Find the 93rd term of the arithmetic sequence -11, -7, -3
Answer:
357
Step-by-step explanation:
hello :
note : the n th term of an arithmetic sequence is :
An =A1+(n-1)d ....a common difference is : d and A1 the first term
in this exercice : d = -3-(-7) =-7-(-11) = 4 A1 = -11
when : n =93 you have the 93rd term A93
so : A93 = -11 +(93-1)(4)
A93 = 357
the length of a rectangle is 5 meters longer than the width. if the area is 23 square meters, find the rectangles dimensions. round to the nearest tenth of a meter
Answer:
The rectangle is 7.9 meters by 2.9 meters.
Step-by-step explanation:
Let l be the length and w be the width
l = w + 5
A = 23 m²
Formula: A = lw
Solve for the dimensions
23 = (w+5)w
23 = w² + 5w
w² + 5w - 23 = 0
Use quadratic formula to find the possible value/s of w
\(w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9\)
Since we're dealing with dimensions, take the positive value which is 2.9.
w = 2.9 m
Substitute the value to l = w + 5
l = 2.9 + 5
l = 7.9 m
What descriptions below accurately describe a function?
Select all that apply
a
A function is a pairing of numbers in which one input is paired with exactly one output
b
In a function, the output is allowed to be shared. This means that different inputs can all share the same output.
c
A function is a pairing of numbers in which one input is paired multiple outputs.
find the value of x. help with geometry pls
Answer:
Find the value of x:-
To find Y, use Pythagorean theorem:- \(c^{2} =a^{2} +b^{2}\)
\((2.1)^{2} =y^{2} +(1.4)^{2}\)
\(2.1^{2}=4.41\)
\(1.4^{2} =1.96\)
\(4.41=y^{2} +1.96\)
subtract 1.96 from both sides
\(2.45=y^{2}\)
\(y=1.5652\)
Now, to find x:-
\(x=y+y\)
\(= 1.5632+1.5652\)
\(x=3.1 \: ft\)
~OAmalOHopeO
The first shelf on Hannah’s bookshelf hoods an equal number of fiction and nonfiction. If Hannah’s selects 5 books randomly, what is the probability that 3 of the books will be fiction and 2 will be nonfiction
Answer:
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
Step-by-step explanation:
What is probability?
Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.
To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.
Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.
Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.
Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.
Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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anyone know? its due tonight
Answer:
12 cm
Step-by-step explanation:
Well first we can cut the triangle in half and use the Pythagorean theorm
a^2+b^2=c^2
In this case we are going to be doing c^2-a^2=b^2
10^2-8^2=b^2
(10*10)-(8*8)=b^2
100-64=b^2
36=b^2
Now we just square root 36 (what number times itself is 36)
\(\sqrt{36}\)
b=6
Since half of the one side equals 6 (DC) then the length of AC is 12!
Answer:
hey mate here is your answer...
Step-by-step explanation:
by using Pythagoras theorem...
BC² = BD² + DC²10² = 8² + DC²DC² = 100 - 64DC² = 36DC = 6DC is the half of AC.Therefore AC = 12 centimetres.hope it helps you ❣️
0015 15% . Fifteen hundredths of the students in the sixth grade wore a blue shirt yesterday, Sort the expressions into the bin that describes whether or not the expression represents the numeral. 6.RP 3 0.15 1,500 Reprots men hundredth Does not represent Mon hundredths 100 0.15%
Answer:
The expressions that represents Fifteen hundreds are;
\(\begin{gathered} 15\text{\% } \\ 0.15 \\ \frac{15}{100} \end{gathered}\)The expressions that does not represents Fifteen hundreds are;
\(\begin{gathered} 0.015 \\ 1,500 \\ \frac{100}{15} \\ 1.5 \\ 0.15\text{\%} \end{gathered}\)Explanation:
Given that Fifteen hundredths of the students in the sixth grade wore a blue shirt yesterday, we want to sort the given expression;
\(\text{Fifteen hundredths = }\frac{15}{100}\)The similar expressions to Fifteen hundreds includes;
\(15\text{\% }=\frac{15}{100}=0.15\)So, the expressions that represents Fifteen hundreds are;
\(\begin{gathered} 15\text{\% } \\ 0.15 \\ \frac{15}{100} \end{gathered}\)the expressions that does not represents Fifteen hundreds are;
\(\begin{gathered} 0.015 \\ 1,500 \\ \frac{100}{15} \\ 1.5 \\ 0.15\text{\%} \end{gathered}\)Help me graph this
Y=x-5
2x+y=4
Answer:
Y=x-5
2x+y=4
Step-by-step explanation:
Answer:
Plot these points:
For the line y = x - 5:
(0, -5)
(1, -4)
For the line 2x + y = 4:
(0, 4)
(1, 2)
Is 6 inches in 10 seconds proportional to 12 inches in 60 seconds?
Answer: No
Step-by-step explanation:
to be proportional, both numbers have to increase by the same number
because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in
A cross-country course is in the shape of a parallelogram with a base of length 3 mi and a side of length 2 mi. What is the total length of the cross-country course.
Based on the fact that the cross-country course is shaped like a parallelogram, the total length of the cross-country course is 10 miles.
What is the total length?The total length of the cross-country course will be the perimeter of the shape that the course is shaped like.
As this course is shaped like a parallelogram, the total length would therefore be:
= Base + Base + Length + Length
Solving gives:
= 3 + 3 + 2 + 2
= 6 miles
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A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)
Answer: 82 sq. units .
Step-by-step explanation:
Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.
Then we plot them on graph ( as provided in attachment)
Length = AB \(=\sqrt{(9+1)^2+(-1-7)^2}\) units [By distance formula : \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)]
\(=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}\) units
Width = BC = \(\sqrt{(-1+5)^2+(7-2)^2}\) units
\(=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}\)
Area = length x width
= \(2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}\)
Hence, the area of the rectangle is 82 sq. units .
WILL MARK BRAINLIST!!!!!!!!!!!!
What is the 21st term of the sequence with a1 = -7 and d = 3?
A . -4
B . -11
C . -21
D . 53
Answer:
\(T_{21} = 53\)
Step-by-step explanation:
Given
\(a = -7\)
\(d = 3\)
Required
Determine \(T_{21}\)
This is calculated using sum of Ap formula
\(T_n = a + (n - 1)d\)
In this case:
\(n =21\)
So, the equation becomes
\(T_{21} = -7 + (21 - 1) * 3\)
\(T_{21} = -7 + 20 * 3\)
\(T_{21} = -7 + 60\)
\(T_{21} = 53\)
Answer:
53
Step-by-step explanation:
9. Find the value of
the expression.
16 + 4 + (42 - 3) =
Answer:
59Step-by-step explanation:
16 + 4 + (42 - 3) = 20 + 39 =59Answer:
59
Step-by-step explanation:
16 + 4 + (42-3) = 59. Do parentheses first. (42-3) = 39. Which changes the equation to 16 + 4 + (39). 39 + 4 = 43. Then the equation changes to 16 + 43. These added together equal 59. Hope this helps!
PEMDAS= Parentheses, exponents, multiplication, division, addition, and then subtraction.
This is the order in which to solve these types of equations, which is why I did the parentheses first.
t Park Junior High, 10%, or 160, of the students, play a musical instrument. How many students attend the school?
A tape diagram. StartFraction part Over whole EndFraction = StartFraction 10 Over 100 EndFraction = StartFraction 160 Over question mark EndFraction
Which statements are correct? Check all that apply.
The total number of students is 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
The percent as a part-to-whole ratio is StartFraction 160 Over 100 EndFraction
There are 1,600 students in the school.
There are 250 students in the school.
Answer:
The total number of students is > 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
There are 1,600 students in the school.
Step-by-step explanation:
got is correct
Answer:
2,3,5 for eg. 2020
Step-by-step explanation:
Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
Pls help and show solution.
The graph would show two lines, one for Tom and one for Steve. Tom's line would be a straight, continuous line with a positive slope representing a constant speed of 80 km/h.
What is graph?Graph is a mathematical structure used to depict relationships among objects. It consists of a set of objects, known as vertices, connected by edges. A graph can represent any kind of relationship between two or more objects, such as a flowchart, a map, or a family tree. Graphs are widely used in computer science, engineering, and mathematics to represent data and solve problems.
Steve's line would start as a straight, continuous line with a positive slope representing a constant speed of 100 km/h. At d = 150, the line would have a break representing the 30-minute rest and then continue on with a positive slope, representing Steve's continued journey at the constant speed of 100 km/h.
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A. The graph for Tom's journey is a straight line with a slope of 80 km/h and the graph for Steve's journey is a piecewise function with a slope of 100 km/h for the first 150 km and 0 km/h for the second 150 km.
What is function?A function is a process or a set of instructions that is used to operate a mathematical or computer program. It is a mathematical entity that takes certain values as inputs, performs certain operations on them, and produces a certain output. Functions are used to simplify complex problems, allowing for efficient and accurate results. They are also used to model real-world systems and processes, allowing for better understanding of those systems.
b i Tom overtakes Steve at t = 1.875 hours and d = 225 km.
ii Steve overtakes Tom at t = 3.75 hours and d = 375 km.
iii At the time Steve arrives at Broken Hill (t = 4 hours), Tom still has to travel a distance of 300 km - 375 km = 25 km to reach Broken Hill.
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What is ¼(2.5 + c) (8) = 11
Answer:
c = 3Explanation:
¼(2.5 + c) (8) = 11
Multiply Both Sides By 4(4) ¼(2.5 + c) (8) = 11 (4)
Simplify8 (2.5 + c) = 44
Divide Both Sides By 88 (2.5 + c) / 4 = 44 / 4
Simplify2.5 + c = ¹¹⁄₂
Subtract 2.5 From Both Sides2.5 + c - 2.5 = ¹¹⁄₂ - 2.5
Simplifyc = 3Find the value of x, 6,4, 3x, 4x+1
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Los organizadores de la Feria de Alimentos colocan un contenedor de agua que mide 2,76 metros de largo, por 23,5 decímetros de ancho y por 196 centímetros de alto. ¿Cuál es el volumen del contenedor? Expresa la respuesta en metros cúbicos con aproximación a centésimos.
The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.
To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.
The length of the container is 2.76 meters.
The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).
The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).
Now we can calculate the volume of the container:
Volume = Length × Width × Height
Volume = 2.76 meters × 2.35 meters × 1.96 meters
Volume ≈ 12.9516 cubic meters (rounded to four decimal places)
Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.
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The tempest on Sunday was 18f. By Monday, the temperature dropped to -5 f. Find the change in temperature
Answer:
The temperature change is 23 because 18 - (-5)=23
Step-by-step explanation:
A car is traveling at a rate of 30 meters per second. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 5 hours? Do not
round your answers.
The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.
What is the speed of the car in kilometers per hour and distance covered after 5 hours?Speed is simply referred to as distance traveled per unit time.
It is expressed as;
Speed = Distance ÷ time.
Given that the car is traveling at a rate of 30 meters per second.
First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.
1 kilometer = 1000 meters
1 hour = 3600 seconds
Hence;
Speed = 30m/s = ( 30 × 3600/1000 )kmh
Speed = 108 kmh
Next, the distance covered in 5 hours will be:
Speed = Distance / time
Distance = speed × time
Distance = 108 kmh × 5 h
Distance = 540 km
Therefore, the disatnce covered is 540 kilometers.
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the white bored is 4.5 feet wide. How many yards wide is the whiteboard?
Based on the table, which function models this situation?
a. f(n) = -3n + 24
b. f(n) = -(1/3)n + 16
c. f(n) = -3n + 64
d. f(n) = -(1/3)n + 8
please show how you got the answer!
Answer:
A is correct. f(n) = -3n + 24
Step-by-step explanation:
We can see in the first two steps that two meals have been served, and six cups of pet food consumed. In other words, six cups are consumed in two meals, therefore three cups are consumed in each meal.
If we look at the remaining numbers on the chart, we can see that this carries through. This tells us that the correct answer must be either a or b, as "-3n" represents the consumption rate. If it were (1/3)n, then only a third of a cup would be consumed per meal.
Finally, we can figure out which of those two equations is correct simply by plugging a value pair into them. Starting with a:
f(1) = -3(1) + 24
= 24 - 3
= 21
correct.
To be certain, let's check with answer c:
f(1) = -3(1) + 64
= 64 - 3
= 61
incorrect.
So we can clearly say that the correct answer is "a". You can plug the other values into it to test that too:
f(3) = -3(3) + 24
= 24 - 9
= 15
correct
So we definitely have the right answer.
Leslie wants to invest $3,800.00 in a savings account that pays 4.8% simple interest.
How many years will it take for this investment to triple in value? Round your answer to the nearest tenth of a year.
It will take _______ years for this investment to triple in value.
Answer:
It will take 41.7 years for this investment to triple in value.
Step-by-step explanation:
Here is the formula for simple interest
\(A=P(1+rt)\)
Lets solve for \(t\).
Divide both sides by \(P\).
\(\frac{A}{P}=rt+1\)
Subtract 1 from both sides.
\(\frac{A}{P}-1=rt\)
Divide both sides by \(r\).
\(\frac{\frac{A}{P}-1}{r} =t\)
To write \(-1\) as a fraction with a common denominator, multiply by \(\frac{P}{P}\) .
\(\frac{\frac{A}{P}-1*\frac{P}{P}}{r} =t\)
\(\frac{\frac{A}{P}*\frac{-P}{P}}{r} =t\)
Combine the numerators over the common denominator.
\(\frac{\frac{A-P}{P} }{r} =t\)
Multiply the numerator by the reciprocal of the denominator.
\(t=\frac{A-P}{Pr}\)
We are given
\(P=3800\\r=0.048\)
We need to find what amount is triple his money.
\(3800*3=11400\)
\(A=11400\)
Substitute our numbers into the equation for \(t\).
\(t=\frac{11400-3800}{3800*0.048}\)
Factor 3800 out of 11400.
\(t=\frac{3800*3-3800}{3800*0.048}\)
Factor 3800 out of −3800.
\(t=\frac{3800*3-3800*-1}{3800*0.048}\)
Factor 3800 out of \(3800*3-3800*-1\).
\(t=\frac{3800*(3-1)}{3800*0.048}\)
Cancel the common factor of 3800.
\(t=\frac{3-1}{0.048}\)
Simplify.
\(t=\frac{2}{0.048}\)
\(t=41.666\)
Merry Christmas!
15m+20g=300
m+g=17
solve by elimination and SHOW YOUR WORK
Answer:
change the order, so the terms line up
20g+15m=300
g+m=17
multiply the second equation by 20, so the 20g and -20g can cancel out
20g+15m=300
-20g-20m=-340
solve the equation, then divide -5 to both sides to isolate the m
-5m=-40
m=8
substitute the value of m into one equation to find the other value
g+8=17
g=9
write them in ordered paired form
(9, 8)
Step-by-step explanation:
hope this helps :)
What is the probability of rolling 5 dice and all of them landing on number 6?
The dice is a 6 sided dice
Answer:
the probability would be 1/6
What did I do wrong here? It's timed so please help me :(
x + 9 = 5x - 11
-5x -5x
-4x + 9 = -11
- 9 -9
-4x = -20
x = -5
Answer:
5
Step-by-step explanation:
5x-x=-11-9
4x=-20/4
x=5
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = \(\frac{1}{2}\) × 100° = 50°
noah has a part-time job at a coffee shop. Last month he earned $160. Noah pays an income tax rate of 10%. How much does Noah earn after tax?
Noah earned $160 last month, and his income tax rate is 10%. To calculate how much he earns after tax, we need to subtract the tax amount from his earnings.
The tax amount is equal to 10% of his earnings, which is:
0.1
×
160
=
16
0.1×160=16
Therefore, Noah's earnings after tax is:
160
−
16
=
144
160−16=144
Noah earns $144 after tax.
Priya hiked 1 2/3 miles. Diego hiked 1/2 mile. How much farther did Priya hike than Diego?
By taking the difference between the distances, we see that Priya hiked (1 + 1/6) miles more than Diego.
How much farther did Priya hike than Diego?To find this, we just need to take the difference betwee the two distances given.
We know that Priya hiked 1 2/3 miles and Diego hiked 1/2 mile, then the difference is:
D = (1 + 2/3) mi - (1/2) mi
D = (1 + 2/3 - 1/2) mi
D = (1 + 4/6 - 3/6) mi
D = (1 + 1/6) mi
We can see that Priya hiked (1 + 1/6) miles more than Diego.
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The distance farther Priya hike than Diego is 1 1 / 6 miles.
How to find distance travelled?Priya hiked 1 2/3 miles. Diego hiked 1/2 mile. Therefore, let's find how much farther Priya hiked than Diego.
Hence,
Distance hiked by Priya = 1 2 / 3 = 5 / 3 miles
Distance hiked by Diego = 1 / 2 miles
Therefore,
Amount of distance farther Priya hiked than Diego = 5 / 3 - 1 / 2
Amount of distance farther Priya hiked than Diego = 10 - 3 / 6
Amount of distance farther Priya hiked than Diego= 7 / 6 miles
Amount of distance farther Priya hiked than Diego = 1 1 / 6 miles
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