a. The set in set builder form A = {x : x ∈ N}
b. the set in descriptive form, A = {set of natural numbers}
What is a set?A set is a collection of well defined items.
What is set builder form?Set builder form is a way of enumerating a set by using a set of rules which define its elements.
What is descriptive form?Descriptive form is a way of enumerating the elements of a set in words.
a. How to write the elements of the set in set builder form?Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N, we identify each element of the set as x and give it a rule that x is an element of N. That is x ∈ N.
So, in set builder form A = {x : x ∈ N}
b. How to write the elements of the set in descriptive form?Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N.
In descriptive form, we write that A = {set of natural numbers}
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please help will mark u brainliest
The expressions that are not polynomials are the second and third ones:
3 + 1/nq^(1/2) + 5Which expressions are polynomials?A polynomial is a lineal combination of terms of powers of variables, such that the exponents must be positive integers or zero.
So, for example, a polynomial of degree n is:
p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x + a₀
Where we also can have more than one variable.
Then, for example the first one:
-4p + 7
Is a polynomial of degree 1.
The options that are not polynomials are:
p(n) = 3 + 1/n
p(q) = q^(1/2) + 5
Which are the second and third options.
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Answer:
Those are the answers
Step-by-step explanation:
3 + 1/n
q^(1/2) + 5
Naomi is cutting patches in the shape of right triangles to make a quilt. Each triangle has a diagonal side of 14.5 inches and a short side of 5.5 inches. What is the length of the third side of each triangular patch?
Find the value of x so that l//m. State the converse used
For the parallel lines (l//m), the value of x is equal to 25 and the converse used is the alternate exterior angle theorem.
What are parallel lines?Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude.
By applying the alternate exterior angle theorem to parallel lines (l//m), we have:
4x - 13 = 2x + 37
4x - 2x = 37 + 13
2x = 50
x = 50/2
x = 25
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please show the work
Step-by-step explanation:
15t + 30 = 20t | -15t
30 = 5t
t = 30/5 = 6
20 + 5t = -6t + 86 | + 6t
20 + 11t = 86 | -20
11t = 66
t = 6
18t + 20 = 24t + 50 | -18t
20 = 6t + 50 | -50
-30 = 6t
t = -30/6 = -5
18t - 2 = 10t + 54 | -10t
8t - 2 = 54 | +2
8t = 56
t = 56/8 = 7
7t - 5 = 15t + 91 | -7t
-5 = 8t + 91 | -91
-96 = 8t
t = -96/8 = -12
What is the slope of a line perpendicular to the line whose equation is 6x + y = 8.
Fully simplify your answer.
Answer:
1/6
Step-by-step explanation:
y = -6x + 8
Perpendicular line would be the reciprocal of the slope
Mrs. Robinson made the table below showing the number of cells in a biology experiment after a number of days. Which type of function best models Mrs. Robinson’s data?
Days / Number of Cells
2 / 4
3 / 8
4 / 16
5 / 32
6 / 64
7 / 128
a) an exponential function
b) a quadratic function
c) an absolute value function
d) a linear function
The type of function best models Mrs. Robinson’s data is A. exponential function.
What is an exponential function?The formula f(x) = a^x defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x. Where an is greater than zero and less than one. x can be any actual number.
Mrs. Robinson created the table, which shows the number of cells in a biology experiment after a certain number of days. The independent variable, or x-value, in an exponential function is the exponent, while the base is a constant.
In this case, we can see that:
2 days = 2² = 4
3 days = 2³ = 8
4 days = 2⁴ = 16
This is an exponential function.
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What is the solution set for 5 - 5 = 15, given the replacement set {0, 1, 2, 3, 4}? O x = 4 O x = 3 O x = 2 O x = 1 x = 0
The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is [tex]\mu = p[/tex].The standard deviation is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The shape is approximately normal.As long as these two conditions are respected:
[tex]n \leq 0.05N[/tex][tex]np(1 - p) > 10[/tex]The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
[tex]\mu = p = 0.388[/tex]
The standard error of the distribution is of:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184[/tex]
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Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?To determine the vertex of a graph, we look for the location of the maximum or the minimum point of the graph
Because the graph is a cubic function, the graph has no maximum or minimum (by definition)
This means that there is absence of a vertex in the graph
The transformation from the parent functionIn (a), we have
We can see that the graph is a cubic function
This function is represented as
y = ∛x
In this graph, we can see that the graph is 4 units to the left i.e. y = ∛(x - 4)
And 2 units below the origin i.e. y = ∛(x - 4) + 2
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Simplify.
ab2−−−√+39ab2−−−−√−34ab2−−−−√
Assume all variables are nonnegative.
Answer:In this item, I take it that we are to get the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.
-64 = (-4)(-4)(-4)
Then,
x6 = x2 (x2) (x2)
and,
y9 = (y3)(y3)(y3)
If we take the cube root, we consider only one item per product. Thus, the answer is,
-4x²y³
Step-by-step explanation:
Un negocio de celulares tiene 360 celulares, 40% Samsung, 5% iPhone, 10%motorola y el resto Huawei, ¿Qué cantidad de celulares hay de cada marca?
The number of cell phone brands will be:
Samsung = 144
iPhone = 18
Motorola = 36
Huawei = 162
How to calculate the value?From the information, the business has 360 cell phones.
Samsung will be:
= Percentage × Total phone
= 40% × 360
= 0.4 × 360
= 144
iPhone = 5% × 360
= 0.05 × 360
= 18
Motorola = 10% × 360
= 0.1 × 360
= 36
Huawei = 45% × 360
= 0.45 × 360
= 162
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Sheri has $15,200 to invest in mutual funds and in bonds. sheri has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. if she wants to earn $548 at the end of the first year, how much does she need to invest into each type of account?
Sheri should invest $2000 in mutual fund and $13,200 in bond.
Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -
1%×x + 4%×(15,200 - x) = 548
x/100 + 60,800/100 - 4x/100 = 548
60,800 - 3x = 54800
3x = 60800 - 54800
3x = 6000
x = 6000 ÷ 3
x = 2000
Amount to be invested in mutual fund = $2000
Amount to be invested in bond = 15,200 - 2000
Amount to be invested in bond = $13,200
Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.
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Above are two different models of the same triangle. If the area of the model on the left is 24 sq cm, what is the area of the model on the right?
A.
120 sq cm
B.
26.5 sq cm
C.
48 sq cm
D.
96 sq cm
The area of the model on the right is given by 96 sq cm
The correct answer option is option D.
What is a Model?A model represents a real object on a drawing paper.
Given that the model is triangular in shape, the model on the right is 2 times the model on the left.
Area of model on the left = 24 square cmTherefore, area of model on the left = area of model on the left × 2².
Area of model on the left = 24 × 4
Area of model on the left = 96 square cm.
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What is 7) 952 divided?
thanks to anyone who answers!
The sum of three consecutive numbers is 84. What is the largest of these numbers?
a 26
b 27
c 28
d 29
Write the equation of the line in slope - intercept form
The equation of line in slope-intercept form is y = 2x + 1
Q. What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
We know the equation of line is
y = mx + b
where,
m = slope
b = y - intercept
To form an equation we need to find 'b' and 'm'.
so, first find 'b' i.e, y - intercept
For that, you just need to see the red line cuts the y-axis at its sharp grid means not in middle of the grid.
So, by observing the graph we see y = 1 where the red line cuts the y-axis
so we get, b = 1 means y-intercept
Now, we need to find slope (m).
For that, we know slope = rise / run
So take any point on graph which is easily to recognize the (x,y) points on graph.
Here I take the point (2, 5).
Now mark that point and find rise and run values.
rise = 4 (count from y = 1 to y = 5 )
run = 2 (count from x = 0 to x = 2)
Now, put the values and get the slope.
slope (m) = 4 / 2
= 2
Now, put the y-intercept and slope values in equation of line .
y = mx + b
y = 2x + 1
Hence, the equation of line in slope-intercept form is y = 2x + 1
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A swimming pool is draining at a constant rate.
The table shows the proportional relationship between
the change in the water level and the number of hours
the pool has drained. Complete the table to show the change
in water level at 9 and 23 hours?
The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;
10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.
b. After 9 hours, the change in the water ls 15.75 inches
c. The change in the water level after 23 hours is 40.25 inches
What is a constant rate?A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?
The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;
Hours Draining [tex]{}[/tex] Change in Water Level (inches)
2 [tex]{}[/tex] -35
9 [tex]{}[/tex] ?
17 [tex]{}[/tex] -29.75
23 [tex]{}[/tex] ?
The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.
Let H represent the hours draining and let C represent the change in water level, we have;
C ∝ H
C = k·H
[tex]k = \dfrac{C}{H}[/tex]
Where;
k = The constant of proportionality, which is the rate at which the water level is changing per hour
a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;
The first pair of points = (2, -3.5)
[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]
The rate at which the water level is changing per hour is -1.75 inches per hour
The water level is decreasing at 1.75 inches per hour
b. The change in water level after 9 hours is found by using the formula;
C = k × H
Where, H = 9, we have;
Change in water level, C = -1.75 × 9 = -15.75
The change in water level after 9 hours is 15.75 inches
c. The change in water level after 23 hours is found by plugging in H = 23 as follows;
C = -1.75 × 23 = -40.25
The change in water level after 23 hours is -40.25 inches
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81% of the tickets sold at an amusement park were discount tickets. If the park sold 800 tickets in all, how many discount tickets did it sell?
Answer:
40% = 0.40800 / 0.40 = 2000 total tickets were sold
Step-by-step explanation:
Answer:
648
Step-by-step explanation:
ans: 81/100 x800
=648
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The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2
The curve opens downward.
from, the graph, the roots of the equation are -4 and 0
so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = [tex]x^{2}[/tex] + 4x
the x coordinate of the vertex = -b/2a = axis of symmetry
where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
substitute x = -2 into y = [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex
y = [tex](-2)^{2}[/tex] + 4(-2)
y = 4 -8
y = -4
vertex = (-2, -4)
The axis of symmetry is -b/2a which is -2
The curve opens downward as the vertex is at -4
In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward
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The graph below illustrates the decay of a radioactive substance over t days.
Use the graph to estimate the average decay rate from t = 5 to t = 15 Note: Your answer will be negative.
The estimate of the average decay rate of change is -0.6
How to estimate the average decay rate of the function?From the question, we have the graph and the interval is given as
t = 5 to 15
This can also be represented and expressed as
(a, b) = [5, 15]
From the attached graph, we have
f(5) = 12
f(15) = 6
The estimate of the average decay rate of change is calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(15) - f(5)]/[15 - 5]
So, we have
Rate = [6 - 12]/[15 - 5]
Evaluate
Rate = -0.6
Hence, the average decay rate of change is -0.6
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Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two
different proportional relationships represented in different ways.
Will give points to first correct answer that follows all the steps right.
Answer:
I Need Help On That Too
Step-by-step explanation:
PLEASE I REALLY NEED HELP I DON'T UNDERSTAND PLEASE THANK YOU GUYS FOR THE HELP!! I APPRECIATE IT!!!
The value of KM in triangle ΔKLM is 110.
What is similarity?Similarity of a triangle is the ratio of their corresponding sides or angles which are equal .
In the given triangle ΔHIJ,
HI=13, HJ=25,
And in triangle ΔKLM,
KL=57, KM=?
triangle ΔHIJ is similar to ΔKLM,
By the property of similarity, HI/HJ=KL/KM
Substitute the values here,
13/25=57/KM
KM=25×57/13
KM=109.6
The value of KM=110.
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You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
Responses
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
The correct option regarding the correlation coefficient is that A. I can’t be confident at all; this is about as close to a random guess as you can get.
What is a correlation coefficient?The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values can range between -1 and 1. A correlation coefficient of -1 denotes a perfect negative, or inverse, correlation, in which values in one series rise while those in the other fall, and vice versa.
A coefficient of one indicates that there is a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 indicates that no linear relationship exists. In science and finance, correlation coefficients are used to assess the degree of association between two variables, factors, or data sets.
In this case, the fat that the person gets 0 implies that it's probably a random guess. In conclusion, the correct option is A.
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Segment RS is reflected over the line y = and then translated by (x +3, y + 4). The resulting segment
R" S" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
R=
S =
Answer:
-1,-2
Step-by-step explanation:
get the x and y value and combine the coordinates using the slope formula
What is the degree of the following
polynomial:
3x^5 + 4x^3 + 8x^2 - 14x +9
Answer:
Step-by-step explanation:
Here is an example:
Use this step by step explanation in your equation to help you find the answer.
For polynomial 2x2 - 3x5 + 5x6.
We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x2 = 2
(ii) the exponent of the second term 3x5 = 5
(iii) the exponent of the third term 5x6 = 6
Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.
Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.
A cockroach can travel at a speed of 80 centimeters per second. A centipede can travel at 30 meters per
minute. Which can travel faster?
Answer:
The cockroach is faster
Step-by-step explanation:
Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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Find the area of the Polyogon below.
A =
12
14.49
Answer: 695.52
Step-by-step explanation:
The area of each triangle is [tex]\frac{1}{2}(12)(14.49)[/tex].
There are 8 triangles in the figure, so the area is [tex]8(1/2)(12)(14.49)=695.52[/tex].
a survey has an error in departure (ed) of 0.35 ft, and error in latitude (el) of 0.82 ft. the total distance covered i the survey is 684.5 ft. compute the precision (choose the answer that is closest)
The correct value for the precision is found to be 0.0013 for the survey.
What is called the precision in surveying?Our measurement processes take into account accuracy and precision. How precisely a measurement or observation compares to a predetermined value or benchmark defines its accuracy. Contrarily, precision is the degree to which a measurement is repeatable precisely without reference to any specific significance or standard.The formula for finding the precision is-
Precision = E(closure)/ Perimeter
E(closure) = √(ed)² + (el)²
Where,
error in latitude (el) = 0.82 ft
error in departure (ed) = 0.35 ft.
Perimeter = 684.5 ft.
Find the E(closure)
E(closure) = √(0.82)² + (0.35)²
E(closure) = 0.89
Precision = 0.89/684.5
Precision = 0.0013
Thus, the correct value for the precision is found to be 0.0013 for the survey.
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250 bicycles must be manufactured to minimize the cost.
The cost C in dollar of manufacturing x bicycles at a production plant is given by:
C(x) = 3x² - 1500x + 198,500
a. To find number of bicycle that can minimize the cost
differentiate C(x) with respect to x
C'(x) = 6x - 1500
equating C'(x) = 0
6x - 1500 = 0
x = 1500/6
x = 250 , is our stationary point
Differentiate C'(x) = 6x - 1500 again and put x = 250,
C''(x) = 6 (positive)
At x = 250 , cost is minimum
Therefore , 250 bicycles must be manufactured to minimize the cost.
b. C(x) = 3x² - 1500x + 198,500
putting x = 250,
C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500
= $11,000 is the minimum cost
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