Answers
Answer:
Convergence
Step-by-step explanation:
Use the Squeeze Theorem,
I know that
[tex] \frac{k \sin {}^{2} (k) }{1 + k {}^{3} } [/tex]
lies between 0 and 1 so
[tex]0 \leqslant \frac{k \sin {}^{2} (k) }{1 + {k}^{3} } \leqslant \frac{k}{1 + k {}^{3} } [/tex]
The final series behaves like
[tex] \frac{1}{k {}^{2} } [/tex]
Using the p series, since p is 2, the series
[tex] \frac{k}{1 + k {}^{3} } \: converges[/tex]
Since the 0 and k/1+k^3 converges, the series converge.
Convergence
Related Questions
2. [5 pts] On a certain route, an airline carries 6,000 passengers per month, each paying $200. A market
survey indicates that for each $1 increase in the ticket price, the airline will lose 100 passengers.
Express the number of passengers per month, N, as a function of the ticket price, x. (Assume x ≥ 200.)
Answers
For the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :
N(x) = 26,000 - 100x where x ≥ 200.
As given in the function,
Number of passengers carried by airlines per month = 6,000
Price of ticket of each passenger = $200
For each $1 increase in the ticket price lose of 100 passengers
Let N(x) be the function representing the number of passengers
And x represents the price of the ticket where x ≥ 200.
Required function to represent the number of passengers is given by :
N(x) = 6,000 -100 ( x -200)
⇒ N(x) = 6,000 -100x + 20,000
⇒ N(x) = 26,000 -100x where x ≥ 200
Therefore, for the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :
N(x) = 26,000 - 100x where x ≥ 200.
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Which of the following traits do histograms, Pareto charts, and scatter plots have in common?
a) They are all bar charts.
b) They are all visual tools to display data.
c) They all show change over time.
d) All of the above.
Answers
The correct option is option (B) .
In other words Histograms , Pareto charts and scatter plots have a common thing that they are all visual tools to display data.
Histogram :
It show continuous data in ordered rectangular columns. There are usually no gaps between columns.
Histograms show the frequency distribution (shape) of a data set.To graphically summarize large datasets.Scatterplot :
A scatterplot is an x-y plot that shows the relationship between two variables. Used to plot data points on vertical and horizontal axes.
Predicts the behavior of the dependent variable based on the scale of the independent variable. If you just want to visualize the correlation between two large datasets without considering hours.Pareto Chart :
A Pareto chart is a common tool used by manufacturers to analyze quality and defect data, providing a quick visual representation of the frequency and cumulative percentage of occurrences of a particular problem.
A Pareto chart is a combination of a bar chart and a line chart.Hence , all of three have a common thing that is they visualize tools to represent the data
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IXL Please Help Fast!
Answers
Answer:
y = 1/2 x + 3/2
Step-by-step explanation:
A perpendicular slope is the opposite reciprocal, so it is 1/2
2 = 1/2(1) + b To solve for b
2 = 1/2 + b Subtract 1/2 from both sides
1 1/2 = b
y = 1/2 x + 3/2
In 2017, the library was able to record 4907 borrow books. By December of the same year, the library has 6 times its January record. The library’s December record is ?
Answers
The library’s December record is 29442
Mathematical Operations:Mathematical operations are Operators which emphasize particular actions like adding, subtracting, adding multiple times, dividing, etc.
There are 4 basic operations in mathematics as given below.
1. Addition => (+)
2. Subtraction => (-)
3. Division => (÷)
4. Multiplication => (x)
Here we have
In 2017 the library was able to record 4907 borrowed books
By December of the same year, the library has 6 times its January record.
[ Here we use Multiplication to find the December record ]
The December record = 6 times of January record
⇒ 6 × January record
⇒ 6 × 4907
⇒ 29442
Therefore,
The library’s December record is 29442
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Which is more, 6 liters or 6,001 milliliters?
Answers
Answer: 6,001 milliliters
Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.
Answer:
I believe 6 liters is more.
Find the retail price of each item. Round to two decimal places when necessary.
Cost of oil change: $18.00
Markup: 70%
Answers
well, we know the price is $18, now, if we jack it up by 70%, well, what's 70% of 18?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 18}}{\left( \cfrac{70}{100} \right)18}\implies 12.6~\hfill \underset{price}{\stackrel{18~~ + ~~12.6}{\text{\LARGE 30.60}}}[/tex]
The height (in feet) of a falling object with an initial velocity of 48 feet per
second launched straight upward from the ground is given by
h(t) =
16t2 + 48t where
is time (in seconds). What iS the average rate of
change of the height as a function of time from
= 1 to
2
Answers
The average rate of change of the height as a function of time from 1 to 2 is 96
Rate of change
Rate of change defines the ratio that compares the change in values of the y variables to the change in values of the x variables.
Given,
The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by h(t) = 16t² + 48t where is time (in seconds).
Here we need to find the average rate of change of the height as a function of time from 1 to 2.
In order to find the average rate of change we need to find the value for the time 1 and time 2.
For, that we have to apply the value on the function,
First, we have to apply the value of t as 1, then we get the value of the function as,
h(1) = 16(1)² + 48(1)
h(1) = 16 + 48
h(1) = 64
Now, we have to apply the value of t as 2, then we get,
h(2) = 16(2)² + 48(2)
h(2) = (16 x 4) + 96
h(2) = 64 + 96
h(2) = 160
Therefore, the average rate of change is,
=> rate of change = (160 -64) / 2 - 1
=> rate of change = 96
Therefore, the average rate of change from 1 to 2 is 96.
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Banerjee Company began its operations in September of the current year. During September, the company paid wages of $23,400. For the last quarter of the year, the taxable wages paid amounted to $64,700. None of the employees was paid more than $7,000 this year. a. Is Banerjee Company liable for FUTA tax this year? Yes b. If your answer to part a above is "Yes", what is the net FUTA tax for the year? Round your answer to the nearest cent.
Answers
Banerjee Company is liable for FUTA tax this year and the net FUTA tax for the year is $528.60.
How to find the net FUTA tax?a. Yes. Banerjee Company liable for FUTA tax this year.
b. FUTA tax
FUTA tax =0.6%
Hence,
Net FUTA tax = (Wages paid × tax rate ) +(Taxable wages × Tax rate)
Net FUTA tax = ($23,400 × 0.6%) + ($64,700 ×0.6%)
Net FUTA tax = $140.40 + $388.30
Net FUTA tax =$528.60
Therefore $528.60 is the Net FUTA tax.
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The length of the vector that represents z₁ = 6-8i is 10 because √6² + (-8)² = √√100 = 10.
a.
Find at least seven other complex numbers that can be represented as vectors that have length 10.
Answers
The vectors having length of 10 units are,
-6 + 8i , 10 , 10i , -10 , -10i , 3 + 9i , -3 + 9i
We have to find the seven complex numbers that have the length of 10 units.
So, the vectors having length of 10 units are,
1) -6 + 8i
2) 10
3) 10i
4) -10
5) -10i
6) 3 + 9i
7) -3 + 9i
Hence, the vectors having length of 10 units are,
-6 + 8i , 10 , 10i , -10 , -10i , 3 + 9i , -3 + 9i
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What is the equation for the parabola graphed below
Answers
Answer:
[tex]y = x^2 - 2x -1[/tex]
Step-by-step explanation:
General Form of a parabola :
[tex]y = a (x - h)^2 + k[/tex]
Solving :
h and k refer to the point of the vertex. In this case, it's (1, -2), so :
[tex]y = a(x - 1)^2 - 2[/tex]
Plug in values for x and y. In this case, they're (0, -1), so :
[tex]-1 = a(0 - 1)^2 - 2\\-1 =a(1) - 2\\1 = a[/tex]
Plug in all values :
[tex]y = ( x - 1)^2 -2[/tex]
Further simplifying :
[tex]y = ( x - 1 )^2 - 2 \\y = (x^2-2x + 1) - 2\\y = x^2 - 2x -1[/tex]
NO LINKS!! Please help me with the Angle Proofs Part 3
Answers
Answers in bold
GivenDefinition of complementaryGivenDefinition of congruenceVertical anglesDefinition of congruenceSubstitution propertyDefinition of complementary==============================================
Explanation:
Always start with what is given. The last statement is the thing we want to prove.
Complementary angles add to 90 degrees. They form a right angle.
When "definition of congruence" is mentioned, we go from two angles being congruent to having them be of the same measure. It's a slight change of notation.
Vertical angles form whenever we cross two lines to form an X shape. The vertical angles are opposite one another, and always congruent.
The substitution property is the idea of replacing one thing with something it is equivalent to. In other words, we plug in the item.
Notice on line 2, if we replace "angle 1" with "angle 4" (valid because the two angles are congruent), and then replace "angle 2" with "angle 3", then we get the result on line 7.
Answer:
1. Given.
2. Definition of complementary angles.
3. Given.
4. Definition of congruent angles.
5. Vertical Angles Theorem.
6. Definition of congruent angles.
7. Substitution Property of Equality.
8. Definition of complementary angles.
Step-by-step explanation:
Statement 1
∠1 and ∠2 are complementary.
Reason: Given.
Statement 2
m∠1 + m∠2 = 90°
Reason: Definition of complementary angles.
Complementary angles are two angles that sum to 90°. Therefore, if ∠1 and ∠2 are complementary, then their measures must sum to 90°.
Statement 3
∠1 ≅ ∠4
Reason: Given.
Statement 4
m∠1 = m∠4
Reason: Definition of congruent angles.
Congruent angles are angles with exactly the same measure. As angle 1 is congruent to angle 4, then their measures are equal.
Statement 5
∠2 ≅ ∠3
Reason: Vertical Angles Theorem.
Vertical angles are always congruent.
Statement 6
m∠2 = m∠3
Reason: Definition of congruent angles.
Congruent angles are angles with exactly the same measure. As angle 2 is congruent to angle 3, then their measures are equal.
Statement 7
m∠4 + m∠3 = 90°
Reason: Substitution Property of Equality.
For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.
As m∠2 = m∠3 and m∠1 = m∠4, replacing them in m∠1 + m∠2 = 90° gives m∠4 + m∠3 = 90°.
Statement 1
∠3 and ∠4 are complementary.
Reason: Definition of complementary angles.
Complementary angles are two angles whose sum is 90°. Therefore, if the sum of m∠4 and m∠3 is 90°, this means that ∠4 and ∠3 must be complementary.
someone please help tysm
Answers
Among the equations and inequality the true expression is 1 / 3 × 9 = 3.
How to solve inequality and equation?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Therefore, let's check the inequality that is true.
Hence,
1 / 4 × 28 > 8
28 / 4 > 8
7 > 8 (false)
1 / 6 × 48 < 5
48 / 6 < 5
8 < 5 (False)
1 / 3 × 9 = 3
9 / 3 = 3
3 = 3(True)
1 / 5 × 25 = 125
25 / 5 = 125
5 ≠ 125(False)
1 / 6 × 24 > 9
24 / 6 > 9
4 > 9 (False)
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If two dice are rolled one time, find the probability of getting these results. Show all possible combinations. Express the probability as a fraction of 36
A 3 on one die or on both dice
A sum greater than or equal to 10
Answers
Step-by-step explanation:
any particular result with 2 dice has a probability of
1/6 × 1/6 = 1/36
a 3 on one die or both simply means at least one 3.
so, if all the 36 different outcomes we are looking at
3 1
3 2
3 3
3 4
3 5
3 6
1 3
2 3
4 3
5 3
6 3
the 3 3 combination can be counted only once !
so, we have 11 desired outcomes out of the possible 36.
so, the probability of getting at least one 3 is
11/36
the sum of at least 10 means the corresponding cases
4 6
5 5
5 6
6 4
6 5
6 6
in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.
so, we have 6 desired outcomes of the 36.
the probability of that is
6/36 = 1/6
help with this question please!
Answers
Answer:
A. TPR
B. NM
C. 6
Step-by-step explanation:
1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.
2. If you flip PRT then TR will match with NM
3. 4x-3=21
4x-3+3=21+3
Simplify: 4x=24
4x/4=24/4
x=6
How many seven-digit numbers can be formed with the digits of 2201213?
Answers
There are 420 arrangements for seven-digit numbers that can be formed with the digits of 2201213 by permutation.
What is permutation?The term permutation is simply the process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.
We can apply the formula for permutation;
[tex]p(n,r) = \frac{n!}{(n - r)!}[/tex]
where n = total number of object and r = number of objects selected.
Total number of digits = 7
number of the digit 2 = 3
number of the digit 1 = 2
number of the digit 0 = 1
number of the digit 3 = 1
so the permutation for the digits 2201213 is calculated as;
7!/(3! × 2! × 1! × 1!)
(7 × 6 × 5 × 4 × 3!)/(2 × 3!) {cancel out 3! with 3! and 4 with 2}
7 × 6 × 5 × 2
420 arrangements
Hence, by permutation, we can say that there are 420 arrangement for which seven-digit numbers can be formed with the digits of 2201213
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(100 POINTS AND BRAINLYEST JUST PLEASE ANSWER)
1.) An algae bloom is threatening to cover Grand Lake St. Mary’s near Celina, Ohio. The EPA needs to calculate the surface area of the lake to treat the algae bloom. Estimate the area of the irregular shape.
A) Draw on the map to show what method was used to find the area of the lake. (2 points)
B) Show work to estimate the area of the lake in square units. Attach additional paper if necessary. (2 points)
C) Each unit on the grid is 0.25 miles. Find the actual estimate of the area of the lake. (2 points)
Answers
The area of the irregular shape is 288 sq. units
Given,
An algae bloom is threatening to cover Grand Lake St. Mary’s near Celina, Ohio.The EPA needs to calculate the surface area of the lake to treat the algae bloomWe have to estimate the area of the irregular shape;
Here,
The shape can be broken down into a trapezoid, a rectangle, and a triangle
The area of the trapezoid = 1/2 × 12 × 9 × (7 + 10) = 76.5 sq. unitsThe area of the rectangle = 7 × 20 = 140 sq. unitsThe area of the triangle = 1/2 × 11 × 13 = 71.5 sq. unitsThe total area = 76.5 + 140 + 71.5 = 288 sq. units
Therefore,
The area of the irregular shape is 288 sq. units
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He purchases a total of 150 containers of popcorn to sell. After he sells 15 containers, he will make a total profit, after his upfront costs, of $5.50. Cassidy’s profit, after upfront costs, can be modeled by a linear function in the form y=mx+b.
What is Cassidy’s profit if he sells all of the popcorn?
HInt:Substitute 150 for x to find the profit if all the popcorn is sold.
Answers
If Cassidy sells all of the popcorn, his profit would be equal to $208.00.
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be modeled by using this linear function:
y = mx + b
Where:
m represents the slope.x and y are the points.b represents the y-intercept.How to determine Cassidy’s profit?In order to determine Cassidy’s profit, we would have to calculate the cost of the containers of popcorn by using this mathematical expression:
Note: the price tag for a container of popcorn is one dollar and fifty cents.
Cost of containers = revenue - total profit
Cost of containers = 1.50(15) - 5.50
Cost of containers = 22.5 - 5.50
Cost of containers = $17.00
Therefore, the linear function which models Cassidy’s profit is given by:
y = 1.50x - 17
If Cassidy sells all of the popcorn, his profit is given by:
Cassidy’s profit, y = 1.50x - 17
Cassidy’s profit, y = 1.50(150) - 17
Cassidy’s profit, y = 225 - 17
Cassidy’s profit, y = $208.00
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Complete Question:
Cassidy is selling popcorn for a fundraiser sale at the price shown.
A photo of a container of popcorn is shown. The price tag reads one dollar and fifty cents.
He purchases a total of 150 containers of popcorn to sell. After he sells 15 containers, he will make a total profit, after his upfront costs, of $5.50. Cassidy’s profit, after upfront costs, can be modeled by a linear function in the form y=mx+b.
What is Cassidy’s profit if he sells all of the popcorn?
HInt: Substitute 150 for x to find the profit if all the popcorn is sold.
In triangle XYZ, m∠Z = (2m − 12)° and the exterior angle to ∠Z measures (3m + 7)°. Determine the value of m.
m = 42
m = 37
m = 19
m = 2.6
Answers
Answer:
m = 37
Step-by-step explanation:
The interior and corresponding exterior angle of a triangle are always supplementary.
Therefore, we can set the sum of the two given angle measures to 180°:
[tex](2m-12) \textdegree + (3m+7) \textdegree = 180 \textdegree[/tex]
and solve algebraically for m.
[tex]2m-12 + 3m+7 = 180[/tex]
[tex](2m + 3m) + (-12+7) = 180[/tex]
[tex]5m-12+7 = 180[/tex]
[tex]5m - 5 = 180[/tex]
[tex]5m = 185[/tex]
[tex]m=37[/tex]
The value of m is 37.
What is Linear pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Given:
m ∠Z = (2m − 12)° and exterior angle ∠Z =(3m + 7)°.
int. m <Z + ext. <Z= 180
2m - 12 + 3m + 7 = 180
5m - 5 = 180
5m = 185
m = 185/ 5
m = 37
Hence, the value of m is 37.
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A house mover towed a historic Victorian home 45 miles to locate it on a new site. On his return, without the heavy house in tow, his average speed was 30mph faster and the trip was 2 hours shorter. How fast did he drive in each direction?
Answers
The required speed is 45 mph in each direction.
What is speed?
The definition of speed is a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.
We know that distance=rate*time
d=rt
45=rt
45=(r+30)(t-2)
rt=(r+30)(t-2)
This shows,
rt=rt+30t-2r-60
0=30t-2r-60
if 45=rt, then r=45/t
substitute in the equation
0=30t-2(45/t)-60
multiply both sides by t
0=30t²-90-60t
on solving this quadratic equation, we get t= 3 s, t=-1 s
consider positive value
t=3 hours
45=rt
45=r*3
r=45/3 =15 mph to new site
r+30=15+30=45 mph returning
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The reflection of (-2,-2) is ...
The reflection of (-1,1) is...
please help meeeeeeeeeee
Answers
The reflection of (-2, -2) and (-1, 1) are
preimage image
(-2, -2) (-4, -2)
(-1, 1) (-5, 1)
What is reflection?Reflection is one of the movements in transformation that involve creation of mirror image
Transformation rule for reflection over x-axis at origin (0, 0)) is
(x, y) → (x, -y)
Transformation rule for reflection over line y-axis at origin (0, 0)) is
(x, y) → (-x, y)
The reflection to be done is over line x = -3
However, reflection over line x = -3 which is (-3, 0) is done as follows
from -2 to -3 = -2 - -3 = 1 unit
reflecting 1 unit over x = -3
-3 - 1 = -4
(-4, -2)
(-2, -2) ⇒ (-2 - -3, -2) ⇒ (1, -2) ⇒ (-3 - 1, -2) → (-4, -2)
from -1 to -3 = -1 - -3 = 2 units
reflecting 2 units over x = -3
-3 - 2 = -5
(-5, 1)
(-1, 1) ⇒ (-1 - -3, 1) ⇒ (2, 1) ⇒ (-3 - 2, 1) → (-5, 1)
The calculation is simply saying put
(-2, -2) this point is just before the reflection line, the image will formed at the point just after the reflection line -3 which is -4 hence (-4, -2)
(-1, 1) this point is a line before the reflection line, the mirror image will be formed skipping a line (-4) to get to -5 hence the point (-5, 1)
the y coordinate is constant for both situations
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Divide.
5.3696
0.001
Answers
I need help with this please help me
Answers
Answer:
m∠1 = 126°
m∠2 = 154°
Step-by-step explanation:
First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)
We know that the measures of the interior angles of a triangle add to 180°.
Therefore,
m∠A + 96° + 30° = 180°
m∠A + 96° = 150°
m∠A = 54°
From this value, we can solve for m∠1, since it is supplementary to ∠A:
m∠A + m∠1 = 180°
54° + m∠1 = 180°
m∠1 = 126°
To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.
First, the measures of the interior angles of a triangle add to 180°:
28° + m∠1 + m∠B = 180°
28° + 126° + m∠B = 180°
m∠B = 26°
Finally, we can solve for m∠2 because it is supplementary to ∠B.
m∠B + m∠2 = 180°
26° + m∠2 = 180°
m∠2 = 154°
In math class 20% of the students did not finish their quiz. If 24 students finished their quiz, how many students are in math class?
Answers
Answer: 30 kids are in the math class
Step-by-step explanation: A simple way to solve this question is by knowing divisors. Since 24 is only 80% of X, then look for common divisors betweet 24 and 80% (4) If 6 is 20%, then 30 is 100%
if parallel lines are cut by transversal then there interior angles on the same side of the transversal are blank.
Answers
Anlges on the same side of the transversal add up to 180 degrees.
What is Transversal?
A transversal is a line in geometry that connects two lines in the same plane at two separate places. Transversals help determine if two or more lines in the Euclidean plane are parallel.
Solution:
Using the property of Lineaar Pair Angle the Interior Angles on the same side of the Transversal add up to 180 degrees.
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Subtract using the number line -2 -(+7)
Answers
The answer is -9.
-2 -(+7) = -2 -7
-2 -7 = -9
Which point below is a solution to the equation y = 2x − 5?
(1, -3)
(4, 2)
(-1, -5)
(2, 0)
Answers
Sorry I don't have the answer but I can rule out 2.
Step-by-step explanation:
4,2 and 2,0 are not going to be correct because I got them wrong on a quiz I had 2 attempts to take.
So its either 1,-3 or -1,-5.
Hope this helps you.
A submarine descends -3.5 meters per minute. How far will the submarine descend in 8 minutes?
How do you know your answer will be negative?
Answers
Answer:
-28 meters
Step-by-step explanation:
The speed of the submarine = (-3.5) per minute
Since it's descending, we know the answer will be negative.
The distance covered by the submarine is 8 minutes = (-3.5) x 8 = -28 meters.
Answer:
28
Step-by-step explanation:
-3.5*8
40 POINTS PLS ANSWER FAST
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS
SSS
SAS
HL
Answers
Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem
Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He
received both payments in May 2019. When is the next time he would receive both
payments in the same month?
Answers
AS per the combination method, Mr. Walters receive both payments in the same month in the 6th time.
Combination method:
A way of adding equations together in such a way that the variables are set aside, one by one is called as combination.
Given,
Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He received both payments in May 2019.
Here we need to find the next time he would receive both payments in the same month.
While looking into the given question we have identified he following things,
Dividend payment = 5 months
Royalty payment = 6 months
Both payment received = May 2019.
So, according to the combination method,
The value of n = 6 and the value of x = 5
So, the next time he would receive both payments in the same month is
=> 6 C 5 = 6! / 5! (6 - 5)!
Which results the value as 6.
Therefore, on 6th time from this payment he will receive both in the same month.
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The lumber store sells planks in 8 foot pieces. They have an error
tolerance of 4%, What is the minimum length that you can buy
and what is the greatest length you can buy?
Answers
The minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot
The length of the planks that lumber stores sell = 8 foot
The error tolerance of the plank = 4%
Then the 4% of the length 8 is
= 8 × (4/100)
Divide the terms
= 8 × 0.04
Multiply the terms
= 0.32
Therefore the error tolerance will be ±0.32
The minimum length that you can buy = 8 - 0.32
= 7.68 foot
The greatest length that you can buy = 8 + 0.32
= 8.32 foot
Hence, the minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot
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