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Work Shown:
Here are the variables we're working with
a = first termb = last term (aka nth term)n = number of termsS = sum of the first n termsIn this case, we know that
a = unknown (what we want to solve for)b = -12 n = 14S = 42We can use this formula to help find the answer
S = (n/2)*(a+b)
This formula only works for arithmetic sequences
So,
S = (n/2)*(a+b)
42 = (14/2)*(a+(-12))
42 = 7(a-12)
42/7 = a-12
6 = a-12
6+12 = a
18 = a
a = 18 is the first term of this arithmetic sequence
That's why the answer is choice D.
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Side note: your book or your teacher may use the notation [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex] but I figured it would be easier to use 'a' and b in place of [tex]a_1[/tex] and [tex]a_n[/tex] respectively.
A sample of radium has a weight of 1.5 mg and decays
by half every 6 years. Circle all of the following
functions that correctly model the amount of radium
f(t) in mg remaining after t years
Answer: [tex](b)[/tex]
Step-by-step explanation:
Given
Initial mass of radium is [tex]A_o=1.5\ mg[/tex]
It decays by half every 6 years i.e. [tex]T_{\frac{1}{2}}=6[/tex]
For radioactive decay, sample at any time is given by
[tex]\Rightarrow A=A_o2^{-\dfrac{t}{T_{\frac{1}{2}}}}[/tex]
Insert the values
[tex]\Rightarrow A=1.5\cdot 2^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot \left(\dfrac{1}{2}\right)^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot (0.5)^{\dfrac{t}{6}}[/tex]
Thus, option (b) is correct.
a model truck is 13.5 inches long 7.5 inches wide. the original truck was 12 feet long. how wide was the truck?
Answer:
w = 6ft 8in
Step-by-step explanation:
the proportions will be the same
w/7.5 = 12/13.5
multiply both sides by 7.5
w = 12/13.5 * 7.5
w = 6.6666666667ft
w = 6ft 8in
The original truck was 6.67 feet wide.
What is ratio?"It is a comparison of two or more numbers that indicates their sizes in relation to each other."
What is proportion?"It is an equation in which two ratios are set equal to each other."
For given example,
A model truck is 13.5 inches long 7.5 inches wide.
The ratio of length to width of a model truck would be,
13.5 : 7.5 ...........................(1)
The original truck was 12 feet long.
This means the original truck was 144 inches long.
Let 'x' be the width (in inches) of the original truck.
So, the ratio of the length to the width of the original truck would be,
144 : x .................................(2)
Also, the ratios given by (1) and (2) must be in proportion.
[tex]\Rightarrow \frac{13.5}{7.5} = \frac{144}{x} \\\\\Rightarrow 13.5 \times x = 144 \times 7.5\\\\\Rightarrow \bold{x=80~inches}\\\\\Rightarrow \bold{x=6.67~feet}[/tex]
Therefore, the original truck was 6.67 feet wide.
Learn more about ratio and proportion here:
https://brainly.com/question/26974513
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If the carrier is continental airlines, what is the chance that I will be denied boarding?
Answer:
Sample Answer for Edmentum
Step-by-step explanation:
Answer: 0.0112%
Step-by-step explanation:
PLEASE HELP ASAPPP!!
Answer:
34
Step-by-step explanation:
im pretty sure its 34.
vertical angles are basically angles from the opposite side of each other, so saying that one of the angles is 68 degrees and they're vertical angles, means that the other unknown angle is 68 degrees.
but in this case it'll be 34 since ur multiplying 2 with 34
2(34) = 68
i hope this helped
y : 11 = 27 : 33 what is y
9514 1404 393
Answer:
y = 9
Step-by-step explanation:
Corresponding parts of the proportion have the same ratios. We notice that 33 is 3 times 11, so 27 is 3 times y.
y = 27/3 = 9
Pleaseeeee help me with this question
Numerical expressions for add 12 to 8 then multiply by 5
Answer:
5(8+12)
Step-by-step explanation:
There are 6 shipping boxes that each contain 36 kg of merchandise from a toy store. Before the boxes are loaded onto a delivery truck, the same amount of additional merchandise is added to each box. The total weight of all of the boxes is 258 kg. How much additional weight was added to each box?
Answer: 7 kg
Step-by-step explanation:
Order the following units of a capacity families to greatest gallon paint cup quart
Answer:
7 yards
Step-by-step explanation:
HELPPP ILLL MARK BRAINLIEST
Which ordered pair represents a solution to both equations?
A (2, 0)
B (-3, -15)
C (0, -21)
D (3, 3)
See picture for Graph
Given f (x) = StartLayout Enlarged left-brace first row x squared minus one-third x, for x not-equals negative 1 second row negative 1, for x = negative 1 EndLayout. What is Limit of f (x) as x approaches negative 1?
Negative five-thirds
Negative four-thirds
Four-thirds
Five-thirds
Answer:
It's C, 4/3! Just did the question and got it right
Step-by-step explanation:
The limit of f(x) as x approaches negative 1 is four thirds.
What is Limits?Limits are defined as the value of a function as the input approaches a certain number. Limits are the concepts used essentially in calculus to define continuity, integrals and derivatives.
Given function is,
[tex]f(x) =\left \{ {{x^{2} -\frac{1}{3}x, x\neq -1 } \atop {-1, x=-1}} \right.[/tex]
We have to find the value of the limit as x approaches to negative 1.
This is not the same value as the value of the function at negative 1. Limit of the function as x approaches some value is the value of the function which is closest to the exact value of the function at the input.
We have,
f(x) = x² - [tex]\frac{1}{3}[/tex] x when x ≠ -1
Substitute x = -1 in the above equation
x² - [tex]\frac{1}{3}[/tex] x = (-1)² - (1 / 3) (-1)
= 1 + [tex]\frac{1}{3}[/tex]
= [tex]\frac{4}{3}[/tex]
[tex]\lim_{x \to -1} x^{2} -\frac{x}{3}[/tex] = [tex]\frac{4}{3}[/tex]
Hence the limit of f(x) = x² - [tex]\frac{1}{3}[/tex] x when x tends to -1 is 4/3.
To learn more about Limits, click on the link given below :
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Estimate: 1/5 + 3/7
Answer:
Answer:1/2
Step-by-step explanation:
PLEASE HELPPPPP
Ethan puts $1200 into a Certificate of Deposit (CD) account that earns 2.1% interest each year. What will be the interest of the CD account earned after 5 years? Round to the nearest cent (hundredths place).
Answer:
126
Step-by-step explanation:
1200x.021=25.20 interest per year
25.20 x 5 years = 126
assumes no compounding
Question 9
Two sides of a triangle have lengths 10 and 15.
What must be true about the length of the third side?
Greater than 5 but less than 25
Less than 15
Less than 25
Answer:
Two sides of a triangle have lengths 10 and 15.
What must be true about the length of the third side?
Greater than 5 but less than 25
Less than 15
Less than 25
Step-by-step explanation:
Eugene and Jenny are selling cookie dough for a school fundraiser. Customers can buy packages
of chocolate chip cookie dough and packages of gingerbread cookie dough. Eugene sold i
package of chocolate chip cookie dough and 10 packages of gingerbread cookie dough for a total
of $174. Jenny sold 4 packages of chocolate chip cookie dough and 2 packages of gingerbread
cookie dough for a total of $50. Find the cost each of one package of chocolate chip cookie
dough and one package of gingerbread cookie dough.
.
.
Two sides of a triangle have lengths 10 and 15.
What must be true about the length of the third side?
Greater than 5 but less than 25
Less than 15
Less than 25
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A study has been done to determine to see if the level of education determines how often people move between different states in America. If a person from the survey is randomly selected , what is the probability that they lived in 2 or more states and that they have a college degree? P( 2 state or more U Degree )
0.655
0.111
0.310
0.500
Solution :
P(2 states or more | college degree)
[tex]$=\frac{\text{P( 2 states or more and college degree)}}{\text{P(college degree)}}$[/tex]
Total number of people = 58
The number of people who lived in two states or more than two states and also have a college degree = 18
Therefore,
[tex]$\text{P(2 states or more states and college degree)} = \frac{18}{58}$[/tex]
The number of people who have a college degree = 20
So, [tex]$\text{P(college degree)} = \frac{20}{58}$[/tex]
Thus,
[tex]$\text{P(2 states or more/college degree)}=\frac{\frac{18}{58}}{\frac{20}{58}}$[/tex]
[tex]$=\frac{18}{20}$[/tex]
= 0.900
The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy
knows the diagonal of the ceiling from corner to corner must be longer than 25 ft,
but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your
work. (Hint: the answers should be the same!)
Please help !!!
Answer:
A. 35 ft.
B. 35 ft
Step-by-step explanation:
Please see attached photo for diagram.
A. Determination of the diagonal using pythagorean theorem.
A square has all sides equal. Thus, the diagonal of the square can be obtained as follow:
Ist leg (L₁) = 25 ft
2nd leg (L₂) = 25 ft
Diagonal (d) =?
d² = L₁² + L₂²
d² = 25² + 25²
d² = 625 + 625
d² = 1250
Take the square root of both side
d = √1250
d = 35 ft
B. Determination of the diagonal using trigonometry.
Since all the sides in a square are equal, the angle between each leg will be 90°. Thus, the diagonal will bisect the angle between the two leg equally i.e
Angle between Diagonal and each leg = 90/2 = 45°
Finally, we shall determine the length of the diagonal. This can be obtained as follow:
Angle θ = 45°
Opposite = 25 ft
Hypothenus = d
Sine θ = Opposite / Hypothenus
Sine 45 = 25 / d
0.7071 = 25 / d
Cross multiply
0.7071 × d = 25
Divide both side by 0.7071
d = 25 / 0.7071
d = 35 ft
Twice a number is 14. What is the number .
Answer: 7
Step-by-step explanation: 7+7=14
Given that y2 is directly proportional to the cube of x and y is always positive. Find the
value of. when x = 3 if y = 18 when x =4
A) 27 B) 11.67 C) 29
Answer:
11.69
Step-by-step explanation:
Given that y2 is directly proportional to the cube of x and y is always positive. then;
y² = kx³
if y = 18 when x =4
18² = k4³
324 = 64k
k = 324/64
k = 5.0625
To get y when x = 3
Recall
y² = kx³
y² = (324/64)3³
y² = 324/64 * 27
y² = 136.6875
y = √136.6875
y = 11.69
Hence the value of y is 11.69
value of. when x = 3 if y = 18 when x =4
A) 27 B) 11.67 C) 29
HURRY!!!!!! 100 POINTS!!!!!!!!!!
WHO ANSWERS THIS FIRST GETS BRALIEIST!!!!!!!!
Arturo received a large cash prize when he was chosen as the winner of a writing contest, and he did something
really nice and totally unselfish with the winnings that he received.
which revision most
effectively shortens the sentence to make it less repetitive and more precise?
Drag the revision into the box
Revision
A.
As the winner of a writing contest, Arturo won money and gave his winnings away.
B.
Arturo did something unselfish with the prize money he won in a writing contest instead of spending it
on himselt
C.
Arturo won a cash prize in a writing contest and donated the money to a local animal shelter.
Answer:
C
Step-by-step explanation:
Solve the following system using any method.
−5x+7y=10
−9x−4y=18
Answer:
-2,0
Step-by-step explanation:
See the steps below:)
Help me please I’m begging worth 40 points!!!!!
help please ande hank ou
Answer:
5/27
Step-by-step explanation:
Encuentre el volumen de 35 kg de oro
I need help on this question
Answer:
C. y = 8x
Step-by-step explanation:
Using the slope formula, we can calculate the rate of Marisol's and Timothy's Machines.
[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]
Marisol:
[tex]m = \frac{18-12}{3-2} \\m=6[/tex]
Timothy:
[tex]m=\frac{54-36}{6-4} \\m=\frac{18}{2} \\m=9[/tex]
Now that we know the rate of their machines, we need to choose a rate that is between 6 and 9. Therefore, the rate of Zorian's machine needs to be y = 8x.
Plz help me well mark brainliest if correct..???
Answer:
23 students letter d ran the 50 yard dash
Answer:
18
Step-by-step explanation:
the time of the students:
23,24,24,28,32,32,34,35,37,37,38,41,43,56,55,55,56,61
there are 18 number so 18 students did it
Pls help me ASAP show work please
Answer:
$3.48 for each pair of socks.
Step-by-step explanation:
It's a little confusing, because it says they're buying 2 socks, but then asks for the price of each of 2 *pairs* of socks. I'm going to believe the first sentence should say they paid for 2 pairs of socks.
They have $10, and get $3.04 in change. So we'll subtract $3.04 from $10 to find out the cost of 2 pairs of socks.
10 - 3.04 = 6.96
Then divide $6.96 by 2 pairs of socks
6.96/2 = $3.48 for each pair of socks.
What is the value of
(5 1/3)^3 ?
Answer:
[tex] \frac{4096}{27} [/tex] or [tex]151 \frac{19}{27} [/tex]Step-by-step explanation:
[tex](5 \frac{1}{3} {)}^{3} [/tex][tex](5 + \frac{1}{3} {)}^{3} [/tex][tex]( \frac{16}{3} {)}^{3} [/tex][tex] \frac{ {16}^{3} }{ {3}^{3} } [/tex][tex] \frac{4096}{27} [/tex][tex]151 \frac{19}{27} [/tex]Hope it is helpful....Answer:
4096/27
Step-by-step explanation:
This is Exact Form
Multiply 3 1/3 x 1 1/7
write the answer in simplest form.
Katherine is 17 years younger than Joe. If Joe is 44 years old, how old is Katherine?
_____years old
Answer:
Katherine is 27 years old.
Step-by-step explanation:
44-17=27.
Answer:
27
Step-by-step explanation:
44 age of Joe
-17 years younger
______________
27 years of age
Perfect square trinomial:
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
Find the product of (k – 9)2 using the perfect square trinomial rule shown on the left.
The product (k – 9)2 can also be written as
.
The product is k2 –
k +
.
Answer:
See work below.
Step-by-step explanation:
[tex](k-9)^2=(k-9)(k-9)\\=k^2-2(k)(9)+9^2\\=k^2-18k+81[/tex]