The subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18) is given as follows:
1.3t³ - 0.2t² - 32t + 18.
How to subtract polynomials?Polynomials are subtracted subtracting the like terms, which are the terms that have the same symbolic variable and the same exponent.
For this problem, the subtraction is given by the expression presented as follows:
(1.3t³ + 0.4t² - 24t) - (0.6t² + 8t - 18).
The like terms of the expression are given as follows:
1.3t³ and 0t³ = 1.3t³.0.4t² - 0.6t² = (0.4 - 0.6)t² = -0.2t².-24t - 8t = (-24 - 8)t = -32t.0 - (-18) = 0 + 18 = 18.Hence the result of the subtraction of the polynomials is given as follows:
1.3t³ - 0.2t² - 32t + 18.
Missing InformationThe problem asks for the subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18).
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A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and
food tickets cost $3.25 each. The family pays a total of $90 for the tickets.
store.
The number of ride tickets that were sold are 8 and the number of food tickets that were sold are 24 .
In the question ,
it is given that
total number of tickets bought by the family at carnival = 32 tickets
total amount spent by the family of tickets = $90
let the number of ride tickets be [tex]=[/tex] x
let the number of food tickets be [tex]=[/tex] y
So , x + y = 32
x = 32 - y
cost of 1 ride ticket = $1.50
cost of 1 food ticket = $3.25
So the total cost is 1.25x + 3.25y = 90
Substituting x = 32 - y in the equation 1.5x + 3.25y = 90 ,
we get ,
1.5(32 - y) + 3.25y = 90
48 - 1.50y + 3.25y = 90
1.75y = 90 - 48
1.75y = 42
y = 24
So , x = 32 - 24 = 8
Therefore , The number of ride tickets that were sold are 8 and the number of food tickets that were sold are 24 .
The given question is incomplete , the complete question is
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets store. How many of each type of ticket were sold ?
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For a floral arrangement class, Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
Alicia wants the arrangement to have twice as many flowers as twigs. Write and solve a system of equations to find the number of twigs and flowers that Alicia will need.
By solving a system of two simultaneous linear equations, it can be calculated that
Alicia will need 3 twigs and 6 flowers
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of two simultaneous linear equation needs to be solved
Let the number of twigs Alicia needed be x and the number of flowers Alicia needed be y
Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
x + y = 9 ..... (1)
Alicia wants the arrangement to have twice as many flowers as twigs
2x = y .... (2)
Putting the value of x in (1)
x + 2x = 9
3x = 9
[tex]x = \frac{9}{3}[/tex]
x = 3
Putiing the value of x in (2),
y = 2 [tex]\times[/tex] 3
y = 6
Alicia will need 3 twigs and 6 flowers
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the american management association is studying the income of store managers in the retail industry. a random sample of 49 managers reveals a sample mean of $45,420. the standard deviation of the population is $2,050. using a 95% level of confidence, what is the confidence interval for the population mean?
Answer:
burgers
Step-by-step explanation:
ahhhhhhhhhhhhhhhhhh
How to solve step by step
Answer: 5
Step-by-step explanation: First we do (-4-(-7))^2 which is 9 and then
(8-4)^2 which is 16 so 9+16=25 and √25 = 5.
Members of the track team can run 400 meters in an average time of 58.2 sec. The fastest and slowest times varied from the average by 6.4 sec.
Write an absolute value equation to model this equation.
The absolute value equation modelling this situation is presented as follows:
|x - 58.2| = 6.4.
What is the absolute value of a number?The function giving the absolute value of another function is defined by the piece-wise rule presented as follows:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.The result is never negative, as the function gives the distance of the function f(x) from the origin, which is the point in which f(x) = 0.
The difference between both the fastest and the slowest time from the average time of 58.2 seconds is of 6.4 seconds, hence the absolute value equation is given as follows:
|x - 58.2| = 6.4.
Which can be solved applying these following rules:
x - 58.2 = -6.4.x - 58.2 = 6.4.To find the fastest and slowest times, respectively.
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Be Precise: Yesterday, Noah ran 2½ miles in 3/5 hour. Emily ran 3 3/4 miles in 5/6 hour. Anna ran 3 1/2 miles in hour. How fast, in miles per hour, did each person run? Who ran the fastest? Help pleaseeee
Answer:
Step-by-step explanation:
Noah- 4 1/6 miles/hour
Emily- 8 1/10 miles/hour
Anna- 3 1/2 miles/ hour
Emily ran the quickest.
Answer:
Anna was the fastest.
Step-by-step explanation:
Following are the steps we take to determine each one's speed:
speed=distance/time
Noah went 4 1/6 miles an hour, Emily went 4 1/2 miles an hour, and Anna went 5 5/9 miles an hour. Therefore, Anna was the fastest.
find the missing side lengths, leave your answer in simplest form.
The missing side lengths are (m = 4[tex]\sqrt{6}[/tex] , n = 6[tex]\sqrt{2}[/tex]).
According to given triangle, Using triangular formula;
tan 30 = [tex]\frac{2\sqrt{6} }{n}[/tex]
⇒[tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\frac{2\sqrt{6} }{n}[/tex]
⇒ n = [tex]6\sqrt{2}[/tex]
n = [tex]6\sqrt{2}[/tex]
Similarly,
sin 30 = [tex]\frac{2\sqrt{6} }{m}[/tex]
⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{2\sqrt{6} }{m}[/tex]
⇒ m = [tex]4\sqrt{6}[/tex]
m = [tex]4\sqrt{6}[/tex]
so,
m = [tex]4\sqrt{6}[/tex] and n = [tex]6\sqrt{2}[/tex]
So, the correct option is D.
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Give the coordinates of each image.
7. R4180°, 0) (GH) for G(2, -9), H(-1, 3)
please explain i dont understand
The coordinates of each image are G'(-2,9), and H'(1,-3).
What are the coordinates?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
Here, we have
R₍₁₈₀°,₀ (GH)
H(-1,3)
G(2,-9)
Now we need to the rotation of 180° about the origin.
By following the rule, we get,
(x , y) ⇒ (-x , -y)
After solving,
G(2,-9) ⇒ G'(-2,9)
H(-1,3) ⇒ H'(1,-3)
Hence, the coordinates of each image are G'(-2,9), and H'(1,-3).
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angela is following this recipe to make biscuits. angela uses 3.3 litres of syrup. how much sugar is needed in kg
The quantity of sugar that is needed in kg would be = 1.8kg
What is recipe?Recipe is defined as the list of components of ingredients that makes up a food product.
From the recipe given by Angela, the quantity of syrup that is used to make up to 14 biscuits= 275 ml.
The quantity of sugar that is used to make up to 14 biscuits= 150g
Therefore the quantity of sugar that would be used for syrup of 3.3 liters would be= X
That is;
275ml = 150g
3.3L = X
Convert 3.3L to ml = 3,300ml , then make x the subject of formula;
X = 3300×150/275
X = 495000/275
X= 1,800g
Then convert 1,800g to kg by dividing through with 1000;
1800/1000 = 1.8 kg
Therefore, the quantity of sugar that would be used for 3.3L of syrup would be 1.8kg.
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Complete question:
Angela is following this recipe to make biscuits.Angela uses 3.3 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 14 biscuits
120 g margarine
150 g sugar
275 ml syrup
200 g oats
60 g sultanas
How much sugar is needed in kg?
What is the value of x?
4
4√3
12
12√2
Answer:
4√3
Step-by-step explanation:
This is a special right triangle with angle measures 30°-60°-90° and side lengths represented with a-a√3-2a respectively to angle measures.
Here, hypotenuse is given as 8 which is represented with 2a, so a = 4
Then x will be 4√3 as it's represented with a√3.
The value of x is [tex]4\sqrt{3}[/tex] .
What is a trignometric function?
The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Mention all trignometric function ?
sinФ ,cosФ ,tanФ ,cosecФ ,secФ ,cotФ
What is the trick to remember trignometric formulas ?
Some People Have Curly Brown Hair Turned Permanently Brown
sinФ=[tex]\frac{p}{h}[/tex]
cosФ=[tex]\frac{b}{h}[/tex]
tanФ=[tex]\frac{p}{b}[/tex]
cosecФ=[tex]\frac{h}{p}[/tex]
secФ=[tex]\frac{h}{b}[/tex]
tanФ=[tex]\frac{b}{p}[/tex]
Given:
A right angled triangle with
base, b
perpendicular, p
hypotenuse, h=8
angle ,Ф = 60°
So by trignometric formulas ,we get
sinФ = sin60° =[tex]\frac{p}{h}[/tex]
⇒[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]
⇒[tex]x = 4\sqrt{3}[/tex]
Hence ,the value of x is obtained .
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find the percentage increase or decrease in each case:
Original value = 70 m3
New value = 98 m3
(98 × 100) ÷ 70
= 140%
or
[(98 - 70) × 100] ÷ 70
2800 ÷ 70
40%
basically, 40% increase
X Solve for x. *
please solve for c and explain
Check the picture below.
Use remainder theorem for x^3+8x^2+11x-20 by x-5
The remainder is 360.
What is the remainder theorem?When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).
Given a cubic polynomial, x³+8x²+11x-20
The zero of the linear polynomial.
Substitute it in the given polynomial.
As a result, we get the remainder.
x - 5 = 0
x = 5
Substitute 5 to x³ + 8x² + 11x - 20:
5³ + 8×5² + 11×5 - 20 = 125 + 8×25 + 55 - 20 = 160 + 200 = 360
Hence, The remainder is 360.
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Can anyone write the equation of the graph?
The equation of the graph is f(x) = |x - 3| + 5
How to determine the equation of the graph?The graph represents the given parameter
From the graph, we have the following highlights:
The graph is an absolute value graphThe graph has its minimum point at (3, 5)This means that
Vertex = (3, 5)
Rewrite the vertex as
(h, k)
An absolute value function is represented as
f(x) = a|x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = a|x - 3| + 5
On the graph, we have
(x, f(x)) = (2, 6)
So, we have
6 = a|2 - 3| + 5
This gives
a = 1
So, we have
f(x) = 1 * |x - 3| + 5
Evaluate
f(x) = |x - 3| + 5
Hence, the graph has an equation of f(x) = |x - 3| + 5
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Factorise the following:
27t squared y - 18ty squared
Answer:
9ty(3t - 2y)
Step-by-step explanation:
27t²y - 18ty² ← factor out 9ty from each term
= 9ty(3t - 2y)
A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = y minus 11 equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus 7 right-parenthesis.(x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.
y = y equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus StartFraction 5 Over 3 EndFraction.x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17
The equivalent linear equation in standard form is 4x + 3y = 5
How to determine the equivalent equations?From the question, we have the following parameters that can be used in our computation:
Points = (-7, 11) and (8, –9)
Point-slope form is y - 11 = -4/3(x + 7).
Recall that the point-slope form is y - 11 = -4/3(x + 7).
So, we have
y - 11 = -4/3(x + 7).
Multiply through both sides by 3
This gives
3y - 33 = -4(x + 7).
Open the brackets
3y - 33 = -4x - 28
Evaluate the like terms
3y = -4x + 5
Add 4x to both sides
4x + 3y = 5
Hence, the equation is 4x + 3y = 5
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what could be the maximum number of deaths if only 27% of the people in a population of eighteen million is susceptible?
The maximum number of deaths could be 5840000.
What is susceptible?Being prone to something indicates you are more likely to get sick from it, such as an infection or an earache.Has something ever been given to you that you didn't want? Well, that is probably going to be the case since the word "susceptible" means "likely to be influenced or affected by." If you're easily swayed by flattery, all someone needs to do to get what they want from you is to pay you one or two compliments. Crack-prone materials won't last very long in good condition.acc to our question-
total popuation= 8000000susceptinlr percentage= 278000000 * 27/10021600008000000 - 21600005840000.hence,The maximum number of deaths could be 5840000.
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3² × 3 = 3² Find the value of x.
The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
According to the question,
We have the following information:
3² × [tex]3^{x}[/tex] = 3²
We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.
Now, we have the following expression:
2+x = 2
x = 2-2
x = 0
Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
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Solve the equality and graph it’s solution.
Answer:
B) n>6
Step-by-step explanation:
-2n<-12
divide both sides by -2
n>6
A and C can not be the answer because it is not equal to therefore the dot should not be filled in
Demi starts a gardening project with 80 sunflower seeds. She plants 12 of the
seeds. Then she gives 5 seeds each to some friends. Which expression represents
the number of sunflower seeds Demi has left after she gives seeds to f friends?
f
5
C 80 12-5-f
A 80-12-
B 80-12-
D 80-12-5f
a bike path is 12.5 miles. Dominic is 70% of the way to the end how far is Dominic on the path
Dominic is on the 8.75 mile of the bike path
How to determine how far on the path is the distance?From the question, the given parameters are:
Proportion of distance = 70% of the bike path Bike path = 12.5 milesThe above parameters implies that
Dominic's position = 70% of the total distance
Represent the total distance with x
So, we have the following representation
Dominic's position = 70% * x
Where
x = 12.5
So, we have
Dominic's position = 70% * 12.5
Evaluate the products
Dominic's position = 8,75
Hence, Dominic's position is 8,75 miles
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which polynomial function has a leading coefficient of 1 and roots (7+i) and (5-i) with multiplicity 1?
The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))
Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.
We want to find the polynomial function.
As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.
So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.
Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i
So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))
Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).
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how many movies did marc watch between the beginning of week 1 and the beginning of week 5? do not include the unit in your answer.
Using the concepts of straight line, we got 7 movies did marc watch between the beginning of week 1 and the beginning of week 5.
From the diagram given, we got that during the week 1 number of movies watch by marc is 2,while at the beginning of the week 5 the number of movies watch by marc is 9.
So, we need total number of movies watched by marc in between week 1 and week 9 which is given by-
Number of movies watch at the beginning of week 5-Number of movies watch at the beginning of week 1
Number of movies=9-2
=>Number of movies watched by marc=7.
Hence, the number of movies marc watch between the beginning of week 1 and the beginning of week 5 is 7.
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(Complete question)
Marc is keeping track of the total number of movies he has watched over time. The line graph below actually shows the data where the number of movies corresponds to number of movies that had been watched at the beginning of week shown on the horizontal axis.
How many movies did Marc watch between beginning of week 1 and the beginning of week 5? Do not include the unit in your answer.
exponential smoothing is meant to be used with time-series data when the data are made up of some or all of the basic components of level, trend, seasonalitiy, and error. if the data series only fluctuates about an average with no trend and no serasonalitiy, which form of smoothing wouldyou employ? if the data include all of these components, which form of smoothing would you employ? how should the smoothing constants be chosen?
Based on the information provided, ETS is an abbreviation for these three terms (Error, Trend, and Season). Following that, Exponential Smoothing Methods for an ETS system can be described, with the details specified in a smoothing style.
=> As should be obvious, combining Error, Trend, and Season on any occasion in three distinct ways yields a plethora of combinations.
=> The trend depicts the overall layout of the time. It communicates with the data's drawn-out model — its tendency.
=> The seasonal section displays the types associated with anticipated events. Finally, the error component explains what the season and trend components do not. The error is due to the disparity between the first data and the combination of trend and seasonality. As a result, if we crystallize all three parts, we will have the first data back.
=> It has a counted substance conduct when the period of seasonal swings remains constant.
=> We can label our model as ETS (M,A,M).
-> Multiplicative Mistake
-> Added substance Trend
-> Multiplicative Seasonality.
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Directions:
Construct the bisector of the following figures.
Bisector-When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector.
What are the steps to create a bisector?
By following these steps to create a bisector in the provided curve:-
1) Join the extreme points and make a line.
2) By using compass, take width as length of a line joined in step 1.
3) Draw a curve taking extreme points.
4) Draw a line from the intersection of the curve to the line.
The above following steps should be performed error free and you will get bisector.
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you and your friends go to joshua tree national park on december 13 to watch the peak of the geminid meteor shower. according to the griffith observatory website, the expected number of meteors you will see is 150150 per hour. what is the probability that you will see at least two meteors in the first minute?
The probability that we will see at least two meteors in the first minute is 1251.5.
What is probability?The probability is the likelihood that something will happen, to put it simply. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several. The study of events that fit into a probability distribution is known as statistics. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.So, the probability that we will see at least 2 meteors in the first minute:
The expected start we can see in 1 hour is 150150.Then, in 1 minute:
150150/60 = 2,502.5Rounding off: 2,503Now, at least 2 meteors in 1 minute:
Probability formula: P(E) = Favourable events/Total eventsSolve as follows:
P(E) = Favourable events/Total eventsP(E) =2/2,503P(E) = 7.99P(E) = 1251.5Therefore, there is a 1251.5 percent probability that we will observe two meteors or more in the first minute.
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calculate the %cw for a sample of 1040 steel that has an original diameter of 12 mm and a final diameter of 10 mm.
The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA
Given original diameter do = 12 mm
Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²
Deformed diameter d =10mm
Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²
Degree of cold work %CW = (Ao - Ad/Ao)X 100
=(113. 097 - 78. 54/113.097) x 100
= 30.56%
% CW is 30.56 %
Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.
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A corporation earned a profit of $2. 5 x 10 to the 4th power for 1 x 10 to the 3rd power days in a row. What was the corporation's total profit during this time period?
Answer in both scientific notation and standard form
The overall profit of the corporation as during time period is $ 2.5 x 10⁷
Define the term scientific notation?Scientific Notation (also known as Standard Form) is a process of presenting numbers in a concise manner. A number expressed in Scientific Notation is a number between 1 and less than 10, scaled by such a power of ten. Move this decimal point such that there one digit (that cannot be zero) before it.As the question expressed-
Earned profit - $2. 5 x 10 to the 4th power
In scientific notation - $2. 5 x 10⁴
Number of days - 1 x 10 to the 3rd power
In scientific notation - 1.0 x 10³
Total profit = Earned profit x Number of days
Total profit = $2. 5 x 10⁴ x 1.0 x 10³
Total profit = $ 2.5 x 10⁷
Thus, the overall profit of the corporation as during time period is $ 2.5 x 10⁷.
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Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height t that is 0.9 times the width w of the rectangle. if the cross-sectional area is a, determine the dimensions of the window which minimize the perimeter.
The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.
height of rectangle = h
height of the triangle = t
T = 0.9
width of the rectangle = w
The formula of Cross-sectional area is,
A = h × w + (1 ÷ 2)T × w
A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)
Perimeter,
P = w + (2 × h) + 2√(T² + (w ÷ 2)²)
P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)
P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w
Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)
minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w
A = (h × w) + [tex]c_{0}[/tex]w²
substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,
P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)
Differentiating both sides,
(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0
[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A
and consequently,
[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A
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1. The slope of the line
y = x + 17 is ___.
2. The slope of the line
y = x - 7/9 is ___.
Explanation:
The slope of the line
y = x + 17 is ___. 1
2. The slope of the line
y = x - 7/9 is ___. 1