 ≤ n
Together the domain of n can be represented as
0 ≤ n ≤ 5
Hope that helps
Related Questions
a blue parallelogram has a height of 6 inches and a base of 10 inches. a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram. what is the area of the green parallelogram?
Answers
On using the scale value of 2 : 1, the area of green parallelogram is obtained as 120 in².
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
Height of blue parallelogram = 6 inches
Base of blue parallelogram = 10 inches
The scale value is given as = 2 : 1
Height of green parallelogram = 6 × 2 = 12 inches
Base of green parallelogram = 10 × 1 = 10 inches
It is known that area of parallelogram = base × height
So, area of green parallelogram is -
= 12 × 10
= 120 in²
Therefore, the area value is obtained as 120 in².
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Area of triangle 8,10,16
Answers
Answer:
Area: T = 24
Perimeter: p = 24
Semiperimeter: s = 12
Step-by-step explanation:
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified.
a=6
b=8
c=10
The triangle perimeter is the sum of the lengths of its three sides
p=a+b+c=6+8+10=24
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.
Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.
which expression is equivalent to -5(8x+9)-7x ?
Answers
The expression -5 (8x + 9) - 7x is equivalent to the expression - 47x - 45
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ -5 (8x + 9) - 7x
Simplify the expression, then we have
⇒ -5 (8x + 9) - 7x
⇒ - 40x - 45 - 7x
⇒ - 47x - 45
The expression -5 (8x + 9) - 7x is equivalent to the expression - 47x - 45
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(x+2)(x+8)=0 show work
Answers
The solutions of the quadratic equation:
(x+ 2)*(x + 8) = 0
are:
x = -2
x = -8
How to solve the quadratic equation?Here we have the following quadratic equation:
(x + 2)*(x + 8) = 0
And we want to solve it for x.
Remember the zero property, for any real number A, the product with zero gives:
A*0 = 0
Then:
(x + 2)*(x + 8) = 0
If either (x + 2) = 0 or (x + 8) = 0
Solving these two we get:
x + 2 = 0
x = -2
x + 8 = 0
x = -8
The two solutions of the quadratic equation are x = -2 and x = -8
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Simplify 6 + 8 / 2* | -3| + 7
Answers
The simplification of the given expression 6 + 8 / 2* | -3| + 7 is 25
The process of simplifying arithmetic operations.The process of simplifying a complex expression with an equivalent, simpler one is known as simplification. There are several strategies for simplifying expressions, depending on the exact expression and what you are attempting to accomplish.
To simplify the given expression:
6 + 8 / 2* | -3| + 7
Divide 2 by 8 = 4
6 + 4 * |-3| + 7
Take the absolute value of |-3| = 3
6 + 4 + 3 + 7
= 25
Therefore, we can conclude that the simplification of the given expression is 25.
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need assistance!!!!!
Answers
Answer:
100 ft^2
Step-by-step explanation:
first we can make this a complete rectangle that is 10 by 12
so we find the area of it
10x12
120
now we have to subtract the triangle from it
we first find the area of the missing piece using triangle formula
bxh/2
the base is 10 and height is 4
10x4/2
40/2
20
now we subtract the area of the triangle from the area of the rectangle
120-20
100 ft^2
hopes this helps
a unit fraction that has 1 as its numerator. write the four greatest unit fractions that are repeating decimals. then write each fraction as a decimal.
Answers
Answer:
Here, we use an underscore preceding the repeating digit(s).
1/3 = 0.3_3
1/6 = 0.16_6
1/7 = 0.142857_142857
1/9 = 0.1_1
Step-by-step explanation:
You want the four largest unit fractions that are repeating decimals, and their decimal equivalents.
Repeating decimalThe decimal equivalent of a fraction will repeat if the denominator of that fraction has factors other than 2 and 5.
Larger fractionsA fraction with a given numerator will be larger if its denominator is smaller.
Largest repeating decimalsThe fractions of interest will have denominators that are the smallest integers greater than 1 that have factors other than 2 and 5. Consider the integers:
2 . . . . factor is 2
3 . . . . suitable denominator
4 = 2² . . . . factors are 2
5 . . . . factor is 5
6 = 2·3 . . . . suitable denominator
7 . . . . suitable denominator
8 = 2³ . . . . factors are 2
9 = 3² . . . . suitable denominator
Using an overline to signify the repeating digits, the fractions of interest are ...
[tex]\dfrac{1}{3}=0.\overline{3}\\\\\text{ }\dfrac{1}{6}=0.1\overline{6}\\\\\dfrac{1}{7}=0.\overline{142857}\\\\\text{ }\dfrac{1}{9}=0.\overline{1}[/tex]
__
Additional comment
The number of repeating digits may be as many as one less than the denominator. This is the case for 1/7, which has 6 repeating digits. 1/17 is another example, with 16 repeating digits.
The four unit fraction that has its numerator as 1 and a repeating decimal is
1/3, 1/6, 1/7, and 1/9What are repeating decimals?A repeating decimal are also called recurring decimal, is a time of decimal number with only digits that repeat after the decimal at regular intervals.
In mathematics, a repeating decimal is written in short form with an overline on the number that repeats
In the problem, the repeating fraction requires to have a unit numerator and the greatest. from knowledge of fractions, the ones with lesser numerators are the greatest.
The greatest is 1/3 = 0. 333.....
others are
1/6 = 0.166.....
1/7 = 0.142957142957.......
1/9 = 0.111111.........
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1. Eleven decreased by k
2. p increased by 9
3. Sixteen multiplied by a number h
4. f less than twelve
5. Sixteen less than m
Answers
All the mathematical expressions are,
1) 11 - k
2) p + 9
3) 16h
4) f < 12
5) 16 < m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
All the algebraic expression are,
1. Eleven decreased by k
2. p increased by 9
3. Sixteen multiplied by a number h
4. f less than twelve
5. Sixteen less than m
Now,
We can write all the expression as,
1. Eleven decreased by k
⇒ k - 11
2. p increased by 9
⇒ 9 + p
3. Sixteen multiplied by a number h
⇒ 16 × h
⇒ 16h
4. f less than twelve
⇒ f < 12
5. Sixteen less than m
⇒ 16 < m
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Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.
Use the polygon tool to graph the dilated figure.
With point at (-2,5), (-2,2), (2,5), (2,2)
Answers
The vertices of the quadrilateral after dilation of 2 are
(-4, 10), (-4, 4), (4, 10), (4, 4).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A quadrilateral with vertices (-2,5), (-2,2), (2,5), (2,2).
Now, Dialating this quadrilateral with a scale factor of 2 centered at the origin would multiply every vertices points by 2.
Therefore, The dilated quadrilateral has vertices,
2[ (-2,5), (-2,2), (2,5), (2,2)].
(-4, 10), (-4, 4), (4, 10), (4, 4).
The figure of this dilated quadrilateral is attached.
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Name a point that is not coplanar with R, S, and T.
Answers
The required point is W.
What is the co-plaer and non co-planer?
Co-planar refers to a set of objects that lie in the same plane or lie on the same flat surface. They have the same elevation and do not intersect each other.
Non-coplanar refers to a set of objects that are not in the same plane or do not lie on the same flat surface. They have different elevations and may intersect each other.
W is a point that is not co-planar with R, S, and T.
Consider the provided plane.
We need to find the point that is not co-planar with R, S, and T.
Co-planar: Two object or points are said to be co-planer if they lie in the same plane.
Non co-planar: Two object or points are said to be non co-planer if they don't lie in same plane.
Now consider the provided plane, the point W is not lie in the plane V.
While point R, S and T lie in the plane V.
Hence, the required point is W.
W is a point that is not co-planar with R, S, and T.
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See attached Screenshot
Answers
The expression ∛(t⁴m²) / (m³t) in the simplified form will be written as [tex]\rm \frac{t^{1/3}}{m^{7/3}}[/tex].
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ ∛(t⁴m²) / (m³t)
Simplify the expression, then we have
⇒ ∛(t⁴m²) / (m³t)
⇒ t∛(tm²) / (m³t)
⇒ ∛(tm²) / (m³)
Simplify the equation further, then we have
[tex]\rm \rightarrow \dfrac{\sqrt[3]{\rm tm^2} }{m^3}\\\\\rightarrow \dfrac{t^{1/3}m^{2/3}}{m^3}\\\\\rightarrow \dfrac{t^{1/3}}{m^{7/3}}[/tex]
The expression ∛(t⁴m²) / (m³t) in the simplified form will be written as [tex]\rm \frac{t^{1/3}}{m^{7/3}}[/tex].
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At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?
x + y < 12
x + y > 12
x + y ≤ 12
x + y ≥ 12
Answers
The inequality which best represents her purchase is x + y > 12.
How to write expressions with inequalities?
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other.
When two expressions are equal, we use the equal sign ( = ). But when we are trying to compare two values or expressions, we use the inequality signs like greater than (>), less than (<), greater than or equal to ( ≥ ) and less than or equal to (≤) .
If x represents the number of hand soaps and y represents the number of lotions she bought. And Gabriela bought more than 12 bottles of hand soaps and lotions
This means the sum of the bottles of hand soaps and lotions she bought is greater than 12. This can be written as follows:
x + y > 12
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Match the inequalities on the left with the correct statement about that inequality on the right.
-4 r ≤ 22
Drop selections here
54 y+-8 ≥ -1
Drop selections here
-7d/4>3
Drop selections here
0>-8 n
Drop selections here
Answers
The statements which are correct about the inequalities in each case as required are as follows;
-4r ≤ 22; Flip the inequality sign.54y + -8 ≥ -1; Do not flip the inequality sign.-7d / 4 > 3; Flip the inequality sign.0 > -8n; Flip the inequality sign.Which statements are correct about the given inequalities?It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.
It is noteworthy to know that the underlying perspective is such that;
If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.
On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.
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A machine running at 100 percent capacity produces 13,000 products each shift. Each product weighs about 2.2 ounces.
How many ounces of product can the machine produce during a shift if it is running at 85 percent capacity?
Answers
The total weight of products produced during a shift at 85 percent capacityy is 11,050 products * 2.2 ounces/product = <<110502.2=24210>>24,210 ounces.
Simplify −7g(2g + 3).
−14g2 − 21g
−14g2 + 3
−14g − 21g
−14g + 3
Answers
Answer:
The first answer
Step-by-step explanation:
-7g(2g + 3) Distribute the -7g
(-7g)(2g) + (-7g)(3)
-14[tex]g^{2}[/tex] - 21g
Answer:
Option A; [tex]-14g^{2}[/tex] - 21g
Step-by-step explanation:
-7g(2g + 3)[tex]-14g^{2}[/tex] - 21g (Use the distributive property)Answer: [tex]-14g^{2}[/tex] - 21gHope this helped! :D
A car traveled 200 kilometers in 3 hours. If the car travels at the same average rate, how far will the car travel in 9 hours?
Answers
Answer: 600km
Step-by-step explanation:
Using the concept of proportion, with the same average rate,
3 hours -> 200 km
9 hours -> A km
Hence,
9/3 = A/200
A = 200 x 9/3 = 200 x 3
= 600
Answer: 600 km
Step-by-step explanation:
We need to apply the concept of Time speed distance here.
When speed is constant, T ∝ D
D = S*T
200 km = 3hrs
X km = 9hrs
X = 200*9/3
= 200*3
= 600km
A number decreased by 20 is 10 less than twice the number
Answers
Answer:
the number is 40
Step-by-step explanation:
A number decreased by 20 is 10 less than twice the number
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40
Angel has a deck that measures 20 feet by 25 feet. He wants to increase each dimension by equal lengths so that its area is increased by 50%. By how much should he increase each dimension?
Answers
Angel should increase the dimensions of the deck by 5 feet each
How to determine by how much the lengths should be increasedFrom the question, we have the following parameters that can be used in our computation:
Length = 20 feet
Width = 25 feet
So, the area is
Area = 20 * 25
Evaluate
Area = 500
When increased by 50%, we have
(20 + x) *(25 + x) = 500 * 1.50
Evaluate
(20 + x) * (25 + x) = 750
Express 750 as 25 * 30
So, we have
(20 + x) * (25 + x) = 25 * 30
This means that
20 + x = 25
25 + x = 30
Solve for x
x = 5 and x = 5
This means that
Increment = 5
Hence, the lengths should be increased by 5 feet
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Pls help…………………………….
Answers
Answer:
m = 3
Step-by-step explanation:
4 - - 2/ 3 - 1
m = 6/2
m = 3
Find the length of the segment indicated.Round your answer to the nearest tenth if necessary
Answers
Answer:
7.9
Step-by-step explanation:
Can anyone please find the slope of the lines? Picture below
Thank you!
Answers
The slope of the first and second lines will be - 3/2 and 3/5, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are (1, 2) and (3, -1). Then the slope of the first line is given as,
m = (-1 - 2) / (3 - 1)
m = - 3 / 2
The points are (-3, 1) and (2, 4). Then the slope of the second line is given as,
m = (4 - 1) / (2 + 3)
m = 3 / 5
The slope of the first and second lines will be - 3/2 and 3/5, respectively.
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How many solutions exist for the system of equations graphed below?
none
one
two
infinitely many
Answers
The number of solutions that exist for the system of equations graphed as shown is B . One .
How to find the number of solutions ?To find the number of solutions that exist in a system of graphs, you need to look at the number of points of intersection that there are.
The number of points of intersection shows the number of solutions. If there is one point of intersection, then there is one solution.
The system of equations graphed, has one point of intersection so there is only one solution .
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What is the diameter of a circle that has an area of 14,400
Answers
Answer: ≈425.39
Step-by-step explanation: First, let's recall the formula for finding the circumference of a circle with the area:
C = 2 [tex]\pi[/tex] r
So, let's set up our equation:
2·[tex]\sqrt{\pi 14,400}[/tex]
So, we need to multiply pi (3.14 [rounded]) by 14,400 and find the square root of that times 2.
We'd get about 425.39.
The following three shapes are based only on squares, semicircles, and quarter circles. find the perimeter and the area of each shaded part. give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
The area and the perimeter of the figure are given as follows:
Area: 36(π + 2) cm².Perimeter: (24 + 4.2425π) cm.How to obtain the area of the figure?The figure is composed as follows:
Right triangle of sides 12 cm.Semi circle with diameter that is the hypotenuse of the right triangle.Applying the Pythagorean Theorem, the diameter of the circle is given as follows:
d² = 2 x 12²
[tex]d = \sqrt{2 \times 12^2}[/tex]
d = 16.97 cm.
Then the radius of the circle is given as follows:
r = 0.5d
r = 0.5 x 16.97
r = 8.485 cm.
The area of a circle of radius r is given by the multiplication of π and the square of the radius, as follows:
A = πr².
Hence, considering that the figure is a semi circle, we have that:
Ac = 0.5 x π x (8.485)²
Ac = 36π
The area of the right triangle is of:
At = 0.5 x 12 x 12
At = 72 cm².
Meaning that the area of the shape is given as follows:
A = Ac + At.
A = 36π + 72
A = 36(π + 2) cm².
How to obtain the perimeter of the shape?The perimeter of the shape is obtained by the sum of 2 times 12 cm and the circumference of the semi circle.
The circumference of a semicircle of diameter d is given as follows:
C = 0.5πd.
Hence:
C = 0.5π x 8.485
C = 4.2425π.
Meaning that the perimeter of the shape is given as follows:
P = (24 + 4.2425π) cm.
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Gina charges an initial fee and an hourly fee to babysit. Using the table below find the hourly fee and the initial fee that
Gina charges to babysit. Show work.
Cost in Dollars
Answers
Answer:
13 dollars
Step-by-step explanation:
Determine the point estimate of the population mean and margin of error for the confidence interval. The lower bound is 17, upper bound is 25. What is the point estimate of the population mean?
Answers
The point estimate of the population mean is 21.
The point estimate of the population mean is the midpoint of the confidence interval.
To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.
On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.
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a right rectangular prism has a base of 20cm2 and a height of 9.2cm what is the volume of the prism
Answers
A right rectangular prism has a base of 20cm² and a height of 9.2cm will have a volume of 184 cm³
What is a right rectangular prism?The right rectangular prism has four rectangle-shaped lateral faces, each of which is perpendicular to one of its bases, and two parallel end faces.
A non-right rectangular prism (oblique prism) has parallelograms for its faces. The term "cuboid" can also refer to a right rectangular prism.
In the given problem the formula used for volume of prism is
= are of base * height
= 20 * 9.2
= 184 cm³
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Mrs. Anna has 96 puzzles to share with 14 students. She wants to give each child the same number of puzzles and keep the remaining puzzles in the classroom.
How many puzzles will she have left over?
A
6 puzzles
B
8 puzzles
C
12 puzzles
D
13 puzzles
Answers
Easiest way to calculate this is by removing 12 puzzles from 96 and divide by 14
6*14 + 12
Answer
6
because, 96 / 14 is 6.8
so unless you round it to 8 it should be 6
Find the term that must be added to the equation 2 - 8x = 9 to make it into a perfect square.
A. 64
B.-9
C. 16
D. 32
Answers
The solution is Option C.
The term that must be added to the equation x² - 8x = 9 is 16 and the equation will be ( x - 4 )² = 5²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - 8x = 9 be equation (1)
( x - a )² = x² + a² - 2ax
So , 2ax = 8x
a = 4
So , the equation will be
( x - 4 )² = x² - 8x + 16
And , adding 16 on both sides of the equation (1) , we get
x² - 8x + 16 = 9 + 16
On simplifying the equation , we get
( x - 4 )² = 25
( x - 4 )² = 5²
Taking square roots on both sides of the equation , we get
x- 4 = 5
Adding 4 on both sides of the equation , we get
x = 9
Therefore , the value of x is 9
Hence , the number to be added to the equation is 16
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3-(-7) find the difference
Answers
Answer:
Step-by-step explanation:
So 3 minus 7. 3 – 7 = -4 *just trust me on that one ;) So the difference of 3 and 7 is -4.
