Based on the information, it can be inferred that the area of the figure is 310 yards²
How to calculate the surface area of this figure?To calculate the surface area of this figure we must find the area of all the faces of the figure:
5 * 10 = 5010 * 7 = 705 * 7 = 35Then we must multiply the area of each face by the number of faces with that area.
50 * 2 = 10070 * 2 = 14035 * 2 = 70Finally we must add the areas of the faces
100 + 140 + 70 = 310According to the above, the total surface area of this figure is 310 yards ²
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Xx
Which equation models the rational function shown in
the graph?
2(x+2)
X-2
O f(x) =
O f(x) = x-2
x+2
2(x-2)
x+2
Of(x)=.
O f(x) = x+2
X-2
At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
From given graph we can see that
At x=2, the function in the graph is approaches to infinity.
It means function is not defined at x=2
We know that a rational function is undefined when denominator is equal to zero.
For equation 1:
f(x)= 2(x+2)/(x-2)
Equating the denominator:
x-2=0
x=2
It means function is not defined at x=2
The y-intercept is: y= -2
The function is passing through the point (1,-6).
When we substitute x=1
Hence, option 1 is true.
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HELPPPP PLS I NEED HELP
According to the given information the lateral surface area of given cylinder is 725.34 in².
What can you say about a cylinder?In mathematics, a cylindrical is indeed a three-dimensional solid that retains two parallel bases spaced apart by a curving surface. These bases frequently have a circular shape (like a circle), and also an axis links their respective centers.
What three qualities does a cylinder have?A cylinder is a three-dimensional form having two parallel, round sides on either end, one side that curves, no vertices or edges.
As we know that the lateral surface area of cylinder (A) = 2πrh
Given
D = [tex]16\frac{1}{2}[/tex]in
h = 14in
r = D/2
= 33/4 in
A = (2 × 3.14 × 33 × 14) / 4
= 2901.36 /4
= 725.34 in²
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If the percentage increase between 2017 of 9,640,000 and 2018 of 9,960,000 continued in 2018 and 2019 , how many households would be there be in 2019 ? Round to the nearest ten thousand
Answer:
Step-by-step explanation:
To determine the percentage increase between 2017 and 2018, we need to calculate the difference between the two years and then divide by the 2017 value and multiply by 100. So, the calculation would be:
(9960,000 - 9640,000) / 9640,000 * 100 = 3.125%
So, the number of households increased by 3.125% from 2017 to 2018.
To find the number of households in 2019, we need to find the increase from 2018 to 2019. We can do this by multiplying the number of households in 2018 by the percentage increase, and then add that to the 2018 value. So, the calculation would be:
9960,000 * (3.125 / 100) + 9960,000 = 10,298,800
Therefore, there would be approximately 10,298,800 households in 2019, rounded to the nearest ten thousand.
Answer the following questions
The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;
(a) 5·x + 3·y = 10
2·x + 6·y = 10
(b) Length of each Plan A workout: 1.25 hours
Length of each Plan B workout: 1.25 hours
What are linear system of equations?A linear system of equation consists of two or more linear equations that share common variables.
(a) The number of Plan A workouts Mary trained on Wednesday = 5
Number of Plan B workouts she trained on Wednesday = 3
The total time (in hours) Mary trained both workouts on Wednesday = 10
Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;
5·x + 3·y = 10
Similarly, the number of Plan A workouts trained on Thursday = 2
Number of Plan B workout trained on Thursday = 6
The duration of training of all workouts on Thursday = 10 hours
Therefore, we get;
2·x + 6·y = 10
The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;
5·x + 3·y = 102·x + 6·y = 10(b) The first equation from the system of equations indicates that we get;
5·x + 3·y = 10
3·y = 10 - 5·x
y = (10 - 5·x)/3Plugging the value of y above into the second equation from the system of equations, we get;
2·x + 6·y = 10
2·x + 6 × ((10 - 5·x)/3) = 10
2·x + 2·(10 - 5·x) = 10
2·x + 20 - 10·x = 10
20 - 8·x = 10
8·x = 20 - 10 = 10
x = 10/8 = 1.25
The length of each Plan A workout, x = 1.25 hoursy = (10 - 5·x)/3,
x = 1.25, therefore;
y = (10 - 5 × 1.25)/3 = 1.25
y = 1.25
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LMNO is a parallelogram. If NM = x + 37 and OL = 5x + 9 find the value of x.
The value for the variable x in the parallelogram is equal to 7.
How to evaluate for the variable x in the parallelogramThe parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.
We shall evaluate for variable x as follows:
5x + 9 = x + 37
5x - x = 37 - 9 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7
Therefore, the value for the variable x in the parallelogram is equal to 7.
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The value of the variable x is 7
How to determine the valueIt is important to note that the opposite sides of a parallelogram are congruent or equal in length.
Then, for the parallelogram LMNO
NM is parallel to OL
Now, substitute the values, we get;
NM = OL
x + 37 = 5x + 9
collect like terms
x - 5x = 9 - 37
subtract the like terms
-4x = -28
Make 'x' the subject
x = 7
Hence, the value is 7
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Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line.
2x+4<10
The solution set of the inequality is [3, ∝)
How to determine the solution setFrom the question, we have the following parameters that can be used in our computation:
2x + 4 < 10
Subtract 4 from both sides of the inequality
So, we have the following representation
2x + 4 - 4 < 10 - 4
Evaluate the like terms
2x < 6
Divide both sides by 2
x < 3
When represented as an interval notation, we have
[3, ∝)
See attachment for the inequality of the solution set
Hence, the solution is [3, ∝)
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Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14). If necessary, round to three decimal places
The statistical measurement known as the Z-score describes the connection between a value and the mean of a set of values and the required z-score to the three decimal places is −2.714.
What is the z-score?The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score.
Standard deviations from the mean are used to measure Z-score.
A Z-score of zero means the data point's score is the same as the mean score.
Your observed value is 2.5 standard deviations from the mean if your Z-score is 2.5, and so on.
Your value is more closely aligned with the mean the closer your Z-score is to zero.
Your value is further from the mean the farther your Z-score is from zero.
So, let's say Rosetta wins the game on Thursday with 110 points.
When x=110, the z-score is -2.714.
The average is 148.
You can see from this z-score that x=110 is 2.714 standard deviations away from the mean.
This formula can be used to determine the z-score:
z = x−μ/σ
=110−148/14
=−38/14
≈−2.714
Therefore, the required z-score to the three decimal places is −2.714.
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gerry's drawer has two black socks and 4 blue socks. if he selects two socks without looking what is the probability that both socks are black
Graph h(x)=−x2+3.
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.
A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.
The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.
To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:
h(-2) = -(-2)^2 + 3
h(-2) = 4 + 3
h(-2) = 7
So the point (-2, 7) is also on the parabola.
With the vertex and one other point on the parabola, you can now graph the parabola.
Step-by-step explanation:
Write an equation for a rational function with the given characteristics.
Vertical asymptotes at x = -2 and x = 3,2-intercepts at (-4, 0) and (-1,0), y-intercept at (0,4).
F(x)=
The equation of the rational function with the given features is given as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
How to define the rational function?A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.
Considering the x-intercepts, the numerator of the function is defined as follows:
y = a(x + 4)(x + 1)
y = a(x² + 5x + 4).
Considering the y-intercept at (0,4), the leading coefficient a is given as follows:
a = 4.
The vertical asymptotes determine the zeros of the denominator, which is given as follows:
(x + 2)(x - 3) = x² - x - 6.
Hence the function is defined as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
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Use calculator to find 61.6 to the nearest hundredth
Answer : 61.60
Step-by-step explanation:
Answer:61.60
Step-by-step explanation:
i just typed it in
10. Susan has $800 in her bank account. Every week, she withdraws $100 for spending money.
A) What is the rate of change (or slope) in this situation?
B)
How much will she have left in her account after five weeks?
A) The rate of change in this situation is -$100 per week.
B) She will have $300 left in her account after five weeks.
More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and now, a cure could be in sight.
Source: The Guardian, November 30, 2018
Make a graph of the production possibilities frontier with HIV/AIDS cases treated on the x-axis and other goods and services on the y-axis before and after the advance in technology.
Question content area bottom left
Part 1
The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated.
Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0.
Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
On solving the provided question, we can say that from the graphs The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technological advancement.
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations οr charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue tοgether the nodes, οften referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of expοnential growth. a logarithmic graph in the shape οf a triangle
The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technοlogical advancement.
Priοr to technological advancement, the opportunity cost of treating HIV/AIDS rises as the wοrld deviates from its PPF. The pοtential cost of treating more HIV/AIDS cases falls as a result of technοlogical advancements since less other commοdities and services must be sacrificed in οrder to treat more HIV/AIDS patients. Alternatively, the world might treat mοre HIV/AIDS patients right now by forgoing the same number of other commοdities and services.
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The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040. Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.
The average hourly wage for police officers is $30.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S.
In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040.
Assume that police officers generally work 40 hours a week.
There are 52 weeks in the year.
The average hourly wage for police officers is,
= 62040 ÷ (52 x 40)
= 62040 / 2080
= 29.8
≈ $30
Therefore, $30 is the hourly wage.
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In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
Somebody help, I don't get this!
The statements are (a) False, (b) True and (c) False
What are Right Angles?Right angles are angles whose measure is 90 degrees.
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
(a) ∠AHB and ∠AHG are vertical angles.
Vertical angles are angles which are formed on the opposite sides of two intersecting lines.
∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.
So the statement is false.
(b) ∠EHF and ∠DHE are adjacent angles.
∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.
So the statement is true.
(c) The measure of ∠FHG is equal to the measure ∠DHF.
We know that DG is a straight line.
∠FHG and ∠DHF are linear pair of angles.
So, ∠FHG + ∠DHF = 180°
Given that ∠FHG is right angle.
90° + ∠DHF = 180°
∠DHF = 180° - 90°
∠DHF = 90°
So the statement is true.
Hence the statements (a), (b) and (c) are false, true and true respectively.
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Your question is incomplete. The complete question with the figure is given below.
i need help on this pleaseee!!
The value of each variable in the quadrilateral can be found such that :
y = 73 degrees z = 101 degrees How to find the value of the variables ?Angle 107 degrees and z degrees will add up to 180 degrees which means that the value of z is:
= 180 - 107
= 73 degrees
Using this value of z as 73 degrees, we can then solve for y because the sum of the interior angles of a quadrilateral need to add up to 360 degrees.
The value of y variable is therefore:
= 360 - 83 - 103 - 73
= 101 degrees
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Square ABCD has diagonal AC with vertices A(1, 1) and C(3, — 1). Find the coordinates of the
remaining vertices.
The coordinates are
Answer:
The coordinates of the remaining vertices are (1, -1) and (3, 1).
Step-by-step explanation:
A square is a quadrilateral with with four sides of equal length. It has two sets of parallel sides and its interior angles are all right angles. Therefore, each vertex shares its x-coordinate with one adjacent vertex, and its y-coordinate with the other adjacent vertex.
If AC with vertices A(1, 1) and C(3, -1) is the diagonal of a square, the coordinates of the remaining vertices will be:
[tex](x_A, y_C)=(1,-1)[/tex][tex](x_C, y_A)=(3,1)[/tex]The square root of a number is greater than the square of the number. For what set of numbers is this true?.
The set of numbers for which the statement that the square root of a number is greater than the square of the number is true, is equals to (0,1). So, right choice is option (a).
In mathematics, when we multiplying the number by itself, the result is called square of number. This is usually equivalent to raising a number to the power of 2. For example, square of 4 is 4² = 16. The square root of a number is that factor of a number which when multiplied by itself the original number. Square root of number is usually equivalent to raising a number to the power of 1/2. It is represented using the symbol '√'. Now, we have to check the options and determine where square root of a number is greater than the square of the number.
a) (0, 1), if we plug f(x) = √x , x∈(0,1) and g(x) = x² , x∈(0,1) on calculator then we get, the value of f(x) is greater than g(x), i.e, x = 1/2 , f(1/2) = 0.70 and g(1/2) = 0.25.
b) [0, 1], if we plug x = 0 then f(0) = 0 , g(0) = 0
that is f(x) is greater than and equal to g(x). But we have to consider only greater than not equal.
c) [1,∞), closed bracket again represents equality which is not consider. So, statement is false for it.
d) (1,∞), here number inbetween 1 and infinite but not for all reals it is true that square root of a number is greater than the square of the number, for example x = 2 , f(2) =1.414, g( 2) = 4 implies f(x)< g(x) for x = 2. So, the statement is false for it.
Hence, required option is option (a).
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Complete question :
The square root of a number is greater than the square of the number. For what set of numbers is this true?
a) (0, 1)
b) [0, 1]
c) [1, ∞ )
d) (1,∞)
Identify true statements about set membership and subsets
The statement that are true are :
a. Z is an element {y,z}
b. {6,7,8 } is a subset of {1,2,3,4......}
c. 3 is an element of {2,3}
d. r is not an element of {s,t,u}
What is set?
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements.
The following statements are true about the set
a. Z is an element {y,z}
b. {6,7,8 } is a subset of {1,2,3,4......}
c. 3 is an element of {2,3}
d. r is not an element of {s,t,u}
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The shape of the distribution of the number of clase friends for the males is best characterized as
The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).
What are shapes called in math?Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza
What are the basic shapes?The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.
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If a rock is thrown upward on an exoplanet of a nearby star with initial velocity…..
the displacement is 23.14m and the velocity is 21.28m/s
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The given equation y = 25t - 1.86t²
at t = 1
So the displacement y = 25-1.86 = 23.14
to find velocity dy/dt = 25- 2(1.86)t
v = 25 - 3.72 = 21.28m/s
Hence the displacement is 23.14m and velocity is 21.28m/s
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Find the length of WB
Answer:
WB = 16 in---------------------------
According to picture we observe:
W is midpoint of AT and B is the midpoint of TE.The segment connecting the midpoints is the midsegment.
As per property of the midsegment, it is parallel to opposite side and is half of its measure.
It tells us that WB is parallel to AE and:
WB = AE/2 WB = 32/2WB = 16 inFind echelon form of this augmented matrix written so 1's on the diagonal
1 -1 2 400
1 0 0 900
1 -3 7 -300
The echelon form of the given augmented matrix with 1's on the diagonal is:
1 -1 0 1000
0 1 0 1100
0 0 1 300
What is the echelon form of this matrixTo find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:
Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:
1 -1 2 400
0 1 -2 500
0 -2 5 -700
Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:
1 -1 2 400
0 1 -2 500
0 0 1 300
Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:
1 -1 0 1000
0 1 0 1100
0 0 1 300
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Use the formula d= vt + 16t2, where d is the distance in feet, v is the initial velocity in feet per second, and it is the time in seconds.
An object is released from the top of a building 480 ft high. The initial velocity is 16 ft/s. How many seconds later will the object hit the ground?
Answer:
5 seconds
Step-by-step explanation:
d = vt + 16t² , that is
vt + 16t² = d
substitute d = 480, v = 16 into the equation
16t + 16t² = 480 ( divide through by 16 )
t + t² = 30 ( subtract 30 from both sides )
t² + t - 30 = 0 ← in standard form
(t + 6)(t - 5) = 0 ← in factored form
equate each factor to zero and solve for t
t + 6 = 0 ⇒ t = - 6
t - 5 = 0 ⇒ t = 5
t > 0 , then t = 5
the object will hit the ground 5 seconds later
Answer:
5 seconds.-------------------------
As per given we have:
d = 480 ft,v = 16 ft/s.Substitute these into given equation and solve for t:
480 = 16t + 16t²30 = t + t²t² + t - 30 = 0t² + 6t - 5t - 30 = 0t(t + 6) - 5(t + 6) = 0(t + 6)(t - 5) = 0t + 6 = 0 or t - 5 = 0t = - 6 or t = 5The first value of t is discarded as time can't be negative, so the answer is 5 seconds.
Money A savings account increases from $200 to $206. What is the percent increase of the savings account?
Answer:
3% increase
Step-by-step explanation:
Solve for x
2,4, and 6 i need help with
Answer: x=56
Step-by-step explanation: Question 2 shows a right angle that is equal to 90 degrees. Since you are already given 34, you just need to subtract 90-34.
Question 4 shows an 180 degree angle and so you need to do the same thing; 180-124
The temperature in a certain location was recorded each day for two months. The mean temperature was 28.8°F with a standard deviation 7.4°F. What can you determine about these data by using Chebyshev's Inequality with =K3?
Answer:
Chebyshev's inequality states that for any given dataset, at least 1 - 1/k^2 of the data will lie within k standard deviations from the mean.
When k = 3, at least 1 - 1/3^2 = 1 - 1/9 = 8/9 of the data will lie within 3 standard deviations from the mean.
So, for the temperature data, we can determine that at least 8/9 of the data will lie between 28.8 - 3 × 7.4 = 7°F and 28.8 + 3 × 7.4 = 50.6°F.
In other words, we can say that at least 8/9 of the temperatures recorded during the two months were between 7°F and 50.6°F.
please help question below
Answer:
Step-by-step explanation:
22
You can work a total of no more than 32 hours each week at your two jobs. Tutoring pays $7 per hour and babysitting pays $8 per hour. You need to earn at least $256 each week to pay your bills.
Let X = the number of hours tutoring. Let Y = the number of hours babysitting
Answer: The correct system of linear inequalities that represents this situation is:
X + Y ≤ 32 (to represent the maximum number of hours you can work)
7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)
X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)
Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.
Step-by-step explanation:
The triangle below is equilateral. Find the length of side � x in simplest radical form with a rational denominator. x 6
The length of the side is 12 units in simplest radical form with a rational denominator.
What is an equilateral triangle?A triangle is said to be equilateral if all of its sides and angles are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees.
Given:
The triangle given in the image is an equilateral triangle.
That means the angle measure of the triangle is 60° each.
And all the sides are equal.
To find the value of x:
Sin(60/2)° = opposite/ hypotenuse.
Sin30° = x/6
x = 6/Sin30°
[tex]x = \frac{6}{1/2}[/tex]
x = 6(2)
x = 12
Therefore, the value of x is 12 units.
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The complete question:
The triangle below is equilateral. Find the length of the side in simplest radical form with a rational denominator.
The image is given below.