Answer:
29th term = 76.4
Step-by-step explanation:
Total terms = 55
aₙ = a + (n - 1) d
5th term = a₅ = 14
a + (5 - 1)*d = 14
a + 4d = 14 --------------------(I)
last term = a₅₅ = 144
a + (55 - 1)d = 144
a + 54d = 144----------------(II)
Multiply equation (II) by (-1)
(I) a + 4d = 14
(II)*(-1) -a - 54d = -144 {Now add and thus a will be eliminated}
-50d = -130
d = -130/-50
d = 2.6
Plug in d = 2.6 in equation (I)
a + 4* 2.6 = 14
a + 10.4 = 14
a = 14 - 10.4
a = 3.6
29th term = a₂₉ = 3.6 + (29 - 1)* 2.6
= 3.6 + 28* 2.6
= 3.6 + 72.8
a₂₉ = 76.4
Answer:
76.4
Step-by-step explanation:
Let the first term and common difference of the AP be a and D respectively.
[tex]t_5 = 14 \implies \: a + 4d = 14....(1) \\ t_{55} = 144 \implies \: a + 54d = 144....(2) \\ subtract \: eqution \: (1) \: from \: equatin \: (2) \\ \\ a + 54d - (a + 4d) = 144 - 14 \\ a + 54d - a - 4d = 130 \\ 50d = 130 \\ d = \frac{130}{50} \\ \huge \red{ \boxed{ d = 2.6}} \\ substituting \: d = 2.6 \: in \: equation \: (1) \\ \\ a + 4 \times 2.6 = 14 \\ a + 10.4 = 14 \\ a = 14 - 10.4 \\ \huge \purple{ \boxed{ a = 3.6}} \\ \\ t_{29} = a + 28d \\ t_{29} = 3.6 + 28 \times 2.6 \\ t_{29} = 3.6 + 72.8 \\\huge \orange{ \boxed{ t_{29} = 76.4}} \\ [/tex]
The number of private investigators is expected to increase from 25,000 in 2009
to 30,000 in 2019. If there are 312,500 police officers in 2009, how many police
officers must there be in 2019 to have a greater percent increase than that of
private investigators? *
Answer:
[tex]375001[/tex] police officers
Step-by-step explanation:
[tex]\frac{30,000}{25,000} = \frac{30}{25} = \frac{120}{100} = 1.2[/tex]
That's a 20% increase.
So increase the police by 20% gets you:
[tex]312500 * 1.2 = 375000[/tex]
Based on the wording of the question, if you want a greater percentage, the answer should be a single policeman more, thus 375,001.
Complete the equation of the line whose slope is -2 and y intercept is (0, -8)
Answer:
y = -2x-8
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2x + -8
y = -2x-8
A Jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not
replaced
P(white, then purple, then black)
Answer:
1 / 36
Step-by-step explanation:
There are 4 + 5 + 1 = 10 chips so there are 10 * 9 * 8 = 720 ways to choose 3 chips and not replace them. There are 4 ways to choose the white chip, 5 ways to choose the purple chip and 1 way to choose the black chip so there are 4 * 5 * 1 = 20 successful ways, therefore, the probability is 20 / 720 = 1 / 36.
Find sin of theta when you only know cos of theta. You have to use the Pythagorean Identity!
Answer:
[tex]\huge\boxed{B. \ sin \theta = \frac{\sqrt{35} }{6} }[/tex]
Step-by-step explanation:
We'll use the following Pythagorean Identity:
[tex]cos ^ 2 \theta + sin^2 \theta = 1[/tex]
Finding sin θ , we'll rearrange the formula as:
[tex]sin \theta = \sqrt{1 - cos^2 \theta}[/tex]
Given that cos θ = - 1 / 6
[tex]sin \theta = \sqrt{1 - (-\frac{1}{6} )^2} \\sin \theta = \sqrt{1-\frac{1}{36} } \\sin \theta = \sqrt{\frac{36-1}{36} } \\sin \theta = \sqrt{\frac{35}{36} } \\sin \theta = \frac{\sqrt{35} }{\sqrt{36} }\\ sin \theta = \frac{\sqrt{35} }{6}[/tex]
For the given word problem, identify the specific quantity. An environmental group is planting trees in a park. The group wants to plant 32 trees in all and have already planted 11 trees. If the group can plant 3 trees per hour, how long will it take it to finish? 11 3 32 t
Answer:
32
Step-by-step explanation:
its the end amount/quanity
Please help me on this question :(
The main table is at the top. This is what it would look like if you filled out your blank boxes. The second section below shows scratch work to help form the more complicated columns.
=========================================================
Explanation:
We have two atomic variables p and q. They can each take on values of True (T) or False (F).
There are 2*2 = 4 combinations of T and F as shown below
T,T ... both trueT,F ... p is true but q is falseF,T ... p is false, but q is trueF,F ... both are falseThat takes care of the first two columns of the table. Note how there aren't any other ways to have two truth values together.
The third column ~q is where we flip everything in the q column. So if q is true, then ~q is false, and vice versa. A similar situation happens with the ~p column as well.
The ~p v q column is where we apply a disjunction to ~p with q. The V stands for "or". It means either ~p is true or q is true. If either are true, then (~p v q) is true. Otherwise it's false. Put another way, (~p v q) is only false when both ~p and q are false together.
The last column is the entire expression ~q ^ (~p v q). We apply a conjunction to the ~q column and the (~p v q) column. Both expressions must be true for the entire ~q ^ (~p v q) to be true, otherwise it's false.
Let me know if you have any questions. It's probably tricky to wrap your head around at first, but hopefully the table clears things up.
The scratch work section is to show how the fifth and sixth columns are formed.
What is the factored form of the expression 9x2 + 6x + 1?
O (3x - 1)2
O (3x + 1)2
O (9x + 1)2
O (9x - 1)
Answer:
(3x + 1)²
Step-by-step explanation:
Given
9x² + 6x + 1 ← is a perfect square of the form
(ax + b)² = a²x² + 2abx + b²
Compare like terms to find a and b
a²x² = 9x² ⇒ a² = 9 ⇒ a = [tex]\sqrt{9}[/tex] = 3
b² = 1 ⇒ b = [tex]\sqrt{1}[/tex] = 1
and 2ab = 2 × 3 × 1 = 6
Thus
9x² + 6x + 1 = (3x + 1)²
Answer:
(3x + 1)^2
Step-by-step explanation:
The first and last terms are perfect squares. From its structure, this is a perfect square trinomial.
All of the symbols in the expression 9x2 + 6x + 1 are positive, so use the rule for the square of the sum of two terms.
In the given expression, a2 = 9x2 and b2 = 1, so a = 3x and b = 1.
2ab = 2(3x)
= 6x
This result matches the middle term in the polynomial expression, 6x, so apply the rule for the square of the sum of two terms.
The expression 9x2 + 6x + 1 is equal to (3x + 1)2.
A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix?
Answer:
18.00 because 1 pound is 5.00, 1 plus 2 is 3 so 5 x 3 = 18
Step-by-step explanation:
6 pounds of a trail mix contains 2 more pounds of raisin than almonds
i.e.
Suppose:
raisins = r; andalmonds = a6 pounds of trails will contain a pound of almond (a) and two more pounds of raisin i.e. (a +2)
∴
a + (a+2) = 6
2a + 2 = 6
2a = 6 -2
2a = 4
a = 2
It implies that there are:
2 pounds of almond; and= (a +2) pounds of raisins
= (2+2) pounds of raisins
= 4 pounds of rasins
Provided that:
a pound of raisins costs = $2.00 a pound of almonds costs = $5.00∴
The total cost of the 6 pounds of trails mix will be:
= 2($4.00) + 2($5.00)
= $8.00 +$10.00
= $18.00
Therefore, we can conclude that the total cost of 6 pounds of trail mix is $18.00
Learn more about word problems here:
https://brainly.com/question/20252231?referrer=searchResults
Write (5)(5)(5)(5) in exponential form. A. 5 to the 4th power B. 4 to the 5th Power C. 625
Answer:
A. 5 to the fourth power
Which measure of center best represents this set of data?
12, 13, 13, 15, 15, 15, 16, 16, 17
•Mean
•Mode
•Median
•Symmetric
Answer:
Mean: 14.67
Mode: 15
Median: 15
Symmetric: Idk
Answer:
Median P.S. The median is 15
Step-by-step explanation:
It is a median because you cross out the highest and lowest numbers out at a time.
What are composite numbers
Answer:
When a number can be divided up exactly and is not a prime number , it is a Composite Number.
The first few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16,........
Hope it helps.
I really need their answers!!!!!!!
Answer:
1.c 1875cm squared.
Step-by-step explanation:
if the area of the park is the area if pool 3 times ... which is 625
so 625×3
=1875cm squared
Answer:
B, C, B
Step-by-step explanation:
24
area of A'B'C'D' = 3 × ABCD = 3 × 625 = 1875 m²
Thus area of park = 1875 - 625 = 1250 m² → B
25
A tangent has only one point of contact with the circle. Thus does not pass through the centre.
26
The inscribed angle subtended by a semi- circle is 90° not 180°
A monitor with dimension ratio of 16:9 is playing a video imagine with a dimension ratio 3:4 at its fullest size which left a pillar boxed imagine what percent of the screen area is occupied the imagine
Answer:
75%
Step-by-step explanation:
The image is 4 : 3 = 12 : 9. It is displayed on a screen that is 16 : 9, so it occupies 12/16 = 3/4 of the screen.
75% of the screen area is occupied
3 cakes
25 people
?
125 people
What is the value of 3 minus (negative 2)?
Answer:
5 I think I'm pretty sure
A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean?
Answer:
26
Step-by-step explanation:
The mean of a set of number is the average the set of number, it is the ratio of the total sum of the terms to the sum of terms.
The standard deviation is the variation of a set of numbers to their mean. A low standard deviation means the value are close to the mean and a high standard deviation means the values are far from the mean. The standard deviation is given as:
[tex]\sigma=\sqrt{\frac{\Sigma (x_i-\mu)^2}{n} }\\ \\\mu=mean,n=number\ of\ terms, \sigma=standard\ deviation[/tex]
Given the numbers:
86, 81, 87, 82. mean = μ = 84
[tex]\Sigma(x_i-\mu)^2=(86-84)^2+(81-84)^2+(87-84)^2+(82-84)^2=4+9+9+4=26[/tex]
Sum of squared deviations = 26
The sum of the squared deviations of the scores from the mean is 26.
-----------------------
The observations are: 86, 81, 87 and 82.The mean of the observations is 84.The sum of the squared deviations of the scores from the mean is the sum of the differences squared of each observation and the mean.Thus:
[tex]S_{ds} = (86-84)^2 + (81-84)^2 + (87-84)^2 + (82-84)^2 = 4 + 9 + 9 + 4 = 26[/tex]
The sum of the squared deviations of the scores from the mean is 26.
A similar problem is given at https://brainly.com/question/17327780
Find the domain and range of the function represented by the graph. A Domain: {−2,−1,1,2} Range: {−2,1,2}{−2,1,2} B Domain: −2≤x≤2 Range: −2≤y≤3 C Domain: {−2,1,2} Range:{−2,−1,1,2} D Domain: −4≤x≤4 Range: −4≤y≤4
Answer:
B) Domain: -2≤x≤2 Range: -2≤x≤3
Step-by-step explanation:
The domain is the x-values, in this case all the numbers between -2 and 2. The range is the y-values, which are the numbers between -2 and 3. So the answer is
B) Domain: -2≤x≤2
Range: -2≤x≤3
(8 x 106 ) / (4 x 103 ) = ?
(the 10 stands for the 0 in scientific notation)
Answer:
3.2 x 10^12
Step-by-step explanation:
80000000/40000
Answer:
Answer:
3.2 x 10^12
Step-by-step explanation:
80000000/40000
What is the domain of g?
Answer: The domain of G is 4
Step-by-step explanation:
The domain is the set of all inputs that makes the function definable. The domain is always represented on the x axis.So looking at g on its x axis you see 4. So the domain is 4.
Answer:
4
Step-by-step explanation:
Sophie opens a new restaurant. The function f ff models the restaurant's net worth (in thousands of dollars) as a function of time (in months) after Sophie opens it.
Based on the graph given, the point of the graph that corresponds with the shop's net worth when Sophie opened it is -5.
What is the minimum of a quadratic function?
The minimum value of the function is the place where the graph has a vertex at its lowest point. In the real world, you can use the minimum value of the quadratic function to determine the minimum cost and area.
What is the minimum amount?
we use minimum to describe an amount which is the smallest that is possible, allowed, and required.
What was the shop worth when it was opened?
The point of the shop were opened is represented by the value of the y axis when it was first crossed.
Looking at the graph, the line first intercepted the y axis at -5 which means that this was the shop's net worth when it was opened by Sophie.
Learn more about quadratic function here https://brainly.com/question/11631534
#SPJ2
Question 2
At how many values of a(0° < a < 360°) does pentagon A'B'C'DE' coincide with pentagon ABCDE? What is significant about this
number?
Answer: each time the pentagon is rotated 72, it maps back onto itself. There are five values of a for which the pentagon maps back onto itself. this is the same as the number of sides of the pentagon.
Step-by-step explanation: edmentum
A regular pentagon has 5 congruent sides and a measure of 360 degrees, at its center.
Pentagon ABCDE and A'B'C'D'E coincide at 4 values of (a)
The angle where pentagon ABCDE and pentagon A'B'C'D'E coincide is:
[tex]\mathbf{\theta = \frac{360}{5}}[/tex]
[tex]\mathbf{\theta = 72}[/tex]
Other angles between 0 and 360 degrees, where pentagon ABCDE and pentagon A'B'C'D'E coincide are multiples of 72.
So, we have:
[tex]\mathbf{a = 72^o,\ 144^o,\ 216^o,\ 288^o}[/tex]
The count of angles is 4
Hence, pentagon ABCDE and A'B'C'D'E coincide at 4 values of (a)
Read more about transformations at:
https://brainly.com/question/15158635
1. Which words represent ADDITION
less than
sum
more than
times
Answer:
more than
Step-by-step explanation:
Which fraction is equivalent to 80%?
Answer:
4/5
Step-by-step explanation:
80% is equivalent to 80/100
80/100 can be simplified into 8/10 by dividing both sides by 10
8/10 can be further simplified into 4/5 by dividing both sides by 2
4/5 can not be simplified any further
which line of best fit should not have been drawn. Give a reason for your answer
Answer:
Diagram B
Step-by-step explanation:
This is because the line only goes through two points and many are dispered from the line, however diagram A and C have points fairly close to them
Visually inspecting the three scatterplots, the line of best fit does not accurately fit the points on the second graph. Hence, line of best fit should not have been drawn for the second graph as the relationship isn't linear.
The line of best fit minimizes the sum of the square of the mean distance between each point. Hence, the distance between the line and the best fit line should be as small as possible.
However, the second graph isn't linear, hence , a linear line cannot model the relationship.
Learn more : https://brainly.com/question/23105648
The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,
Answer:
-26
Step-by-step explanation:
Given the sequence:
16, 9, 2, –5, ...,
To find:
7th measurement, if the above sequence continues:
Solution:
Let us examine the given sequence first:
First term is 16
Second term = 9
Third term = 2
Fourth term = -5
Difference between 2nd and 1st term = 9 - 16 = -7
Difference between 3rd and 2nd term = 2 - 9 = -7
Difference between 4th and 3rd term = -5 - 2 = -7
We can see that there is a common difference of -7 between each term.
That means, the sequence is in Arithmetic Progression.
whose first term, [tex]a=16[/tex]
Common difference, [tex]d=-7[/tex]
To find:
7th term i.e. [tex]a_7=?[/tex]
Solution:
Formula for [tex]nth[/tex] term of an Arithmetic Progression is given as:
[tex]a_n=a+(n-1)d[/tex]
Let us put [tex]n=7[/tex]
[tex]a_7=16+(7-1)\times (-7)\\\Rightarrow a_7=16+6\times (-7)\\\Rightarrow a_7=16-42\\\Rightarrow \bold{a_7=-26}[/tex]
7th measurement will be -26.
Answer:
7th measurement= -26
Step-by-step explanation:
The sequence is 16, 9, 2, –5, ...,
First term( a)= 16
Second term=9
Common difference (d) = 9-16
Common difference= -7
The sequence is a arithmetic progression
For AP's ,the terms formula is
Term(n) = a + (n-1)d
Where n represent the term to be found
In this case,we Are looking for the 7th term , so n= 7
Term(7) = 16+ (7-1)-7
Term(7)= 16 +6(-7).
Term (7) = 16-42
Term(7) = -26
7th term =-26
Which fraction is equivalent to
2/5
Answer:
To make equivalent fractions, what we have to do is multiplicate or divide the numerator or denominator by the same number.
In our case:
[tex]\frac{2}{5}=\frac{2*2}{5*2}=\frac{4}{10}[/tex]
[tex]\frac{2}{5}=\frac{2*6}{5*6}=\frac{12}{30}[/tex]
[tex]\frac{2}{5} = \frac{2*12}{5*12}=\frac{24}{60}[/tex]
That are only three examples, but there are infinite.
We could also obtain equivalent fractions dividing, for example, [tex]\frac{3}{9}[/tex]:
[tex]\frac{3}{9}=\frac{\frac{3}{3}}{\frac{9}{3}}[/tex] = [tex]\frac{1}{3}[/tex]
The square of a whole number is between 6400 and 7000. The number must be between ?
Answer:
The number must be between 80 and 83.666002653408
Step-by-step explanation:
The square root of 6400 is 80 and the square root of 7000 is 83.666002653408 so it would be between those numbers.
what is −10x + 1 + 7x = 37
Answer:
x = -12
Step-by-step explanation:
−10x + 1 + 7x = 37
Combine like terms
-3x+1 = 37
Subtract 1 from each side
-3x +1-1 = 37-1
-3x = 36
Divide each side by -3
-3x/-3 = 36/-3
x = -12
Answer:
x = -12
Step-by-step explanation:
[tex]-10x+1+7x=37\\\\\mathrm{Group\:like\:terms}\\-10x+7x+1=37\\\\\mathrm{Add\:similar\:elements:}\:-10x+7x=-3x\\-3x+1=37\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\-3x+1-1=37-1\\\\Simplify\\-3x=36\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{36}{-3}\\\\x =-12[/tex]
Can you guys help me with this ?
Answer: think it’s b
square root of 141 '