The simplification 5/8(x )+ 1/2 ( 1/4( x) +10) is 3/4(x) + 5
What is simplification of fractions?The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.
For example 25/100 can be simplified by cutting down 25 and 100 by their common factor which is 25.
25/100 = 1/4
⅝(x) + 1/8(x) + 5
= 6/8(x) +5
= 3/4(x) + 5
therefore the simplification of 5/8(x )+ 1/2 ( 1/4( x) +10) is 3/4(x) + 5
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Jane and some friends entered a snowman building contest I don't winter carnival before getting started they predicted the height of a snowman what build when they finish the snowman with 80 inches taller prediction was 10% lower than that how tall are the group predicted the snowman will
The answer is the tall are the group predicted the snowman will 800/9 or alternative form was 88.8.
What is meant by predicted?
Predict is often used interchangeably with the words forecast, foretell, prognosticate, and prophecy. All of these phrases refer to "telling in advance," but predict typically connotes drawing conclusions from known facts or natural principles.A predicted grade is the level of proficiency that an applicant's school or college predicts they will achieve under ideal conditions.Universities and colleges utilize these predicted grades to understand the potential of applicants as part of the admissions process.When a model is expected to produce a prediction in relation to what it is predicting is known as the prediction time. For systems that change dynamically throughout time, it is crucial to comprehend prediction time, when events have occurred, and when predictions are being produced.Based on the given conditions, formulate :: 80 ÷ (1 - 10%)
Calculate the sum or difference:
= 80 / 1 - 0.1
= 80 / 0.9
Multiply both the numerator and denominator with the same integer : 800 / 9 or alternative form was 88.8
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which description best describes the three-dimensional object that is formed when the shape is rotated about the axis as shown? responses a rectangular prism that is open on the ends a rectangular prism that is open on the ends a square pyramid a square pyramid a flat disk with a hole in the center a flat disk with a hole in the center a hollow cylinder a hollow cylinder a vertical line labeled as axis is drawn. a vertical rectangle is drawn on the left side of the line that does not touch the line. an arrow rotated around the line in a clockwise direction is drawn.
The three-dimensional object formed when the shape is rotated about the axis is a hollow cylinder.
This object is generated by taking a vertical rectangle and rotating it around the vertical axis. Mathematically, this can be described as a revolution of the rectangle about the y-axis in which the points of the rectangle are shifted a certain distance away from the axis. The three-dimensional object formed when the shape is rotated about the axis is a hollow cylinder.The formula used to calculate the volume of a hollow cylinder is V = π(r^2)h, where r is the radius of the cylinder, and h is the height. For example, if we have a cylinder with radius 4 and height 8, the volume would be V = π(4^2)8 = 128π cubic units.
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Use spherical coordinates to show that the triple integral from negative infinity to infinity of the (sqrt of x^2+y^2+z^2 * e^-(x^2+y^2+z^2)) dxdydz = 2pi
The improper triple integral is defines as the limit of a triple integral over a solid sphere as the radius of the sphere goes to infinity. (Hint: write inequalities for a solid sphere of radius p, and then let p -> infinity)
We have used spherical coordinates to show that the triple integral from negative infinity to infinity of the [tex]\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]
What is meant by triple integral?Triple integrals, as their name suggests, are three sequential integrations that can be used to determine a volume or to integrate in a fourth dimension over three other independent dimensions.
The total amount of heat in the three-dimensional room can be calculated using this triple integral.
We understand that triple integrals have several uses if "dimension" can refer to something other than a spatial dimension. We could determine a 3-D object's overall inertia or the gravitational attraction on a basketball.
The sum of an infinite number of rectangular prisms across a bounded region in three-space is a double integral, which represents the volume beneath the surface above the xy-plane.
[tex]$$To show that $\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$, begin by converting the integral into spherical coordinates. Recall that $\rho^2=x^2+y^2+z^2$ and $d V=\rho^2 \sin \phi d \rho d \phi d \theta$. To convert the bounds, notice that as $x, y$, and $z$ expand infinitely in both directions, this can be modeled to a sphere of an infinite radius.\\$$[/tex]
[tex]$$This means that the new bounds become $0 \leq \rho \leq \infty, 0 \leq \phi \leq \pi$, and $0 \leq \theta \leq 2 \pi$. Because the integral is infinite, let the upper limit of $\rho$ be $R$ and take the limit as $R$ goes to infinity. To evaluate with respect to $\rho$, first use $u$ substitution by letting $u=\rho^2$ and then integrating by parts$$[/tex]
[tex]$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z$[/tex]
[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0 \int_0^R \sqrt{\rho^2} e^{-\left(\rho^2\right)} \rho^2 \sin \phi d \rho d \phi d \theta \\& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^\pi \int_0^R e^{-\rho^2} \rho^3 \sin \phi d \rho d \phi d \theta \\[/tex]
[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^2 \sin \phi\left[\frac{1}{2}\left(-e^{-\rho^2}\left(1+\rho^2\right)\right)\right]_{\rho=0}^{\rho-R} d \phi d \theta \\& =\frac{1}{2} \lim _{R \rightarrow \infty} \int_0^{2 \pi \pi} \int_0^\pi \sin \phi\left[-e^{-R^2}\left(1+R^2\right)+e^{-0^2}\left(1+0^2\right)\right] d \phi d \theta\end{aligned}$$[/tex]
[tex]$$\\\text{Use L' Hospital's Rule to simplify the limit}$$\begin{aligned}& \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z \\& =2 \pi(1)-2 \pi \lim _{R \rightarrow \infty}\left(\frac{2 R}{2 R e^{R^2}}\right) \\& =2 \pi-\lim _{R \rightarrow \infty} \frac{1}{e^{R^2}} \\& =2 \pi-0 \quad \text { As } \lim _{x \rightarrow \infty} \frac{1}{e^x}=0 . \\& =2 \pi\end{aligned}$$[/tex]
[tex]$$Therefore,$$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]
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the terminal point determined by tge real number , t is given. find sin t cos t tan t (root5/5, 2 root 5/5)
sint= [tex]y=\frac{\sqrt{5} }{5}[/tex], cost= [tex]x=\frac{2\sqrt{5} }{5}[/tex], tant=2.
If the terminal point P(X, Y) is determined as a real number, t lies on the unit circle then:
sint=y cost=x tant=y/x
we are given a terminal point of P [tex](\frac{\sqrt{5} }{5} ,\frac{2\sqrt{5} }{5} )[/tex] but not given that t lies on the unit circle. we must then first verify that P lies on the unit circle:
The equation of the unit circle is:
x²+y²=1
After substituting the given points in the above equation:
[tex](\frac{\sqrt{5} }{5} )^{2} +(\frac{2\sqrt{5} }{5} )^2=1[/tex]
Now evaluate the powers we get:
[tex]\frac{5}{25} +\frac{20}{25} =1[/tex]
Adding the equation we get:
1=1
Since P [tex](\frac{\sqrt{5} }{5} ,\frac{2\sqrt{5} }{5} )[/tex] lies on the unit circle, then:
[tex]sint=y=\frac{\sqrt{5} }{5}\\\\cost=x=\frac{2\sqrt{5} }{5} \\\\tant=\frac{y}{x}=\frac{\frac{2\sqrt{5} }{5} }{\frac{\sqrt{5} }{5} }[/tex]
By solving the tant we get:
tant=2.
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Mrs. Menswar is selling chocolate bars and yogurt cups. The cost of the chocolate bar is $3.00
and the yogurt cups are $5.00. She sold 11 more chocolate bars than yogurt cups and earned $233.
Write and solve a system of equations to represent this situation. Then describe what the solution
means.
Answer:
36 chocolate bars and 25 yogurt cups were sold
Step-by-step explanation:
c= # of choc. bars sold = y + 11
y = # of yogurt cups sold
3(y + 11) + 5y = $233
3y + 33 + 5y = 233
8y = 200
y = 200/8 = 26
c = y + 11 = 25 + 11 = 36
Schools, churches, and corporations are examples of __________ groups.a. secondaryb. actingc. primaryd. informal
Schools, churches, and corporations are examples of Secondary Groups.
What does a secondary formal group mean?
A secondary group is a comparatively larger group made up of impersonal, purpose-driven, and frequently transient interactions.
These groups typically involve significantly less emotional engagement and are built around reaching a goal that is unrelated to the relationship itself.
What do main and secondary social institutions entail?
Small and distinguished by long-lasting, close-knit ties, primary groups are common. Non-personal, ad hoc, and goal-driven interactions are examples of secondary groupings.
An exchange of implicit goods, such as love, care, concern, support, etc., is what constitutes a primary group. Family units, romantic partnerships, crisis support networks, and religious organizations are a few examples of these.
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Why is f not a function from R to R if
a) f (x) = 1/x?
The function:
f(x) = 1/x
Does not has 0 on its domain, then the domain is not R, that is why the function is not from R to R.
What is a function from R to R?A function from R to R is a function where the domain is the set of all real numbers and the range is also the set of all real numbers.
Here the given function is rational, and it is:
f(x) = 1/x
Remember that we can't divide by zero, so the input x = 0 can't be on the domain of function f(x).
Thus, the domain is not the set of all real numbers.
That is why the function f is not from R to R, because the domain is not R.
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Determine the range of the following graph:
Step-by-step explanation:
The vertical extent of the graph is all range values 3 and -2, so the range is (−2,3]
f(x) = x-1 /5
g(x) = 2x + 7
For what value of x is g(x) = ƒ−¹(x) true?
-1
According to the given statement, The value of x = -5 / 36.
What is a variable (x) ?The x variable is ubiquitous in math and stands for an unknown. It doesn't always have to be an x - any letter of our alphabet can represent an unknown. To work with variables, the first step is to identify the unknown and label it. Next is writing an equation you can solve to find the unknown.
Given: f(x) = x-1 /5
g(x) = 2x + 7
Solving for g(x) = ƒ(x),
2x + 7 = x-1 /5
10x + 35 = 5x - 1
5x = -36
x = -36 / 5
Hence, the value of x for g(x) = ƒ−¹(x) is x = -5 / 36.
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finance the median player salary for the new york yankees was $1.6 million in 2001 and $5.2 million in 2009. write a linear equation giving the median salary y in terms of the year x. then use the equation to predict the median salary in 2017.
The median salary in 2048 will be 2.853 million
What is meant by equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. A condition on a variable (or variables) that ensures that two expressions in the variable (or variables) have the same value is known as an equation. An equation remains the same if the LHS and the RHS are switched; this value of the variable is referred to as the solution or root of the equation.A general linear equation is given by:
y=a × x + b
Where the slope is a and the y-intercept is b.
We shall discover that the linear equation for this scenario is
y = 0.033 × x + 1.269
And we may anticipate that in 2048, the median salary will be 2.853 million.
The slope can be expressed as if the line passes through the points (x1, y1) and (x2, y2).:
[tex]$a=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, we know that whereas the median player pay in 2007 (x = 7) was y = 1.5 million, it was y = 1.7 million in 2013 (x = 13).
The following two points can be written as follows:
(7,1.5)
(13,1.7)
Note that the y-value is in millions.
Then the slope of the linear equation will be:
[tex]$a=\frac{1.7-1.5}{13-7}=0.033[/tex]
So the linear equation is something like:
y=0.033 × x + b
Remember the point (7,1.5), which indicates that for x=7, we also get y=1.5, so we can substitute these in the equation above:
1.5=0.033 × 7+b
1.5-0.033 × 7 = b = 1.269
Then the linear equation is:
y=0.033 × x+1.269
b) Now we want to predict the median salary in 2048 . For 2048 the
x-value is x=48
So we just need to evaluate this in the linear equation:
y = 0.033 × 48 + 1.269 = 2.853
Then the median salary in 2048 will be 2.853 million
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Write an equation of the line below
The line touches -x axis at 3 and touches y axis at 3
P(x,y) = (-3,3)
α+ β = -3
α β = 3
[tex] {x}^{2} - ( \alpha + \beta {)}^{2} + \alpha \beta \\ = {x}^{2} - ( - 3)x + 3 \\ {x}^{2} + 3x + 3 = 0[/tex]50.25.2 rewritten correctly using the commutative property and then simplified correctly?
Answer:
2.25.50
Step-by-step explanation:
it is simplified since 25 is not divisible by 2
203,199,195 find the 35th term
Answer:
67
Step-by-step explanation:
The given arithmetic sequence is,
203, 199, 195,......
In the sequence, the first time a = 203,
And common difference of the sequence d = -4
Formula for nth term of the sequence,
aₙ = a + (n-1) . d
To find 35th term of the sequence, substitute n= 35,
a₃₅ = 203 + (35-1).(-4)
= 203 + 34x-4
= 203 - 136
= 67
©Thank You
Answered By Solution 49
camille can buy up to 5 shirts. how much money could she have? enter the correct answers in the boxes in dollars and cents.
Camille can buy maximum of 3 shirts with the amount with him and left with $24 after buying 3 shirts .
Price of each shirt is $32 and the maximum she can buy is 5 shirts
suppose he buys x shirts from the money he initially have
so 32*x<=120
=> x<=3.75
solving the inequality we get:
so x=3 so maximum he can buy is 3 shirts.
Cost of each shirts is $32 so the cost of 3 shirts is given by:
=>3*32
=> $96
so the amount of money left with him = 120 -96
=> 24
so total $24 she can save after buying 3 shirts.
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Complete question:
camille have $120 with him he can buy upto 5 shirts and cost of each shirt is $32 .how much money could she have and how manu shirts he buys? enter the correct answers in the boxes in dollars and cents.
This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs? The answer is Segments A and C only. Explain.
The correct option for the given question is an option (C) which is Segments A and C only.
The goal of image segmentation techniques is to separate the image's various components according to the region of interest. Videos are collections of images, therefore motion segmentation separates them into moving foreground and background by separating the elements that exhibit various motion patterns.
We can extract visual information by classifying visual elements from the scenes into different groups and analyzing these spatial and temporal changes that take place in the image sequence. Each group represents an object's motion in the dynamic sequence.
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The complete question is:
This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs?
A) None of the segments could represent work being done by springs.
B) Any of the segments could represent work being done by springs.
C) Segments A and C only.
D) Segments B and D only.
E) Segment A only.
Given the function: x(t) = 6T3 - 7+2
- 6t + 50. What is the
value of x
at t = 7?
the value of the function at t = 7 is 1723.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given the function: x(t) = 6T³ - 7t²- 6t + 50.
the value of x at t = 7
Substitute the value of t in the given function
x(7) = 6 * 7³ - 7*7² - 6 * 7 +50
x(7) = 1723
Therefore, the value of the function at t = 7 is 1723.
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Stainless steel contains at least 10.5% chromium. If a steel container that weighs 40 grams contains 5 grams of chromium, does it meet the standard for stainless steel?
The steel container meet the standard for stainless steel because it contains 12.5% of chromium.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Stainless steel contains at least 10.5% chromium.
We need to determine if a steel container that weighs 40 grams contains 5 grams of chromium is stainless steel.
Therefore:
Percentage of chromium in the steel container = (5 grams / 40 grams) * 100% = 12.5%
12.5% > 10.5%, hence the steel container meet the standard for stainless steel
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Eric fell asleep at 3:15 pm he woke up after 2 hours and 35 minutes what time did eric wake up
when u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin.
The span of the two vectors is the set of all linear combinations of the two vectors. This means that any point on the line through u and the origin, as well as any point on the line through v and the origin, can be written as a linear combination of u and v.
1. Start by taking two non-zero vectors u and v.
2. The span of the two vectors is the set of all linear combinations of the two vectors, which means that any point on the line through u and the origin, as well as any point on the line through v and the origin, can be written as a linear combination of u and v.
3. Therefore, span{u, v} contains the line through u and the origin, as well as the line through v and the origin.
The span of two non-zero vectors u and v contains the line through u and the origin, as well as the line through v and the origin. Any point on these two lines can be written as a linear combination of u and v.
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Write an equation of the line containing the given point and parallel to the given line.
(7.-5); 4x - 5y = 2
The equation of the line containing point (7, -5) and having slope 4/5 is found as y = 4/5x - 3/5.
Explain the term slope intercept form?A line's equation of the type y = mx + b can be written in slope intercept form. The m stands for the line's slope, and the b for the y-intercept. When you need to find a point on the a line or solve for y given x, you utilise the slope intercept form.The given data:
Passing points (x1, y1) = (7, -5)Parallel line's equation: 4x - 5y = 2Comparing eq with standard form:
5y = 4x - 2
y = 4/5 x - 2/5
slope m = 4/5
As both lines are parallel, the slope of both lines will be equal.
Thus, using slope intercept form
y - y1 = m(x - x1)
y + 5 = 4/5 (x - 7)
y + 5 = 4/5x - 28/5
y = 4/5x - 3/5
Thus, the equation of the line containing point (7, -5) and having slope 4/5 is found as y = 4/5x - 3/5.
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The ratio of 1.5 to 29 is the same as the ratio of 4.5 to
Answer:
4.5:87
Step-by-step explanation:
First, we can set up an equation because 1.5:29 is equal to 4.5:x
[tex]\frac{1.5}{29} = \frac{4.5}{x}[/tex]
Now, we can solve for x by:
1.5x = 4.5 * 29
1.5x = 130.5
x = 87
The ratio will be 4.5:87
Read and solve... 1-Tony walked 7/10 of a Kilometer fr Express the distance as adecimal. 2. Volet spent 0.5 hour reading a Pocket She spent reading as 9. fraction. th
Tony walked 7/10 km which in decimal will be 0.7 km
Volet spent 0.5 hrs reading a pocket which in Fraction will be 5/10 = 1/2
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
Tony walked 7/10 km which in decimal will be 0.7 km
Volet spent 0.5 hrs reading a pocket which in Fraction will be 5/10 = 1/2
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what is the average class score ? round your answer to the nearest whole number
match each term on the left column with the appropriate description from the right column description. each answer choice will only be used one time. group of answer choices mean [ choose ] median [ choose ] mode [ choose ] range [ choose ] variance [ choose ] standard deviation
Extreme values are present in a set of data in business. which of the following descriptive summary measures are most appropriate interquartile range and median.
Range is the maximum easy and normally comprehensible measures of dispersion. Range is described because the distinction among the highest (or largest) and lowest (or smallest) determined fee in a series. Therefore, it's miles the maximum affected measures of dispersion via way of means of the acute values of the series.
The median offers the best weight to factors withinside the center of the ordered records. When there are intense numbers withinside the records set (very low or very excessive numbers), the median is a great data preference for a degree of principal tendency.
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question if s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of nst ?
If s and t are integers greater than 1 and each is a factor of the integer n, then the product nst must be divisible by both s and t. This is because s and t are factors of n, which means that n is divisible by s and t.
The product of two integers is divisible by the factors of each of those integers. Therefore, since n is divisible by s and t, and nst is the product of n, s, and t, nst must also be divisible by s and t. This can be proven by the definition of divisibility: if a number, in this case n, is divisible by an integer, in this case s or t, then the product of that number and another integer, in this case t or s, is also divisible by the initial integer.
For example, if n = 24, s = 4, and t = 3, we can see that 4 and 3 are factors of 24, since 24 is divisible by 4 and 3. The product of 24, 4 and 3 is 2443 = 288. 288 is also divisible by 4 and 3.
In summary, if s and t are integers greater than 1 and each is a factor of the integer n, then s and t must be factors of nst.
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50 POINTS + BRAINLIEST
Answer:
I believe the answer may be 31.5cm.
Step-by-step explanation:
I first found the area of the total region which was 70cm. From there I found the area of the triangle to the left of the region by doing 6x7 which is 42, and multiplied by 1/2 because it is a triangle. I did the same to the triangle on the right, doing 5x7 which is 35, and multiplied by 1/2 since this is also a triangle. Finally, I subtracted both totals of 21, and 17.5 from the 70, getting a grand total of 31.5cm.
Answer:
31.5 cm²
Step-by-step explanation:
To find the area of the crossed region, subtract the areas of the two triangles from the area of the rectangle.
Formulae:
Area of a rectangle = length × widthArea of a triangle = ¹/₂ × base × heightArea of the rectangle
⇒ A = (4 + 6) × 7
⇒ A = 10 × 7
⇒ A = 70 cm²
Area of triangle 1
⇒ A = ¹/₂ × 6 × 7
⇒ A = 3 × 7
⇒ A = 21 cm²
Area of triangle 2
⇒ A = ¹/₂ × 5 × 7
⇒ A = 2.5 × 7
⇒ A = 17.5 cm²
Area of the crossed region
⇒ A = 70 - 21 - 17.5
⇒ A = 49 - 17.5
⇒ A = 31.5 cm²
Choose the system of inequalities that best matches the graph below.
The set of inequality that most closely resembles the graph below is called y<4 , [tex]$y \geq 4 x-4$[/tex].
What is the system of inequality ?Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.
At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.
Therefore the correct answer is option A ) y<4 , [tex]$y \geq 4 x-4$[/tex]
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PLEASE HELP!
Q: Match the key aspect of a function's graph with its meaning.
x-intercept
f(x) < 0
y-intercept
f(x) > 0
Matching the Meaning of Key Featu
Intro
↑
↑
intervals of the domain where the
graph is below the x-axis
location on graph where output is
zero
intervals of the domain where the
graph is above the x-axis
location on graph where input is zero
Done
Question
Answered step-by-step
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An investor has asked his stockbroker to rate three stocks (A, B, and C) and list them in the order in which she would recommend them. Consider the following events: i. iii. iv. V. ● · · L: Stock A doesn't receive the lowest rating M: Stock B doesn't receive the lowest rating N: Stock C receives the highest rating Define the random experiment and list the simple events in the sample space List the simple events in each of the events L, M, and N List the simple events belonging to each of the following events: (L or N), (L and M), and M Is there a pair of mutually exclusive events among L, M, and N? Is there a pair of exhaustive events among L, M, and N?
Intuitively speaking two events are independents when the occurrence of one event (A) does not exert influence over the event (B)
How do you know if two events are exhaustive?Symbolic speaking in terms of sets
P(A∩B)= P(A) * P(B)
Examining each alternative
A. Flipping two coins and having one show a head and the other show a head
Independent. Each flipping coin does not exert any influence on the other
B. Being sneezed on and catching a cold
Dependent. This sequence of events expresses cause consequences effects.
C. When rolling a pair of dice, getting a total of 6 and having one die show a 3
Dependent
Under these conditions, the second event is dependent since all we need is a sum of six, having the first dice showing three. The second one has to show three. So it does exert influence under the result.
D. Rolling a 4 on one die and rolling a 2 on another die
Independent. To get a 4 does not exert any influence on getting a 2 on another dice.
E. Seeing clouds and winning the lottery
Independent.
There is no influence seeing clouds and winning the lottery.
To learn more about exhaustive events refer
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An equilateral triangle has a perimeter of 159 centimeters. Find the length of each side of this triangle.
The length of each side of the equilateral triangle is ____ cm
Answer: 53
Step-by-step explanation: We know that the a triangle has three sides.
We also know that all of the sides are equal. And all the sides equal 159. So do 159/3 which equals 53.
