Answer:
[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]
Step-by-step explanation:
The nth term of an arithmetic sequence is obtained using the formula:
[tex]a_n=a+(n-1)d[/tex]
Given that: [tex]a_5=23$ and a_{20}=98.[/tex]
a_n=a+(n-1)d
[tex]a_5=23=a+(5-1)d \implies a+4d=23\\a_{20}=98=a+(20-1)d \implies a+19d=98\\$We solve simultaneously$:\\a+19d=98\\a+4d=23\\15d=75\\d=5\\Recall:a+4d=23\\a+4(15)=23\\a=23-60\\a=-37[/tex]
Therefore, the first 60 terms of the sequence are:
[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]
First 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.
Arithmetic sequence: If two consecutive terms of a sequence has a common
difference 'd', sequence will be an arithmetic sequence and the
explicit formula for the nth term of the sequence will be,
[tex]A_n=a+(n-1)d[/tex]
Here, [tex]a=[/tex] First term
[tex]n=[/tex] nth term
[tex]d=[/tex] common difference
Given in the question,
Two terms [tex]a_5=23, a_{20}=98[/tex]
If 5th term of the sequence is 23,
[tex]23=a+(5-1)d[/tex]
[tex]23=a+4d[/tex] -------(1)
If 20th term of the sequence is 98,
[tex]98=a+(20-1)d[/tex]
[tex]98=a+19d[/tex] ----------(2)
Subtract equation (1) from equation (2),
98 - 23 = a + 19d - (a + 4d)
75 = 15d
d = 5
Substitute the value of 'd' in equation (1),
23 = a + 4(5)
a = 23 - 20
a = 3
Therefore, first 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.
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Suppose you roll a number cube. What is the theoretical probability of rolling a 5?
Answer:
1/6
Step-by-step explanation:
There are 6 possible outcomes when you roll a die
1,2,3,4,5,6
P(5) = number of outcomes with a 5/ total outcomes
=1/6
2) The volume of water in swimming pools in a local neighborhood are normally distributed. What is the percentage of
volumes that are within 3 standard deviation of the mean?
Answer:
The percentage of volumes that are within 3 standard deviation of the mean is 99.73%.
Step-by-step explanation:
We want to calculate the area under the curve within 3 standard deviations from the mean.
If we use the standard normal distribution, this probability can be calculated as the diference between P(z<3) and P(z<-3).
[tex]P(-3<X<3)=P(z<3)-P(z<-3)\\\\P(-3<X<3)=0.9987-0.0013=0.9973[/tex]
The area under the curve for the standard distribution and for any normal distribution within 3 standard deviation from the mean is 0.9973.
The percentage of volumes that are within 3 standard deviation of the mean is 99.73%.
Three congruent isosceles triangles $DAO$, $AOB$ and $OBC$ have $AD=AO=OB=BC=10$ and $AB=DO=OC=12$. These triangles are arranged to form trapezoid $ABCD$, as shown. Point $P$ is on side $AB$ so that $OP$ is perpendicular to $AB$.
Point $X$ is the midpoint of $AD$ and point $Y$ is the midpoint of $BC$. When $X$ and $Y$ are joined, the trapezoid is divided into two smaller trapezoids. The ratio of the area of trapezoid $ABYX$ to the area of trapezoid $XYCD$ in simplified form is $p:q$. Find $p+q$.
Answer:
p+q = 12
Step-by-step explanation:
Let's draw the diagram obtained from the given information. Find attached the diagram.
When X and Y divides the line AD and line BY into half respectively, the diagram splits into two trapezoid.
See attachment for diagram.
Ratio of area ABYX to XYCD = p:q
p+q = ?
Area of trapezoid = ½(base 1 + base 2)height
For trapezoid ABYX:
Base 1 = AB = 12, Base 2 = XY
Using Pythagoras theorem to find height of ∆AOB
AO² = AP² + PO²
PO² = (10²-6²) = (100-36)
PO = √64 = 8
height of trapezoid ABYX =h = ½ PO
= 8÷2 = 4
base of triangles in trapezoid ABYX:
base² = 5² -4² = (25-16)
base = √9 = 3
XY = 12+3+3 = 18
Area of trapezoid ABYX = ½(AB + XY)height
= ½(12+18)×4
= ½(120) = 60
Area of trapezoid XYDC = ½(XY + DC)height
Height of both trapezoid = ½ PO = 4
base of triangles in trapezoid XYCD = 3
DC = 3+18+3 = 24
= ½(18+24)×4
= ½(168) = 84
Ratio of both areas
p:q = 60: 84
p:q = 5:7
p+q = 5+7
p+q = 12
(Will mark brainliest if corret.)
Margaret is saving money for her summer vacation. She calculates that her starting amount is 0.4% of the total amount she wants to save. What is 0.4% written as a decimal?
Answer:
0.4% = 0.40 or 0.4
What is the degree of the polynomial given below?
F(x) - 2x3 - x2 +5x - 3
Answer:
3
Step-by-step explanation:
3 is the degree of polynomial [tex]f(x) = -2x^3-x^2+5x-3[/tex]
=> Degree of the polynomial is the highest power/exponent contained by the variable in the expression.
Answer:
The degree of the polynomial would be 3, since 3 is the largest exponent
Step-by-step explanation:
expression
equation
formula
identity
inequality
term
factor
multiple
Choose only two words from the box above to make this statement correct.
8y is a _____in the_____7x + 8y
Answer:
Term
Expression
Step-by-step explanation:
8y is a term in the expression
7x + 8y
There are two terms in the expression 7x + 8y
First is 7x
Second is 8y
7 and 8 are coefficient of x and y respectively
7x+8y is an expression because there is no equality sign(=), it doesn't equate to any value.
Unlike an equation that has the Equal to sign(=)
There are three basic types of expression:
1. Arithmetic expression
2. Character expression
3. Logical or relational expression
Rewrite the function by completing the square
Answer:
[tex](x+10)^2-186[/tex]
Step-by-step explanation:
One line passes through the points (−3,−1) and (1,−9). Another line passes through points (1,4) and (5,6). Are the lines parallel, perpendicular, or neither?
Answer:
the lines are perpendicular
Step-by-step explanation:
the first step to this question will be to find the slope intercept form of each of these lines. to do this we will first:
find the slope-
(-3,-1) and (1,-9)
y2-y1 / x2- x1
-9 - (-1) / 1 - (-3) (negative - negative = positive)
-8 / 4
therefore the slope is:
-2
we know that slope intercept form is y=mx+b
so.. y= -2x +______
I left the last part blank, because we only have the first half of the equation, now we will substitute the value of x and y into the equation from one of the coordinate points given above.
(-9) = -2(1) + _____
now we can simplify:
-9 = -2
this equation (-9 = -2) is not true, therefore we need to determine what we have to do to -2 to make it equal to -9.
-9 = -2 - 7 is true
therefore the answer is :
y= -2x-7
therefore the slope intercept form is y= -2x - 7
now that you know how to find the slope intercept form, you can find the other slope intercept form, and i'll provide the answer:
the slope intercept form you should find is
y= [tex]\frac{1}{2}[/tex]x + [tex]\frac{7}{2}[/tex]
now when we plot both of these lines we can see that:
the lines are perpendicular, meaning the lines pass through each other.
Answer:
the two lines are perpendicular to one another
Step-by-step explanation:
Find the slopes of the two lines and then compare them.
If the slopes are the same, the lines are parallel.
If the slopes are negative reciprocals, the lines are perpendicular.
If neither of these conditions hold, then the lines are neither parallel nor perpendicular.
(−3,−1) and (1,−9): As we go from the first point to the second, x (the "run") increases by 4 and y (the "rise") decreases by 8. Thus, the slope of the line through (−3,−1) and (1,−9) is m = rise / run = -8/4, or m = -2.
(1,4) and (5,6): As we go from the first to the second, x increeases by 4 and y increases by 2. Thus, the slope of the line through (1,4) and (5,6) is
m = rise / run = 2/4 = 1/2.
Because 1/2 is the negative reciprocal of -2, we know that the two lines are perpendicular to one another.
A trader claims that the proportion of stocks that offer dividends is different from 0.14. If the trader wants to conduct a hypothesis test, should they use a left-, right-, or two-tailed hypothesis test to analyze whether the proportion of stocks that offer dividends is different from 0.14? Select the correct answer below: Left-tailed test Right-tailed test Two-tailed test
Answer:
The correct option is;
Two-tailed test
Step-by-step explanation:
From the interpretation of the question statement, the trader wants to conduct a hypothesis test on the trader's claim that the proportion of stocks that offer dividends is different from 0.14
Given that the difference is hypothesized, then the null hypothesis, H₀ and the alternative hypothesis, H₁ should be written as follows;
H₀: Null hypothesis (no difference, or no change)
H₁: μ ≠ μ₀ which is hypothesizing difference which is known as a two-tailed test
The confidence level is then selected and the test statistic is calculated
Can anyone help me do this
Answer:
260% of 420=1092
166 2/3%of 60= 100
PLEASE HURRY Quadilateral abcd is inscribed in circle z such that AB is parallel to DC and m
Answer:
41°
Step-by-step explanation:
Looking at the attached diagram
A central angle of a circle is always congruent to its intercepted arc.
Therefore, m arc BC = m∠BZC
Again, m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its intercepted arc.
This gives us the following results:
= m∠BZC = 82°
= m arc BC = m∠BZC
= m arc BC = 82°
= m∠BAC = 1/2 × 82°
= m∠BAC = 41°
Note that:
∠DCA ≅ ∠BAC because alternate interior angles are congruent.
So m∠DCA = m∠BAC.
Hence, m∠DCA = 41°.
Which graph represents the solution set for the system x + y> 5 and -3x + 2y< -2.
Choose the equation that represents a line that passes through points (-1, 2) and (3, 1).
0 4x - y = -6
O x + 4y = 7
Ox - 4y = -9
O 4x + y = 2
Answer:
The answer is x + 4y = 7
Equation of a line is y = mx + c
Where m is the slope
c is the y intercept
Slope of the line between the points
(-1, 2) and (3, 1) is
Slope = 1-2/ 3+1 = - 1/4
Equation of the line using point
(-1, 2) is
y - 2 = -1/4(x + 1)
4y - 8 = - x - 1
x + 4y = 7
Hope this helps you
Which simplified fraction is equivalent of 5.6 3/15 14/25 5/6 14/250
Answer:
4/25
Step-by-step explanation:
Find the missing length to the attached triangle.
Answer:
x = 135
Step-by-step explanation:
Use the right triangle altitude theorem and similar triangles.
x/81 = 225/x
x^2 = 81 * 225
x = 9 * 15
x = 135
Answer:
135
Step-by-step explanation:
Which points lie on more than one plane?
O A ands
X and Y
O Mands
M and R
Answer:
x and y
Step-by-step explanation:
x and y are on the intersection of the 2 planes, meaning they lie on more than 1 (two) planes.
If we're being technical, it's all of them, because an infinite amount of planes go through 2 points.
Figure JUMP is a parallelogram. Which of these is congruent to UM?
A. JP
B. UJ
C. MP
D. UP
The sum of all the interior angles in a triangle is blank degrees.
Answer:
180 degress
Step-by-step explanation:
triangles always add up to 180
What is the formula for finding the area of a regular polygon with perimeter P and apothem length a? A. A = 1/2(Pa) B. a = PA C. A = Pa D. a = 1/2(PA)
Answer:
The answer is A.) A=1/2(Pa)
Step-by-step explanation:
The area of a regular polygon with perimeter 'P' and apothem length 'a' is [tex]\frac{1}{2}Pa[/tex] .
What is a regular polygon?A polygon is a two-dimensional geometrical figure that has 'n' number of equal sides.
Given, the perimeter of the regular polygon is 'P'.
Apothem length of the polygon is 'a'.
Therefore, the area of a regular polygon is
[tex]= \frac{1}{2}Pa[/tex]
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Can you find the missing segment to the triangle in the image
What point is a solution to the inequality shown in this graph
Answer: A
Step-by-step explanation:
The solution to the graph of inequality given above is the shaded portion or the shaded part of the graph.
Since the point ( -3, -3) and ( 3, -1 ) are on the point line, and the line is a broken line, the inequality means greater than. That means that solution must be greater than those point. They are therefore not part of the solution.
Point ( 5, -5), where x = 5 and y = -5, according to the graph, the shaded portion does not cover y at -5.
Option C is therefore the correct answer which is within the shaded portion. (1, 5)
Question 3(Multiple Choice Worth 1 points)
(06.02 LC)
A scatter plot is shown below:
Graph shows numbers from 0 to 10 at increments of 1 on the x axis and number s from 0 to 10 at increments of 1 on the y axis. Scatter plot shows ordered pairs 1, 9.1 and 2, 8 and 3, 7.6 and 4, 6.1 and 5, 5 and 6, 4 and 7,4 and 8, 3 and 9, 2.5 and 10, 1.
Which two ordered pairs can be joined to draw most accurately the line of best fit for this scatter plot?
(4.5, 10) and (10, 6.5)
(0, 9.8) and (10, 1.2)
(0, 4) and (5, 0)
(0, 6) and (7, 0)
Answer:
(0,9.8) and (10,1.2)
Step-by-step explanation:
it makes the best line
The two ordered pairs can be joined to draw most accurately the line of best fit for this scatter plot are (0, 9.8) and (10, 1.2).
Option B is the correct answer.
What is a scatterplot?A scatterplot is a type of graphical display that is used to represent the relationship between two continuous variables.
In a scatterplot, each point represents the values of the two variables, with one variable being plotted along the x-axis and the other variable being plotted along the y-axis.
The position of each point on the graph represents the values of both variables for that particular observation.
We have,
To determine which two ordered pairs can be joined to draw the most accurate line of best fit for the scatter plot, we need to look for pairs of points that are representative of the overall trend in the data.
We can plot the given points and visually inspect the scatter plot to find the line of best fit.
10| o
| o
9 | o
| o
8 | o
| o
7 | o
| o
6 | o
|o
5 |o
| o
4 | o o
| o
3 | o
| o
2 | o
| o
1 | o
|____________________________
0 1 2 3 4 5 6 7 8 9 10
From the scatter plot, we can see that there is a general downward trend from left to right and that the points are somewhat scattered around this trend.
One possible way to draw the line of best fit is to connect the points (0, 9.8) and (10, 1.2).
This line represents the overall trend in the data and passes close to many of the given points.
Therefore,
The two ordered pairs can be joined to draw most accurately the line of best fit for this scatter plot are (0, 9.8) and (10, 1.2).
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NO is parallel to ML. How long is OL?
2/3ft
6ft
8ft
12ft
Answer:
Step-by-step explanation:
Basic Proportionality Theorem: Basic Proportionality Theorem states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".
Hence, KN/MN=KO/OL.......by bpt
i.e.= 3/9=2/OL
18/3=OL
6feet =OL
answer is b)6feet
pls mark brainliest if it helps
PLEASE HELP! DUE BY MIDNIGHT!
Answer:
it's over already? or what?
Gasoline prices are rising at a rate of 0.5% per month. What is their doubling time? By what factor will prices increase in one year? In six years?
Answer:
double: 1%
year6%
6 year: 36%
Step-by-step explanation:
5.2 is 23.7 % Of what number? (Round to the nearest hundredth.)
Answer:
21.94
Step-by-step explanation:
Convert the percentage to a decimal.
23.7% = 0.237
Divide the number the decimal.
5.2/0.237 = 21.94
The answer is 21.94.
can anyone help me on both please dont put stupid awsers to get the points
Answer: Ok for the second one because I don't really get the wording in the first one (thats cuz i SUCK at vocabulary) the answer is 756,100 and a number greater is any number from 756,073-756,149
Step-by-step explanation:
ok so 756072 rounds to 756100 because 72 is closer to 100 than it is to 0
from 50 on, you would round up so to round up to 756100 the smallest possible number is 756050 since the 50 will round up
the highest number is 756149 because from 50 onwards it will round to 756200 instead.
so you can choose any number from 756050-756149
Solve for x
X-5= -9 please help
Answer:
A. x = -4
Step-by-step explanation:
We are given the equation:
x - 5 = -9
In order to solve for x, we must "undo" the -5 by adding 5 to both sides:
x - 5 + 5 = -9 + 5
x = -4
The answer is thus A.
~ an aesthetics lover
x-5= -9
we need to put everything in the right part to easily calculate it:
x=5 -9 or you can write (-9+5)
then, we have that x= -4
Mathematics, Help, not sure about my answer on this one
Answer:
F. 2 1/9
Step-by-step explanation:
Step 1: Substitute q
[tex]r = 3(\frac{1}{3^n} )+2[/tex]
When you plug in n = 1, 2, 3:
n(1) = 3
n(2) = 2.11111
n(3) = 2.3333
So our answer is F.
1. Label and display your new polynomial identity 2. Prove that it is true through an algebraic proof, identifying each step 3. Demonstrate that your polynomial identity works on numerical relationships (x + y)* (x^2 + 2xy + y^2) the new polynomial
Answer:
(ax+b) (x+a)
Step-by-step explanation: