The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.
When data is graphed, which data can be modeled best using a line?The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.
Why does it makes sense to have a linear graph?Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.
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Pat's Pizza made
21
2121 cheese pizzas,
14
1414 veggie pizzas,
23
2323 pepperoni pizzas, and
14
1414 sausage pizzas yesterday.
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?
Choose the best answer.\
Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The total number of pizzas made yesterday can be determined using the information provided as follows:
2121 cheese pizzas total.
Pizzas with vegetables: 1414
2323 pepperoni pizzas total.
1414 sausage pizzas were consumed.
Total pizzas produced were
=>2121 + 1414 + 2323 + 1414 = 7272.
Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.
The likelihood that the following pizza will be a cheese pizza is calculated as follows:
=> 2121 / 7272
The likelihood that the next pizza prepared won't be a cheese pizza is thus:
=> 1 - (2121 / 7272) = 5151 / 7272
Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
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The area of this rhombus is 20 square miles. One of its diagonals is 10 miles. What is the length of the missing diagonal?
========================================================
Work Shown:
[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]
The other diagonal is 4 miles long.
20a +5,600 < 21,000 solve the following inequality and answer in interval notation
Answer: 20a +5,600 < 21,000
move the content to the right
20a < 21,000 -5600
calculate
20a<15400
20a <15400
divide both sides of the inequality by 20
a<770
which expresions are equivalent to 1/2³
1/8
(1/2)^3 1^3 2^3 1/8 or:(1/2)^3 (1/2) (1/2)(1/2)1×1×1/2×2×1/8
Twice the difference of a number and three is the sum of that number and four
Answer:
Step-by-step explanation:
Answer:
-20
Step-by-step explanation:
We can set up an equations with the conditions we are given. Let's use x for the missing number.
2(x-4)=3(x+4)
2x-8=3x+12
-20=xWe can set up an equations with the conditions we are given. Let's use x for the missing number.
2(x-4)=3(x+4)
2x-8=3x+12
-20=x
Three expressions that are equivalent to 3/5a+10?
In •A find CE if BA=7.35.
The value of CE is 14.7 units.
What if the diameter of a circle?The diameter of a given circle is a straight line which passes through the center of the circle and divides it into two equal semi-circles.
So that in the given circle with center A, we have;
CE = BD (diameter of a given circle)
BA = EA = CA = DA (radius of a given circle)
CE is the diameter of the circle, and BA is the radius, so that;
CE = 2*BA
= 2*7.35
= 14.7
CE = 14.7
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dertermine if T:R^3-R^2 defined as T(x1,x2,x3)=(x1+x3,2x2-x3) is a linear transformation
Yes, [tex]T(x_1,x_2,x_3)=(x_1+x_3,2x_2-x_3)[/tex] is a linear transformation.
What is a linear transformation?A linear map is a mapping V to W between two vector spaces in mathematics, more specifically in linear algebra, that keeps the operations of vector addition and scalar multiplication. The more broader example of modules over a ring also uses the same terminology and definition are Module homomorphism.
What is homomorphism?The maps between algebraic objects are known as homomorphisms. Group homomorphisms and ring homomorphisms are the two basic categories. In Other words ,homomorphisms of modules, algebras, and vector space homomorphisms, which are also known as linear maps.
Two properties must be satisfied if T is a linear transformation:
T(x+ y) = T(x) + T(y) for any x, y in [tex]R^3.[/tex]
homogeneity is T(ax) = a T(x). For all scalars a and x in [tex]R^3.[/tex].
let a consider
L.H.S,T(x+y)= T[tex]((x_1+y_1),(x_2+y_2),(x_3+y_3[/tex]))= [tex](x_1+y_1+x_3+y_3, 2x_2+2y_2-x_3)[/tex]
R.H.S. T(x) + T(y) =[tex](x_1+x_3, 2x_2-x_3) +(y_1+y_3, 2y_2-y_3) =(x_1+y_1+x_3+y_3, 2x_2+2y_2-y_3).[/tex]
L.H.S.=R.H.S.
So,The first property is satisfied i.e. T(x+ y) = T(x) + T(y) for any x, y in [tex]R^3.[/tex]
For homogeneity,
let a consider ,
L.H.S. T(ax) = T[tex](ax_1,ax_2,ax_3) = (ax_1+ax_3, 2ax_2-ax_3).[/tex]
R.H.S. a T(x) = a T[tex](x_1,x_2,x_3) = a(x_1+x_3, 2x_2-x_3) = (ax_1+ax_3, 2ax_2-ax_3).[/tex]
L.H.S.=R.H.S.
So, T(ax) = a T(x). for all scalars a and all vectors x in [tex]R^3.[/tex].are satisfied
A linear transformation from [tex]R^3[/tex]to[tex]R^2[/tex] . is therefore represented by T.
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3. Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day that the fair
arrives at the fairground and then continues to work on finishing the setup for about a week to have the rides
ready to go in time for the opening of the fair. The scatter plot shows Anika's setup time on different days and
the linear model for the data.
Anika's Setup Times
The equation of the line representing the linear model of the data in slope-intercept form is; y = -1.25·x + 17.5
What is the slope-intercept form of the equation of a line?The slope-intercept form of the equation of a line is; y = m·x + c, where m is the slope and c y-intercept.
The possible question includes;
What is the equation for the line in slope intercept form;
The points on the line are; (2, 15), and (6, 10)
The slope is; (10 - 15)/(6 - 2) = -5/4
The equation of the line is therefore;
y - 15 = (-5/4)·(x - 2)
-5/4 = -1.25
y = -1.25·x + 5/2 + 15 = -1.25·x + 17.5
y = -1.25·x + 17.5
The equation of the line in slope-intercept form is; y = -1.25·x + 17.5Learn more on the slope-intercept form of the equation of a line: https://brainly.com/question/28584447
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If f(x)=⎧⎩⎨⎪⎪2x−3x2x+5ifififx≤−4−4
?
A. 25
B. 7
C. -4
D. 10
The function (5) is 10 given that f(x) = x + 5 if x ≥ 0
How do we solve for the f(5) given the function rule?To solve for f(5), we have to look at the function rule that says f(x) = x + 5 if x ≥ 0. Following this rule we say f(x) = 5 + 5 = 10. The number 10 is greater than 0 which make it valid.
All other rule does not apply to finding f(5).
The above answer is in response to the full question below
if f(x) = { 2x−3 if x ≤ -4
{ x² If -4 < x < 0
{ x + 5 if x ≥ 0
What is f(5)?
A. 25
B. 7
C. -4
D. 10
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An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. She wants a 95% confidence interval with a margin of error at most =0.025
. She has no idea what the true proportion could be.
How large a sample should she take?
The instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.
What is confidence interval?A confidence interval is a range of values that, with a certain degree of certainty, is likely to contain the real value of a population parameter. It is typically used in inferential statistics, where we use a sample to make inferences about a larger population.
According to question:To determine the sample size required to construct a 95% confidence interval with a margin of error of 0.025 or less, we need to use the formula:
n = (Z² * p * (1 - p)) / E²
where:
n = sample size
Z = Z-score corresponding to the desired level of confidence (in this case, 95%, which corresponds to a Z-score of 1.96)
p = estimated proportion of students repeating the class (since we have no prior information, we will use 0.5 as a conservative estimate)
E = maximum allowable margin of error (in this case, 0.025)
Plugging in the values, we get:
n = (1.96² * 0.5 * (1 - 0.5)) / 0.025²
n = 384.16
Rounding up to the nearest whole number, the instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.
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find the value of 5 1/10 minus 1 9/10
The value after solving mixed fraction is 32/10=3.2
What is fraction?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.
What is mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.
according to question,
=51/10 - 19/10
=32/10
=3.2
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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.
What is mixed fraction?It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.
To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.
5 1/10 can be converted to an improper fraction as follows:
5 1/10 = (5 x 10 + 1)/10 = 51/10
1 9/10 can be converted to an improper fraction as follows:
1 9/10 = (1 x 10 + 9)/10 = 19/10
Now we can subtract the two fractions:
51/10 - 19/10 = (51 - 19)/10 = 32/10
32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.
So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.
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Which equation is true?
An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication law of exponents for powers to each of the expressions, we have the following:
4 × n × n × n × n = 4n⁴
4 × n⁴ = 4n⁴
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AB and BC are perpendicular lines
Fine the value of x
Answer:
25 + x + x = 90
2x = 65
x = 32.5°
A parallelogram has one angle that measures 12°. What are the measures of the other three angles in the parallelogram?
Answer:
I think like 60∘, 60∘, 60 ∘ , 60 ∘ , and 120∘?
A cylinder has a radius of 5 inches and a height of 8 inches. What is its volume rounded to the nearest tenth?
Answer:
630
Step-by-step explanation:
v= pi×radius squared×hight so its 3.14×5 sqared×8 628 and 628 rounded to the nearest tenth is 630 hope this help
Help me on number 4. 14 points
Answer:[tex]18\frac{3}{8}[/tex] yards
Step-by-step explanation:
Formula:
Base x Height ---> [tex]3\frac{1}{2}[/tex] x [tex]5\frac{1}{4}[/tex] = [tex]18\frac{3}{8}[/tex]
If f(x)= e³x, then d/dx(e³x)=? A. 3e³x B. e³x C.ex D. 9e³x
Answer:
the answer is D. 9e³x.
Step-by-step explanation:
If f(x) = e³x, then we can find its derivative using the chain rule of differentiation as follows:
d/dx(e³x) = 3e³x * d/dx(3x) = 3e³x * 3 = 9e³x
= D. 9e³x.
Answer:
A
Step-by-step explanation:
Hey can you please help me because I don’t understand this question
The area of the shaded region is 88π square inches.
What is the area of the circle?To find the area of the shaded region, we need to subtract the area of the inner circle (with a radius of 9 inches) from the area of the outer circle (with a radius of 13 inches).
The area of a circle is given by the formula A = πr^2, where r is the radius.
Area of outer circle = π * (13²) = 169π square inches
Area of inner circle = π * (9²) = 81π square inches
Area of shaded region = Area of outer circle - Area of inner circle
= 169π - 81π
= 88π square inches
So, the area of the shaded region is 88π square inches.
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See text below
A ring-shaped region is shown below. Its inner radius is 9 in, and its outer radius is 13 in.
9 in
13 in
Find the area of the shaded region.
Use 3.14 for π. Do not round your answer.
2
in2
X
G
This equation shows how the total number of postcards Cooper buys is related to the number of days he spends on vacation. p = 9d The variable d represents the number of days he spends on vacation, and the variable p represents the total number of postcards he buys. After 2 days of vacation, how many total postcards will Cooper have bought?
The variable d represents the number of days he spends on vacation, and the variable p represents the total number of postcards he buys Cooper will have bought a total of 18 postcards after 2 days of vacation.
If p = 9d represents the total number of postcards Cooper buys in relation to the number of days he spends on vacation, we can substitute d = 2 into the equation to find the total number of postcards he buys after 2 days of vacation:
p = 9d
p = 9(2) [Substitute d = 2]
p = 18
Therefore, Cooper will have bought a total of 18 postcards after 2 days of vacation.
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Someone please answer this question
Some forms of cardiovascular disease involve the buildup of plaque on the inside walls of blood vessels. The buildup can put added stress on the heart and vessels, reducing or preventing blood flow to vital organs of the body.
Imagine that the diagram is a circular cross section of a blood vessel. What is the area of the inside of the blood vessel (i.e., the yellow part) in square units? Round your answer to the nearest tenth. The equation for the area of a circle is A = πr2, where A is area, π ≈ 3.14, and r is the radius. Recall that the radius is half of the diameter.
Answer:
153.94 cm2
Step-by-step explanation:
Circle area = π * r² = π * 49 [cm²] ≈ 153.94 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 7 [cm] * 2 = 14 [cm]
MARK AS BRAINLIEST PLS I TOOK 3 HOURS THINKING ABOUT THIS
A theater is hosting a film festival for Hispanic Heritage Month. The Moore family buys
5 tickets and spends $28.75 at the concession stand. Each ticket costs the same amount.
They spend a total of $76.75. Which equation shows the cost of each ticket, t?
Answer:t = 9.6.
Step-by-step explanation:
can someone please help me
What is the image of ( − 8 , 2 ) after a reflection over the line y=x?
Answer: The reflection of (-8,2) after a reflection over the line y=x is (2,-8)
Step-by-step explanation: The reflection on a graph refers to the preimage that has been reversed.
So, if we take an example of (x,y), over a reflection on the y-axis, then the answer would be (y,x)
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What is the length of RP
The zero product property's assistance. The RP measures 14 cm in length.
What is the Length?The length of a thing refers to its size or length measured from end to end. Or, to put it a different way, it is the larger of a geometrical shape's upper two or three dimensions.
(x+x+2) * (x+2) = (4+6)*4
Conjoin similar terms
(2x+2)(x+2)=10*4
2(x+1)(x+2) = 40
Divide by 2
(x+1)(x+2) = 20
FOIL
x²+2x+x+2=20
x²+3x+2=0
Subtract 20
x²+3x-18=0
Factor
(x +9) (x-6) = 0
Utilising the zero sum property
x+9=0 x-6 =0
x= -9 x=6
The length cannot be negative, hence
x=6
RP = x+2+x
= 6+2+6
= 14
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A mirror is placed 45 feet from the base of a waterfall by a hiker. The hiker walks backwards until they are 7.5 feet from the mirror. Determine how tall the waterfall is if the hiker is 6 feet tall.
36 ft
39.5 ft
56.25 ft
72 ft
If the hiker is 6 feet tall, then the height of the waterfall will be: 32.57 feet.
How to determine the height of the waterfallWe can solve this problem using similar triangles. Let us call the height of the waterfall "h". Then, the distance from the base of the waterfall to the mirror is also "h" (since the mirror reflects the top of the waterfall down to the hiker's eye).
Using similar triangles, we can set up the following proportion:
(h + 6 feet) / 45 feet = 6 feet / 7.5 feet
Cross-multiplying and simplifying, we get:
h + 6 feet = 270 feet / 7
h + 6 feet = 38.57 feet
h = 32.57 feet
So, the correct height given the variables is 32.57 feet.
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Answer:
36 ft
Step-by-step explanation:
We can use the concept of similar triangles to solve this problem. The ratio of the heights of the hiker and the waterfall is the same as the ratio of their distances to the mirror.
Given:
Distance from mirror to waterfall = 45 feet
Distance from mirror to hiker = 7.5 feet
Hiker's height = 6 feet
Let's set up a proportion:
(Hiker's height) / (Hiker's distance to mirror) = (Waterfall's height) / (Waterfall's distance to mirror)
Substitute the given values:
6 / 7.5 = (Waterfall's height) / 45
Now solve for the height of the waterfall:
Cross-multiply:
6 * 45 = 7.5 * (Waterfall's height)
270 = 7.5 * (Waterfall's height)
Divide by 7.5:
Waterfall's height = 270 / 7.5
Waterfall's height = 36 feet
So, the height of the waterfall is 36 feet.
Among the provided options, the correct answer is:
a) 36 ft
50 Points Please help quickly
Answer:
Step-by-step explanation:
The first one is C!
And the second one is E!
If this helps, go to math-way, and type in each of the equations and it will graph it for you!
Consider the following.
f(x) = x^5 − x^3 + 4, −1 ≤ x ≤ 1
(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.
what is function?Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.
A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.
To obtain the absolute maximum and lowest values of the function over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.
We first take the derivative of f(x) and set it to zero to determine the critical points:
The function is then assessed at these pivotal points and the interval's endpoints:
As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).
We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4
According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).
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Lighthouse B is 9 miles west of lighthouse A. A boat leaves A and sails 4 miles. At this time, it is sighted from B. If the bearing of the boat from B is N65degreesE, how far from B is the boat? Round to the nearest tenth
(Note: Needs 2 Answers)
PLEASE HELP I'M GOING INSANE
*please include work/formulas for every step when needed*
Boat is 4.195 miles or 6.749755 km far from the lighthouse B.
How to find the distance?The boat has moved 4 kilometers from point A to point x. The distance between B and x is what we're looking for.
Trigonometry can be used to overcome this issue. Let's abbreviate the distance "d" from A to x. Then, we can apply the following formula:
tan(65°) = (9 / d)
We can rearrange this formula to solve for d:
d = 9 / tan(65°)
We find that:
tan(65°) = 2.1445
So, d = 9 / 2.1445
= 4.195 miles (rounded to the nearest tenth)
or 6.749755 km.
Hence, Boat is 4.195 miles or 6.749755 km far from the lighthouse B.
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Identify the coordinate of any local and absolute extreme points and inflection points. Graph the function.
Y=5x+5 sin x, 0
The inflection occurs at x = n*pi, while the absolute extreme points, while the critical points can be found with the expression 5 + 5cos(x) = 0.
What are the extreme and inflection points?To find local extreme points, absolute extreme points, and inflection points, we will first take the first and second derivatives of the function.
y = 5x + 5sin(x)
y' = 5 + 5cos(x)
y'' = -5sin(x)
To find critical points, we set the first derivative equal to zero.
5 + 5cos(x) = 0
cos(x) = -1
x = pi
This is the only critical point, so we only need to evaluate the function at x = pi to find any extreme points.
y(pi) = 5pi - 5
So the absolute minimum occurs at (pi, -5).
To find inflection points, we set the second derivative equal to zero.
-5sin(x) = 0
sin(x) = 0
x = k*pi, where k is an integer.
So the inflection points occur at x = n*pi, where n is an integer.
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