Guyton can make the 72,072 distinct arrangements of the flowers.
Given, that Guyton bought 13 plants to arrange along the border of his garden.
Now, we are asked that how many distinct arrangements he can make.
As, we know that to arrange 13 plants comprised of 5 tulips, 5 roses, and 3 daisies,
we need to apply Permutations over 13 objects among which 5 are tulips, 5 are roses and 3 are daisies.
Now, on applying the permutations, we get
13 plants can be arranged in 13! ways,
but as among them 5 are tulips, 5 are roses and 3 are daisies.
So, Guyton can arrange the flowers in 13!/(5!×5!×3!).
= (6,22,70,20,800)/(120×120×6)
= 72,072
So, the arrangement can be done in 72,072 ways.
Hence, he can make the 72,072 distinct arrangements.
Learn more about Permutations and Combinations here https://brainly.com/question/1216161
#SPJ1
Suppose that F(x) is a differentiable function such that F(1) = 9.4 and F'(1) = 0.3. Using local linearity, estimate F(1.2).
Using local linearity, f(1.2) = 9.46
What is local linearity?Local linearity is the aprroximation of a curve at a point into a linear function.
How to use local linearity to estimate F(1.2)?For a locally linearized function f(x) about a point x'
f(x + Δx) = f(x) + f'(x)Δx
Now, since we desire to use local linearity to estimate f(1.2)
f(1.2) = f(1 + 0.2)
So, we have that comparing the with f(x + Δx) above, we have
f(1 + 0.2) = f(1) + f'(1)(0.2)
Given that
f(1) = 9.4f'(1) = 0.3Substituting the values of the variables into the equation, we have
f(1 + 0.2) = f(1) + f'(1)(0.2)
f(1 + 0.2) = 9.4 + (0.3)(0.2)
f(1 + 0.2) = 9.4 + 0.06
f(1 + 0.2) = 9.46
f(1.2) = 9.46
So, f(1.2) = 9.46
Learn more about local linearity here:
https://brainly.com/question/7977644
#SPJ1
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 3 ≤ x ≤ 4.
If the function over the interval 3 ≤ x ≤ 4 then, the average rate of change, in simplest form, is 9.
What is average rate of change?
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
m = dy/dx
m =y₂ - y₁ / x₂-x₁
The function over the interval 3 ≤ x ≤ 4.
Using the coordinate points from the table (3, 31) and (4, 22)
Here, y₂ = 22, y₁ = 31 , x₂= 4, x₁ = 3.
Substitute the coordinate into the expression:
= 22 - 31 / 4 - 3
= 9 / 1
m = 9
Hence, the function over the interval 3 ≤ x ≤ 4 ; the average rate of change is 9.
To know more about average rate of change check the below link:
https://brainly.com/question/24313700
#SPJ1
Given: O is the midpoint of PT and RS
Prove: APOR = ATOS
Given O is the midpoint of PT and RS
Therefore, In triangles POR and TOS, we have
PO = TO (O, the midpoint of PT);
∠POR=∠TOS, (vertically opposite angles);
RO=OS, (O, the midpoint of RS)
So by SAS postulate, we have
△POR = △TOS Hence proved
What is the midpoint?
The midpoint is a line segment's center point in geometry. The midpoint is also the centroid of the segment and the endpoints are equally spaced from both endpoints. The midpoint can also be described as a point that divides a segment in half or as one that is equally spaced from both ends of a line.
To learn more about midpoint, use the link given
https://brainly.com/question/5566419
#SPJ1
At what rate will a sum of money triple itself in 10 years?
Answer:
20%.
Step-by-step explanation:
A sum of money will triple itself in ten years at an annual interest rate of 20%.
1. Directions
Drag and drop the correct answer choice to each answer blank.
What is the equation in slope-intercept form of the line that passes through the points (-1, 10) and (5, -8)?
Move the correct answer to each box. Not all answers will be used.
4
7
y =
-8
-3
X +
5
The slope-intercept representation of the linear function that passes through the points (-1, 10) and (5, -8) is:
y = -3x + 7.
What is a linear function?The slope-intercept representation of a linear function is presented by the equation shown as follows:
y = mx + b
The coefficients of the function, along with their meaning, are presented as follows:
m is the slope of the function, representing the change in the output variable y divided by the change in the input variable x.b is the y-intercept of the function, representing the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0.The two points that belong to the linear function are given as follows:
(-1, 10) and (5,-8).
Given two points, the slope is calculated as the change in y divided by the change in x of the points, hence:
m = (-8 - 10)/(5 - (-1)) = -18/6 = -3.
Then the format of the equation is:
y = -3x + b.
When x = -1, y = 10, hence the y-intercept of the function is obtained as follows:
10 = -3(-1) + b
10 = 3 + b
b = 10 - 3
b = 7.
Hence the equation is:
y = -3x + 7.
A similar exercise, also featuring linear functions, is presented at https://brainly.com/question/24808124
#SPJ1
How to find median of 12 numbers number with 2 in middle
What is the sum, in degrees, of the measures of the interior angles of a stop sign,
which is in the shape of an octagon?
(1) 360 (3) 1,440(2) 1,080 (4) 1,880
Evaluate the expression with the given replacement values. x^5; x=−3
Answer:
-243
Step-by-step explanation:
x^5 = x * x * x * x * x
( - 3 )^5 = (-3) * (-3) * (-3) * (-3) * (-3) = -243
Use a calculator to estimate the values of the limits correctly to two decimal places.
*h is approaching 0 in both of these limits
[tex]\lim_{h \to \0} \frac{2.7^h-1}{h} \\\\ \lim_{h \to \0} \frac{2.8^h-1}{h}[/tex]
Try this option ↓
Step-by-step explanation:
1) if to evaluate the given limits using math methods, then:
[tex]\lim_{h \to 0} \frac{2.7^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.7^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.7^h*ln2.7}{1} =ln2.7;[/tex]
and
[tex]\lim_{h \to 0} \frac{2.8^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.8^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.8^h*ln2.8}{1} =ln2.8;[/tex]
2) for more info see the attached graphs; note, ln2.7≈0.993252, ln2.8≈1.029619 and the function is undefined in the points where x=0.
Allie is single, has an adjusted gross income of $26,045 and one exemption of $12,400.
How much is her tax according to the table?
Hint: find taxable income first.
$1294
O $1368
O $1438
O $1444
Im
Answer:
$1,078
Step-by-step explanation:
The tax amount is taken out of his taxable income,
The tax amount is $1583.
What is tax?A tax is a mandatory contribution that a local, regional, or national government collects from individuals or businesses. Public works and services like roads and schools, as well as programs like Social Security and Medicare, are financed by tax revenue.
In economics, taxes go to whoever has to pay them, whether it's the entity being taxed, like a business, or the people who buy the goods from the business. Payroll taxes, federal and state income taxes, and sales taxes are just a few of the taxes to take into account from an accounting perspective.
Given
adjusted gross income = $26,045
exemption = $12,400
to find tax by taxable income
taxable income = adjusted gross income - exemption
taxable income = 26,045 - 12400
taxable income = $13,645
The question is incomplete, the table is attached
Therefore, I will employ the 2016 single taxable income tax bracket and rate table.
Using the table, the tax amount on an income of $13,645 is:
Tax = $927.50 + 15% × (Amount - $9275)
So, we get:
Tax = $927.50 + 15% ×($13645 - $9275)
$1583,
Hence, Allie's tax amount is $1583.
Learn more about tax;
https://brainly.com/question/16423331
#SPJ2
The table for Question is in image attached.
Select the answers that best complete the given tables.
Parabola opens Vertex Location Number of x-intercept(s)
down Quadrant II
Parabola opens Vertex Location Number o (s)
down Quadrant II
2
1
0
3
Answer:
I think it 3 or 2 but mainly 2
factor by grouping
8x^3-8x^2+x-1
The factors are (x-1) (8x²+1).
What is a factor?
A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.
For example, 3 and 8 are factors of 24 because 24 ÷ 3 = 8 exactly and 24 ÷ 8 = 3 exactly. The other factors of 24 are 12, 4,6
8x³-8x²+x-1
Take out 8x² as common
8x² ( x-1) + (x-1)
Take out (x-1) as common
(x-1) (8x²+1)
So, the factors are (x-1) (8x²+1).
To learn more about the factor from the given link
https://brainly.com/question/25829061
#SPJ1
Last week, Sally bought 8 ½ gallons of
gas at $2.30 per
gallon. This week, she bought 4 ½ gallons at $2.20 per
gallon. What was her total cost?
Answer:
her total cost is $29.45
Step-by-step explanation:
last week - 8 1/2 gallons times $2.30 = $19.55
this week - 4 1/2 gallons times $2.20 = $9.90
$19.55 + $9.90 = $29.45
. Which segment is a dilation of BC using A as the center of dilation and a scale
factor of ?
2. Which segment is a dilation of BC using A as the center of dilation and a scale
factor of ?
3. Which segment is not a dilation of BC, and how do you know
Using A as the center of dilation and a scale factor, BC is dilated by 12 units.
What is scale factor?In the ratio indicated by the scale factor, a line segment dilates by becoming longer or shorter. The segments (sides) of the image will be longer than the corresponding sides of its pre-image if the scaling factor is more than 1 (k > 1). (an enlargement).If both the new and original dimensions are known, the scaling factor may be determined. A figure's scale factor can be calculated using the following simple formula: Dimension of the original shape minus the dimension of the new shape is the scale factor.To learn more about scale factor refer to:
https://brainly.com/question/2826496
#SPJ1
Which sets of ordered pairs represent functions?
The ordered pair in roaster form {(2,8), (3, 12), (4, 16), (5, 20)} is a function.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
We know a function can be many one which means different inputs leads to same output but one to many is not a function as same input can not lead to different outputs.
{(2,8), (3, 12), (4, 16), (5, 20)} is a function as each different input leads to a different output.
learn more about functions and sets here :
https://brainly.com/question/12979762
#SPJ1
7. Write the equation using the given
information:
Vertex: (3,-2)
Point: (1, 2)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=3\\ k=-2 \end{cases}\implies y=a(x-3)^2 -2\hspace{5em}\textit{we also know that} \begin{cases} x=1\\ y=2 \end{cases} \\\\\\ 2=a(1-3)^2 -2\implies 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a \\\\[-0.35em] ~\dotfill\\\\ y=1(x-3)^2 -2\implies {\Large \begin{array}{llll} y=(x-3)^2 -2 \end{array}}[/tex]
Find the slope of the line that passes through (2, 12) and (8, 5)
Answer:
-7/6
Step-by-step explanation:
You can get the slope of the line that passes between two points by taking the difference of the y values and dividing that by the difference of the x values:
[tex]\frac{12-5}{2-8} =\frac{7}{-6} =-\frac{7}{6}[/tex]
A spherical granite boulder weighs 560 tons. Specific gravity of granite is 2.6 - 2.7. What is the diameter of the boulder assuming a sphere.
The diameter of the boulder assuming a sphere. is 38m
Specific gravity is defined as density of a substance to the density of water
SG = density of boulder/ density of water
Since (at standard temperature and pressure) water has a density of 1
SG = mass of boulder / volume of boulder
2.6 = 560 x 1000/ x
x = 56000/2.7
x = 20740.74
The volume of a sphere = 4/3 πr³ =
20740.74 = 4/3 (3.14) r³
r³ = 4953
r = 17.04
Diameter = 2r = 2x17.04 = 38.08
Therefore, the diameter of the boulder assuming a sphere. is 38m
To learn more about volume refer here
https://brainly.com/question/10171109
#SPJ9
the frequency of the letter e in written English is about 13%. On a page of a novel that has bout 2000 letters per page, about how many occurrences of the letter e can we expect to find?
260 occurrences of the letter e we can expect to find.
Frequency = 13%
Total letters = 2000
E letters = 13% of 2000
= (13/100)*2000
= 13*20
= 260
Hence, there are 260 e letters in 2000 of total letters.
To learn more about occurrences here:
https://brainly.com/question/28953812
#SPJ1
Explain how the graph of the function f(x) = 4x^2 compares to its parent function f(x)=x^2 in terms of whether it faces up or down, has a maximum or minimum, and if it’s stretched or compressed.
Answer:
f(x)=4x^2 is facing up, it has a minimum, and it's horizontally compressed
Step-by-step explanation:
It's facing up because there's no negative sign in front of the coefficient of x.
It has a minimum because any quadratic function that faces up will have a minimum, and any quadratic function that faces down will have a maximum.
It's horizontally compressed because as can be seen in the picture below, f(x)=4x^2 (red) has more "slope," so it's condensed toward the y-axis. Hence, if the coefficient is bigger than 1, then the function will be horizontally compressed, and if the coefficient is smaller than 1, then the function will be horizontally stretched.
{Question 8} Please help! Need this by tonight! {Click on picture}
The cost per message is $0.025 and the graph that represents the Jerry's text message plan is graph 2
The cost of every 30 messages = $0.75
To find the cost of one message we have to use the unitary method
The cost of 1 message = The cost of every 30 messages / 30
Substitute the values in the equation
The cost per message = 0.75 / 30
Divide the terms
= $0.025
Next find the cost 40 messages = The cost per message × 40
Substitute the values in the equation
The cost of 40 messages = 0.025 × 40
= 1
Using these details the graph that represents the Jerry's text message plan is graph 2
Hence, the cost per message is $0.025 and the graph that represents the Jerry's text message plan is graph 2
Learn more about unitary method here
brainly.com/question/22056199
#SPJ1
I wILL GIVE BRAINLIEST AND LOTS OF POINTS
Find the length of side x to the nearest tenth.
Type here to search
x
1
Answer:
∴ x = 0.707 (to 3sf)
Step-by-step explanation:
Following the Pythagoras' Theorem,
1² = x² + x²
2x² = 1
x² = [tex]\frac{1}{2}[/tex]
∴ x = 0.707 (to 3sf)
help me please (15pts)
Answer:
The Graph On Letter C
Step-by-step explanation:
It's going at a rate of change/slope of -5/2.
$11,900 is invested, part at 8% and the rest at 5%. If the interest earned from the amount invested at 8% exceeds the interest earned from the amount invested at 5% by $441.00, how much is invested at each rate? (Round to two decimal places if necessary.) Define variables x and y and set up a system of two linear equations that represents the information given in the problem.
$7969.24 invested at 8% and $3930.76 invested at 5%
From given information,
Amount invested = $11,900
Rate of interest for first part = 8%
Rate of interest for second part = 5%
Let the amount invested for 8% be 'x'.
Let the amount invested for 5% be 'y'
According to question, we get an equation,
0.08x - 0.05y = 441
x + y = 11,900
x = 11,900 - y
0.08(11,900 - y) - 0.05y = 441
952 - 0.08y - 0.05y = 441
-0.13y = -511
y = (-511)/(-0.13)
y = 3930.76
so, x = 11,900 - 3930.77
x = 7969.23
Therefore, $7969.24 invested at 8% and $3930.76 invested at 5%
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ1
Express each percent or decimal as a fraction in simplest form. 54% 0.22
The value of 54% as a fraction is 27/50.
The value of 0.22 as a fraction is 11/50.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case 54% will be:
= 54 / 100
= 27 / 50
Also, the value of 0.22 will be:
= 22 / 100
= 11 / 50
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Identity the property of equality that was used for each step
Addition property
Subtraction property
Multiplication property
Division property
Transitive property
Symmetric property
Substitution property
Reflexive property
Distributive property
Properties used for each steps are Division property, Multiplication property, Addition property, Subtraction property and Distributive property.
Given equation is {2(2/5 x + 8)}/2 = {4(14- 1/5 x)}/2
1) Here first we used Division property
we divide both the equation by 2 then the equation become
(2/5 x + 8) = 2(14-1/5 x).
2) Now we will use Multiplication property,
2/5 x + 8 = 28 - 2/5 x
Interchanging the terms we get
2/5 x + 2/5 x = 28-8
3) By Addition property
4/5 x = 28-8
4) And by Subtraction property we get
4/5 x = 20
5) Lastly by Distributive property we find the value of x,
x = (20 × 5)/4
x = 100/4
x = 25
To know more about Multiplication property here
https://brainly.com/question/29528704
#SPJ1
use the given triangle to solve for x.
Answer:
X=5
Angle c is 42 degrees
Step-by-step explanation:
sum of all angles in a triangle equal 180 degrees so we set all these angles equal to that
(9x-3)+(22x+1)+(42-3x)=180
31x-2+42-3x=180
28x+40=180
-40. -40
28x=140
/28. /28
x=5
So now to find angle c we just fill in X
9(5)-3
45-3
42
Hopes this helps please mark beainliest
The graph of g(x) is the result of translating the graph of f(x) = 3* six units to the right. What is the equation of g(x)?
O g(x)= 3x-6
Og(x)=3x+6
Og(x)=3*-6
Og(x)=3* +6
The equation of the graph g(x) is [tex]3^{x-6}[/tex]
What is a graph ?
A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;
In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.
The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)
If the graph of the function f(x) = 3^x is translated 6 units to the right , then the function becomes
g(x) = f(x - 6)
= [tex]3^{x-6}[/tex]
To learn more about graph from the given link
https://brainly.com/question/515573
#SPJ1
Find the measure of angle b
Answer:
b = 65°
Step-by-step explanation:
Now we have to,
→ find the required value of b.
Forming the equation,
→ 115° + b = 180°
Then the value of angle b is,
→ 115° + b = 180°
→ b = 180° - 115°
→ [ b = 65° ]
Hence, the value of b is 65°.
Which expression is equivalent to 2(3x^2-6x+4)+2(-2x+25x+100)?
The expression that is equivalent to 2(3x^2-6x+4)+2(-2x+25x+100) is 2(3x² + 1x + 104)
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
This will be illustrated as:
2(3x^2-6x+4)+2(-2x+25x+100)
= 6x² - 12x + 8 - 4x + 50x + 200
= 6x² +34x + 208
= 2(3x² + 1x + 104)
The equivalent expression is 2(3x² + 1x + 104).
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
