The free fall speed of a parachutist can exceed 216 kilometres per hour. During his 20 seconds of free fall, the parachutist will plunge 1960 metres.
What is Acceleration ?Every time an object is subject to a net force that is greater than zero, acceleration happens. You can experience it when riding down a steep hill on your sled in the snow or when you slightly accelerate or decelerate in an elevator. Furthermore, we know that the universe as a whole is expanding at an even faster rate because to the general theory of relativity. This implies that the distance between two places is always enlarging, yet we are oblivious to this on a daily basis because every scale in the universe also expands.
During free only acceleration due to gravity(g) acts on the parachutist. Assuming acceleration due to gravity is positive i.e. g=9.8m/s² .
For conversion we know that
1 km = 1000 m and
1 hr = 3600 seconds
216 km/hr = 60 m/s
Location of parachutist during 20 seconds
[tex]h = \frac{1}{2} \times g \times t^2[/tex]
[tex]h=\frac{1}{2} \times 9.8 \times 20^2[/tex]
h = 1960 meters
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WHAT WILL YOU WEAR?
You are getting ready for Thanksgiving dinner and trying to find the perfect outfit. You want to wear your new sweater from Infinity21. The manufacturer advertises that this sweater is most comfortable to wear when the temperature satisfies |t-56| ≤6 degree: Fahrenheit. The weaather report says it will be 53°F on Thanksgiving Day at mealtime.
Can you wear your new sweater comfortably?
By solving a linear inequation, it can be concluded that
The sweater can be worn comfortably
What is a linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥
A one degree inequation is known as linear inequation.
Here, the given linear inequation is
[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]
As 53° F lies between 50 and 62, the sweater can be worn comfortably
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convert 1/2 into a decimal
Answer:0.5
Step-by-step explanation:
here you go
Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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Why is it important to make ten?
It is important to make a ten in lower grades to make students understand the subtraction.
According to the question,
We have the following information:
Making a ten
Now, we know that in making a ten method we take 1 from the next left digit of the number from which we are subtracting any other number. Now, this number 1 is treated as 10 instead of 1 and then 10 is added to the digit to ease subtraction in lower grades.
Now, the subtraction can be easily performed by subtracting the smaller number from the larger number.
Hence, it is important to make tens in lower grades to make students understand the subtraction.
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if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
please rate as brainliest
Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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Find the number of distinguishable permutations of the letters in each word below.
(a) bigger
(b) Hollywood
(c) possess
The number of distinguishable permutations in the given letters are:
a.) Bigger= 720
b.) Hollywood = 362,880
C.) possess = 5040
What is permutation?Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.
The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720
For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880
For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.
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if somthing costid 64 dolers and thay sold it for 90% of the originol price how much wold it be
?
Answer:
6.40
Step-by-step explanation:
For this we will divide,
look below for a explanation
Purchase Price:
$64
Discount:
(64 x 90)/100 = $57.60
Final Price:
64 - 57.60 = $6.40
Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
problem A: What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
Problem B: What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
problem C: What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green?
problem D: Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probability for each event are
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
[A] -
{3/12} x {3/11} x {4/10} =
36/1320
[B] -
{3/12} x {4/11} x {3/10}
36/1320
{C} -
{4/12} x {3/11} x {3/10}
36/1320
D) The probability doesn’t change in any order.
Therefore, the probability for each event are -
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
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Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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How do you know if AB and CD are congruent?
If the length of two segments is equal then the two segments are congruent.
If l(AB) = l(CD) then seg AB ≅ seg CD.
Two line segments to be congruent if and only if they have the same length.
Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.
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André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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A recipe for flapjacks uses only syrup, butter and oats, in the ratio 1: 2: 3
a) Trevor makes some flapjacks using this recipe and uses 200g of syrup.
(i) What quantity of butter should he use? _________g
(ii) What quantity of oats should he use? _________g
b) Using this recipe, 150g of syrup are needed to make 8 flapjacks. Find the quantity of oats needed to make 16 of these flapjacks.
Answer: _____g
By using Unitary method, it can be calculated that
a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) 900 g of oats is required to make 16 flapjacks
What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here Unitary method will be required
a) Let Trevor use x g Syrup, 2x g butter and 3x g oats
Trevor uses 200 g syrup
So x = 200
i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) To make 8 flapjacks 150 g of syrup is used
To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used
To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used
To make 16 flapjacks 300g of syrup is used
To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used
To make 16 flapjacks 900 g of oats is used
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help me i dont get this at all
Answer: 18
D
Step-by-step explanation:
The constant of proportionality is y/x, not x/y, which is what your friend found.
X= 1
y=18
18/1=18
EVALUATE ₈C₇ and ₁₁P₅
₈C₇=
₁₁P₅=
The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440
How to determine the permutation and combination expressions?From the question, we have
⁸C₇ and ¹¹P₅
The combination expression: ⁸C₇
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 8 and r = 7
Substitute the known values in the above equation
Total = ⁸C₇
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
⁸C₇ = 8!/7!1!
Evaluate
⁸C₇ = 8
(b) The permutation expression: ¹¹P₅
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 11 and r = 5
Substitute the known values in the above equation
Total = ¹¹P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)
So, we have
¹¹P₅ = 11!/6!
Evaluate
¹¹P₅ = 55440
Hence, the values are 8 and 55440
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Look at the transformation of a 2-dimensional shape on the coordinate plane.
(x, y)→(−y,−x)
Which statement is true?
In the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x), the statement which is true is that: d. Transformation preserves distance and angle measure both.
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
Based on the transformation rule (x, y) → (-y, -x), we can reasonably infer and logically deduce that it represents or models a rotation of the geometric shape, followed by a reflection, which both preserves distance and angle measure based on these transformation rules:
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Complete Question:
Look at the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x). Which statement is true?
a. Transformation preserves only distance.
b. Transformation preserves only angle measures.
c. Transformation preserves neither distance nor angle.
d. Transformation preserves distance and angle measure both.
You read 6 chapters. Each chapter has 8 pages. Your brother reads the same number of pages. His chapters have 12 pages. How many chapters does your brother read?
The sixth chapter's Brother 0.66 pages were read.
How to calculated the chapters in 12 pages?According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.
Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.
Assumed the question is how many pages are in each chapter.
Let it be x:
6x + 8 = 12
6x = 4
x = 4 /6
x = 0.66.
The sixth chapter's Brother 0.66 pages were read.
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5 2/3 divided by 2 1/8 Perform the indicated operation.
Answer: 2 and 2/3
Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.
You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.
So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.
This gives us 17/3 ÷ 17/8.
When we divide fractions, we just change the division sign
to multiplication and take the reciprocal (flip) the second fraction.
So we have 17/3 · 8/17.
before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.
So we have 1/3 · 8/1 which is 8/3.
Now since 3 goes into 8 twice, our we have 2 as our whole fraction.
Since there is 2/3 left over, we have a fraction of 2/3.
So our final answer is 2 and 2/3.
What is the rule of proof?
The rules of proof is that every statement should be justified and never assume things when proofing in contradiction
The basic rules of proofs are as followings:
Each assertion should be legitimate.A support can allude to earlier lines of the verification, the speculation as well as recently demonstrated explanations from the book.Cases are frequently expected to finish a proof which has proclamations with an "or" in them.A logical inconsistency is reached when an assertion goes against any of the speculations, an earlier line of the confirmation, or any well established truth .A proof by logical inconsistency is possibly finished when a logical inconsistency has been arrived at for each situation.On the off chance that you can't find a defense and you are certain it is valid, you might wish to compose a separate verification as an after thought to demonstrate that support and afterward apply it to your unique circumstanceDuring a proof you might present new factors by saying "Let x be..."To know more about Proof here
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Match each equation with a graph above:
log (x) a. red R
10× b. black K
e× c. green G
ln (x) d. blue B
The equations are matched as below and the graph is plotted and attached
log (x) b. black K 10× d. blue Be× c. green Gln (x) a. red RWhat is logarithm graph?A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.
The exponential graph is the opposite of logarithmic graph
In the given functions
log (x) is logarithmic function
10× is exponential function
Similarly, the natural exponent graph is the opposite of natural logarithm graph
in the given functions
e× is the natural exponential
ln (x) is the natural logarithm
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what are the 12 kinds of polygons
The 12 kinds of polygons are:
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Tridecagon
Tetradecagon
Polygons:
A polygon is a closed shape figure that has a minimum of three sides and three vertices.
Poly → many
gon → angle
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Look at the pattern.
72, 67, 62, 57
Which of these is the rule for the pattern?
a
b
d
subtract 5
add 5
subtract 9
add 9
Answer:
Subtract 5
Step-by-step explanation:
72 , 67, 62, 57,..
Each term is obtained by subtracting 5 from the previous term.
72 - 5 = 67
67 - 5 = 62
62 - 5 = 57
What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 80 less than the sum of the measures of the base angles?
Answer: 65 °
Step-by-step explanation:
Let x = measure of a base angle
Base angles of an isosceles triangle are equal
Sum of interior angles of a triangle is always 180:
x + x + (2x - 80) = 180
4x - 80 = 180
4x = 260
x = 65
This exercise uses, the population growth model
A culture starts with 8300 bacteria, After 1 hour the count is 10,000 .
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t)=8300(1)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
17485.75 x bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
50times
P is equal to 8700% for population x time in hours.
What is population growth model?P is equal to 8700% for population x time in hours. 2Ae%5E%28kx%29
K's model must be solved. ln%28p%29=ln%288700%29%
2Bkx%2Aln%28e%
29\skx%
2A1=ln%28p%29-ln%288700%
29\sk=%281%
2Fx%29%
28ln%28p%29-ln%288700%29%29
Replace the point (1,10000).
k=%281%
2F1%29%
28ln%2810000%
29-ln%288700%
29%
29\sk=ln%2810000%
29-ln%288700%
29 k=0.13926, which you might only desire to three or maybe even two significant figures.
You may just enter 10000% if you want p after two hours.
And it SHOULD be the same as 8700% (2810000%2F8700%).
Just give it a shot and see, 2Ae%5E%280.139%2A2%29. More particular, the model is highlighted by p=8700%. 2Ae%5E%280.139% 2Ax%29% 29.
Determine how long to double x.
Take the logs on both sides, then find x.
To put it more simply, start with this form: 2=1%2Ae%5E%280.13926%2Ax%29
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Graph -7x+5y=35−7x+5y=35minus, 7, x, plus, 5, y, equals, 35.
Answer:
835786543225644323567
A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
Write an expression to represent: 8 less than the product of 2 and x.
please help!
Jocelyn has a points card for a movie theater.
She receives 25 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Jocelyn can make to earn her first free movie ticket.
Answer:
25 + 12.5v ≤ 170
Step-by-step explanation:
which number line represents the solution set for the inequality 4x 3 2 2x
The solution to the inequality expression is x ≥ - 5
what is inequality expressions ?
Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.
solution:
The given expression - 4(x + 3) ≤ –2 – 2x
- 4x - 12 ≤ -2 - 2x
-4x + 2x ≤ -2 + 12
-2x ≤ 10
-x ≤ 5
Multiply both sides by - 1
Then x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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What does it mean when the discriminant is greater than 0?
We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.
An discriminant value definition ?
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
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