Here, use this to help you: https://www.map.mathshell.org/download.php?fileid=1676
provide the correct reason for the statement in line 4. (please help)
The property that completes the proof is the transitive property
How to determine the statement that represents the reason in the proof?From the question, we have the following parameters
The point C is the midpoint of AE
BC = CD
The above implies that
AC = CE
And it also means that:
The line segment BC and the line segment CD have equal lengths
According to the transitive property of equation, we have:
If A = B and B = C, then A = C
This can also be represented as
If A + B = C + D and C + D = E + F, then A + B = E + F
Using the above as a guide, we have (in step 3)
AB + BC = AC
CD + DE = CE
This implies that
AB + BC = CD + DE
Hence, the statement that represents the reason 4 in the proof is (b) transitive property
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a(1)= -13
a(n)= a(n-1)+4
Find the 2nd term in the sequence
The second term of the arithmetic sequence is:
a₂= -9
How to find the second term in the sequence?Here we have an arithmetic sequence, such the the recursive formula is:
aₙ = aₙ₋₁ + 4
So to get each term, we need to add 4 to the previous one.
We know that the first term is:
a₁ = -13
Then the second term will be:
a₂ = a₁ + 4 = -13 + 4 = -9
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15) A sample of 4 different calculators IS randomly selected from a group
containing 46 that are defective and 26 that have no defects. What is the
probability that all four of the
calculators selected are defective? Round to four
decimal places.
A) 0.1021
B) 0.1586
C) 0.1666
D) 10.9154
Answer:
C) 0.1666
Step-by-step explanation:
The probability of selecting a calculator that is defective can be defined as: [tex]\frac{46}{46+26}[/tex]
The 46 in the numerator is the number of calculators that are defective in the group. The 46 + 26 represents the total amount of calculators since 46 are defective and 26 are not defective and assuming a calculator can only be defective or not defective then these are the total number of calculators in the group.
This gives you a probability of approximately: [tex]\frac{46}{72}[/tex] or approximately 0.638889
We can multiply independent events to find the combined probability of these events occurring. So we have to assume you put the calculator back into group after selecting one.
If this is the case we simply multiply 46/72 * 46/72 * 46/72 * 46/72 or (46/72)^4 to get an approximate probability of: 0.1666
5. Geometry Audrey draws a triangle that has
these sides: s, s, and is. When the length of s
is doubled, the new perimeter is twice the old
perimeter less 14. What are lengths of
the triangle?
The length of each side is less than sum of the lengths of the other two sides and greater than the difference between these lengths.
2s is not less than 1/2s+ 2/3s
What is a triangle?A triangle is polygon with the three edges and three vertices. It is one of the basic shapes in the geometry. A triangle with the vertices A, B, and C is denoted Δ ABC.
In the Euclidean geometry, any three points, when the non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. two-dimensional Euclidean space). In the other words, there is the only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only Euclidean plane, there is only one plane and all triangles are contained in it; however, in the higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in the Euclidean geometry, and in the particular, the Euclidean plane, except where otherwise noted.
new triangle perimeter is = 2s + 1/2s + 2/3s
This new triangle, however, cannot be created physically because
The length of each side is less than sum of the lengths of the other two sides and greater than the difference between these lengths.
2s is not less than 1/2s+ 2/3s
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For f(x) = 3x²-x+5, 2f(-3) - f(2)
Answer:
55
Step-by-step explanation:
First solve for f(-3):
[tex]f(-3) = 3(-3)^2-(-3)+5[/tex]
[tex]f(-3)=3(9)+3+5[/tex]
[tex]f(-3)=27+3+5[/tex]
[tex]f(-3) = 35[/tex]
Second solve for f(2):
[tex]f(2) = 3(2)^2-(2)+5[/tex]
[tex]f(2) = 3(4)-(2)+5[/tex]
[tex]f(2) = 12-2+5[/tex]
[tex]f(2) = 15[/tex]
Now plug in f(-3) and f(2) to the expression:
[tex]2(f(-3))-(f(2)) =[/tex]
[tex]2(35)-(15)=[/tex]
[tex]70-15=55[/tex]
Stella signed up for a streaming music service that costs $9 per month. The service allows Stella to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song. How much total money would Stella have to pay in a month in which she downloaded 40 songs? How much would she have to pay if she downloaded ss songs?
The money would Stella have to pay in a month in which she downloaded 40 songs is $59.
The amount that she has to pay if she downloaded ss songs is 9 + 1.25s.
How to illustrate the information?From the information, Stella signed up for a streaming music service that costs $9 per month and the service allows Stella to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song.
The money would Stella have to pay in a month in which she downloaded 40 songs is:
= 9 + 1.25s
where s = number of songs
= 9 + 1.25s
= 9 + 1.25(40)
= 9 + 50
= $59.
The amount that she has to pay if she downloaded s songs is:
= 9 + 1.25(s)
= 9 + 1.25s
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2. A different pool had an area that is of the form
▢ × 102 + ▢ × 101 + 6
and that can be written in the form x3 ,
where x is a whole number.
A) Decide what your number could be.
B) What is the perfect square number that is closest to the number you chose? What would the side length of a square pool with that area be?
C) Estimate the side length of a square pool with the area you chose in part a).
The area of the pool given by the expression, ∆ × 102 + ∆ × 101 + 6, gives;
A) The whole number x = 33
B) The perfect square number closest to 33 is 36
The side length of a square pool with an area of 36 square units is 6 units
C) The side length of a square pool with the area chosen in part A is 33•√33
What is a mathematical expression?An expression is a mathematical statement which consists of 2 or more numbers and, or variables joined together by mathematical operators.
A) The given equations for the pool is presented as follows;
Area of the pool = ∆ × 102 + ∆ × 101 + 6
Area of the pool = x³
x = A whole number
Expressing the word problem mathematically gives;
∆ × 102 + ∆ × 101 + 6 = x³
203•∆ + 6 = x³
Which gives;
[tex] \displaystyle{ \triangle = \frac{ {x}^{3} - 6}{203} }[/tex]
Using a graphing calculator, when x = 33, we get;
[tex] \displaystyle{ \triangle = \frac{ {33}^{3} - 6}{203} = 177 }[/tex]
The value of the number is x = 33 and ∆ = 177
B) The perfect square that is closest to x = 33 is 36
The side length of a square pool with an area of 36 is √(36) = 6
C).The area of the pool chosen is 33³ = 35937
The side length of a square pool with an area of 35937 is √(35937) = 33•√(33)
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write 7843 to nearest thousand with explanations
The number of pairs of shoes owned by a sample of seven students are given below. Match the measure to its value.
3, 3, 5, 9, 12, 13, 15
1. range
2. variance
3. standard deviation
12
5
25
According to the solving the given data the values of :
Range = 12
Variance= 25
Standard deviation= 5
What does "variance in statistics" mean?Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value. Finding the predicted difference between the deviation from the actual value and the variation.
What do you mean by range?In statistics, range is the distinction between the most and least values in a set. Mathematics' interval, also known as range, is a collection of real numbers that contains all values that fall between any two other values.
According to the given data:Given data: 3, 3, 5, 9, 12, 13, 15
Range = Highest value - lowest value
= 15 - 3
= 12
Mean of the given data:
xi = 3, 3, 5, 9, 12, 13, 15
n = 7
S² = ∑(xi - x)²/(n - 1)
= (30.25 + 30.25 + .25+ 12.25 + 20.25 + 42.25 + 12.25)/6
= 147.75/6
= 24.6
= 25
Finding the standard deviation:
√S² = 25
S = 5
According to the solving the given data the values of :
Range = 12
Variance= 25
Standard deviation= 5
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Please Help me solve this
The value of f'(x) at x = 1 is 1 for first order derivative of x^x^3.
A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. It is also termed the differential coefficient of y with respect to x. Differentiation is the process of finding the derivative of a function.
Given that, x^x^3 and we have to find the first order derivative with respect to x and then find the value at x = 1.
Let's proceed to solve this question accordingly.
let f(x) = x^x^3
The first order derivative = f'(x) = d/dx(x^x^3)
First apply the generalized power rule, then we have
= x^x^3.d/dx(ln(x)x^3)
Applying the power rule, we get
= x^x^3 (d/dx(x^3).ln(x)+x^3.d/dx(ln(x)))
= x^x^3 (3x^2 ln(x) +x^3.1/x)
= x^x^3 (3x^2ln(x) +x^2)
On simplifying, we will get
= x^x^3+2(3ln(x)+1)
f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1)
Now, at x = 1, we get
f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1
Therefore, f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1 is the required answer.
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(11, 3) and (4, 3) on a coordinate plane?
The midpoint of the given points (11, 3) and (4, 3) on the coordinate plane is ( 15/2, 3 ).
How calculate the midpoint between two point?A midpoint is simply a point that divides a line segment into two equal halves.
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point 1( 11, 3 )
x₁ = 11y₁ = 3Point 2( 4, 3 )
x₂ = 4y₂ = 3Midpoint = ?
To find the midpoint, plug the given points into the midpoint formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ( 11 + 4 )/2, ( 3 + 3 )/2 )
M = ( ( 15 )/2, ( 6 )/2 )
Midpoint M = ( 15/2, 3 )
Therefore, the midpoint of the given coordinates is ( 15/2, 3 ).
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Write the fractions in order from least to greatest: 2/9, 1/6, 1/5, 3/10
Answer:
1/5,1/6,2/9,3/10
Step-by-step explanation:
hope it helps helps and have a nice day! :)
Members of the marching band line up in 6 rows of 8.
Answer: 6x8
Ur answers should be 48 and again we did repeated addition so
6+6+6+6+6+6+6+6 or we can do 12+12+12+12 or 24+24 which we should know use 48
Step-by-step explanation:
Nidia cut a rectangle into 2 pieces as shown below.
12 ft
20 ft
20 ft
12 ft
She put the pieces together to form a parallelogram. What is the area of the parallelogram?
The area of the parallelogram is 240 feet.
What is area of parallelogram?A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.
A quadrilateral's interior angles add up to 360 degrees.
The area of a parallelogram can thus be written as :
Area = Base × Height
In this diagram it is given that the Base = 20 feet and the height = 12 feet
Thus the area can be obtained by simply multiplying these two dimensions
So area = 20 × 12 = 240 feet .
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Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C. Are the events of selecting an order that is not accurate and selecting an order from Restaurant C disjoint events?
The probability is 0.334 and the events are not disjoint events
How to determine the probability?The table of values represents the given parameters
The probability to calculate is given as
The probability of getting an order that is not accurate or is from Restaurant C
This can be represented as
P(Not accurate or Restaurant C)
This is calculated as
P(Not accurate or Restaurant C) = [n(Not accurate) + n(Restaurant C) - (Not accurate and Restaurant C)]/Total
So, we have
P(Not accurate or Restaurant C) = (37 + 52 + 34 + 19 +237 + 34 - 34)/(330 + 276 + 237 + 150 + 37 + 52 + 34 + 19)
Evaluate the sum and the difference
P(Not accurate or Restaurant C) = 379/1135
Evaluate the quotient
P(Not accurate or Restaurant C) = 0.334
Lastly, the events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint events
This is so because it is possible to select an order from restaurant C that is not accurate
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Gina is driving 76 miles to her brother's house. If she stops for gas after driving 34 miles, how many miles does she have to go before she gets to her brother's house?
Answer:
42
Step-by-step explanation:
76-34
I need help with this problem
)
2) So, let's begin with the lower-left product of matrices:
[tex]\begin{gathered} \begin{pmatrix}-2 & 12 \\ -1 & -3\end{pmatrix}\times\begin{pmatrix}2 & 1 \\ 4 & 2\end{pmatrix}= \\ \begin{pmatrix}\left(-2\right)\cdot \:2+12\cdot \:4&\left(-2\right)\cdot \:1+12\cdot \:2\\ \left(-1\right)\cdot \:2+\left(-3\right)\cdot \:4&\left(-1\right)\cdot \:1+\left(-3\right)\cdot \:2\end{pmatrix} \\ \begin{pmatrix}44&22\\ -14&-7\end{pmatrix} \end{gathered}[/tex]Now for the next pair of matrices in the middle:
[tex]\begin{gathered} \begin{pmatrix}2 & 0 \\ 1 & 0\end{pmatrix}\times\begin{pmatrix}3 & -1 \\ 2 & 2\end{pmatrix}= \\ \begin{pmatrix}2\cdot \:3+0\cdot \:2&2\left(-1\right)+0\cdot \:2\\ 1\cdot \:3+0\cdot \:2&1\cdot \left(-1\right)+0\cdot \:2\end{pmatrix} \\ \begin{pmatrix}6&-2\\ 3&-1\end{pmatrix} \end{gathered}[/tex]Notice that each row is multiplied by each correspondent column.
And finally, the pair on the lower-right:
[tex]\begin{gathered} \begin{pmatrix}5&-2\\ \:\:\:4\:&-3\end{pmatrix}\times \begin{pmatrix}2&-1\\ \:\:3&1\end{pmatrix} \\ \begin{pmatrix}5\cdot \:2+\left(-2\right)\cdot \:3&5\left(-1\right)+\left(-2\right)\cdot \:1\\ 4\cdot \:2+\left(-3\right)\cdot \:3&4\left(-1\right)+\left(-3\right)\cdot \:1\end{pmatrix} \\ \begin{pmatrix}4&-7\\ -1&-7\end{pmatrix} \end{gathered}[/tex]) Thus, the se are theanswers .
Find the direction angle of v for the following vector.v=−6i−2jWhat is the direction angle of v?
Given:
v is the given vector.
[tex]v=-6i-2j[/tex]To find:
Find the direction angle of v.
Formula to find the direction:
[tex]\tan \theta=\frac{y}{x}[/tex]From the given vector x and y are:
[tex]x=-6\text{ \& y=-2}[/tex][tex]\begin{gathered} \tan \theta=\frac{-2}{-6} \\ \theta=\tan ^{-1}(\frac{1}{3}) \\ \theta=18.4\degree \end{gathered}[/tex]I’m struggling on question number 16, me and friend are getting VERY different answers and I would like to get a good grade in this class!
Solution:
Given a sphere of diameter, d, 2.5ft.
To find the volume, V, of the sphere, the formula to apply is
[tex]V=\frac{4}{3}\pi r^3[/tex]Where, the radius, r, is
[tex]\begin{gathered} r=\frac{d}{2}=\frac{2.5}{2}=1.25ft \\ r=1.25ft \end{gathered}[/tex]Substitute for r into the formula to find the volume of a sphere above
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\times\pi\times1.25^3 \\ V=8.18123\text{ ft}^3 \\ V=8.2\text{ ft}^3\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Hence, the volume, V, of the given sphere is 8.2 ft³ (the nearest tenth)
Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created? (10 points)
A situation in which positive and negative numbers are used to describe values that have opposite meaning is that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.
The thing that 0 represents is the addition in the sea level.
How to illustrate the information?Based on the information illustrated, the situation will be that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.
Therefore, the addition will be:
= 2000 + (-2000)
= 2000 - 2000
= 0
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how to find the measure of L
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
he deatails of the solution are as follows:
rom tjhe triangle, we can see that Traingle KLM is an isosceles triangle, such that Angle J = 52.3 degrees suchn that:
[tex]Angle\text{ J = Angle K = 52. 3}^0(\text{ base angles are equal\rparen}[/tex]Now, we have that:
[tex]\begin{gathered} Angle\text{ J +Angle K + Angle L = 180}^0 \\ 52.\text{ 3}^0+52.\text{ 3}^0+\text{ Angle L = 180}^0 \\ 104\text{. 6 }^0+\text{ Angle L = 180}^0 \\ Angl\text{e L = 180}^0-104\text{. 6}^0 \\ Angle\text{ L = 75.4}^0 \end{gathered}[/tex]ONCLSUSION:
The measure of Angle L =
[tex]75.\text{ 4}^0[/tex]Please help with the following question:
Using the combination formula, it is found that:
a) There are 210 distinct ways to choose the problems.
b) The probability is of 0.1667 = 16.67%.
c) The probability is of 0.3333 = 33.33%.
What is the combination formula?[tex]C_{n,x}[/tex] gives the number of different combinations of x objects from a set of n elements, according by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The order in which the problems are chosen is not important, which is the reason for the use of the combination formula in this problem.
4 problems are chosen from a set of 10, hence the number of ways to choose the problems is given by:
[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]
The number of ways to choose 4 problems that she can solve is:
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
Hence the probability is:
p = 35/210 = 0.1667 = 16.67%.
For item c, the desired outcomes are as follows:
0 problems is not possible, as she knows 7 out of 10 and 4 will be chosen.1 problem: 7 x C(3,3) = 7.2 problems: C(7,2) x C(3,2) = 21 x 3 = 63.Hence the probability is:
p = (7 + 63)/210 = 70/210 = 0.3333.
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please help me to do this problem.
3 is dividing on the right, then it will multiply on the left
B is multiplying on the right, then it will divide on the left
[tex]\frac{V\cdot3}{B}=h[/tex]Taylor wants to use a scale factor of 12 to make a smaller drawing of the door image shown. Part of her work is shown. Finish her work to find the height and width of her scale drawing
the height and width of her scale drawing is respectively:
height = 1*1/2inch
width = 3/4 inch
what is dimension?Dimension are the measure of the size or distance of an object or region or space in one direction.
so, all we needs to do is multiply is dimension of the original door image by the scale factor , to get the height and width of the scale drawing.
height: 3 inch x 1/2 =3x1/2=3/2=1x1/2 inch
width: 1x 1/2 inch x 1/2 =3/2 x 1/2= 3x1/2x2=3/4 inch
hence , the height and width of the scale drawing is respectively= 1x 1/2 inch ,3/4 inch
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An actor bought a pearl, diamond, and ruby necklace for his famous wife for $54,000. In 2011 this necklace was auctioned for $11,379,600. The auction price was what percent of the original purchase price?
This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.
Given that,
For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.
We have to find what percentage of the initial purchase price was represented by the auction price.
Let us take the percentage as x%.
Necklace sold at auction=the percentage multiplied by the actual price
We get,
$11,379,600 =x%($54,000)
x%=$11,379,600/$54,000
x%=2.1%
Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.
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If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has which of the following?
A. No solution
B. Infinitely many solutions
C. One solution
D. Two solutions
Answer:
C. One solution
Step-by-step explanation:
You want to know the number of solutions of a system of equation such that the graph of the linear function touches the graph of the quadratic function at its minimum.
SolutionsThe number of real solutions of the system of equations is equal to the number of points of intersection of their graphs. The problem statement tells you the graphs intersect at one point, so there is one solution.
__
Additional comment
The linear function can only touch the minimum of a quadratic if its graph is a horizontal line.
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3) Travis International has a one-time expense of $1.13 million that must be paid two years from today. The firm can earn 4.3 percent annually, compounded monthly, on its savings. How much must the firm save each month to fund this expense if the firm starts investing equal amounts each month starting at the end of this month?
A) $38,416.20
B) $45,172.02
C) $51,300.05
D) $47,411.08
E) $53,901.15
What is the percent change if you paid $1.87 per gallon on February 6th and $1.80 per gallon on February 17th?
The percent change formula is:
[tex]\frac{\text{new price - previous price}}{\text{previous price}}\cdot100[/tex]In this case, the percent change is:
[tex]\frac{1.8-1.87}{1.87}\cdot100=-3.74\text{ \%}[/tex]b(x)=18-0.5x 6 and 18
The solution of B(x) = 18 - 0.5x with x being -2, 0, 5 is 19, 18 and 15.5.
How to evaluate functions?Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function. Simply swap out all instances of x with the value of x to do this. For example, if we are requested to evaluate f(4), then the value 4 has been given to x.Given:
B(x) = 18-0.5x
x = -2, 0, 5
Putting the values of x to find the result of the function.
B(-2) = 18 - 0.5 × (-2) = 18 + 1 = 19
The required solution of the function at x = -2 is f(-2) = 19.
B(0) = 18 - 0.5 × (0) = 18
The required solution of the function at x = 0 is f(0) = 18.
B(5) = 18 - 0.5 × (5) = 18 - 2.5 = 15.5
Thus, the required solution of the function at x = 5 is f(5) = 15.5.
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The complete question is :"How do you solve B(x) = 18-0.5x with x being -2, 0, 5."
List the angles of the triangle in order from largest to smallest.Question options:A) ∠A, ∠C, ∠BB) ∠C, ∠B, ∠AC) ∠B, ∠C, ∠AD) ∠A, ∠B, ∠C
Angles opposite to shorter sides are shorter. Then, the shortest angle is opposed to the shortest side.
Since the shortest side has a length 2.8 and is opposed to the angle A, then the shortes angle is A.
The next shortest side is that opposite to B, which has a length of 3.4.
And finally, the largest side has a length of 4.7 and it's opposite to the angle C.
Therefore, the list of angles from largest to smallest, is:
[tex]\angle C,\angle B,\angle A[/tex]