The rectangle's area is growing at a rate of 170 cm per second.
Given that,
Area of Rectangle given by.
A = length x width
A = LW
L =length of Rectangle
W =width of Rectangle
Now, dA/dt = W dl/dt + l dw/dt
dA/dt is the rate of change of area of the rectangle
dl/dt is the rate of change of length of the rectangle
dw/dt is the rate of change of width of the rectangle
at L = 40cm, W= 15 cm
dw = 2 cm/s,
dl = 6 cm/s,
dA = ?
dA/dt = W dl/dt + l dw/dt
= 15x6 + 40x2
= 90 +80
=170 cm /sec
Thus, the area of the rectangle increasing at 170 cm /sec
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how do you find proportional relationships? also, while answering this could you give me an example? Whoever CAN ANSWER THIS FIRST I WILL GIVE YPU 20 POINTs
Answer:
A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph.
Step-by-step explanation:
Answer:
simply just divide!
Step-by-step explanation:
okay, here is one example:
in 3 hours, you went 126 miles
In 4 hours, you went 168 miles
In 5 hours, you went 210 miles
So what is the unit rate of the miles(x) per hour(y).
The smallest number would be easier to divide. So you divide 126 and 3 and would be 42 miles.
Then find the quotient for the other ones.
168 divide 4 = 42
210 divide 5 = 42.
What is the same of all of them? 42 is the factor to all of the problems. So the proportional relationship (k) is 42. In a equation it would be y=42x (y=Kx)
To find the next number in the sequence you just multiply (x) with the factor.
In how many ways can a committee of five be selected from eight students if two particular students are to be included
There are 56 ways to choose a committee of students.
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
A committee of five be selected from eight students if two particular students are to be included.
Now,
Since, 2 members are must be included.
So, We have to choose 3 student from 8 student to form a committee.
Hence, The number of ways to choose 3 students from 8 students is,
= [tex]^{8} C_{3}[/tex]
= 8! / (8-3)! 3!
= 8! / 5! 3!
= 8 x 7 x 6 / 3 x 2
= 56
Thus, There are 56 ways to choose a committee of students.
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Rod is looking for professional financial assistance. Rod has a solid grasp of how investing works, but needs a way to handle the actual buying and selling of stocks. Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. Recommend an appropriate financial professional for Ro
If Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. The appropriate financial professional for Rod is: a. Discount broker.
Who is a discount broker?A Discount broker can be defined as a type of broker which gives out discount to investor to offers lesser commission fees or rate to investors
Discount broker tend to as well help to handle the buying and selling of stocks and they as well rendered different services to investors. Most investors tend to make use of discount broker instead of full service broker because of the lower commission fees that discount brokers often charge.
Based on the given scenario i will recommend Rod to make use of discount broker as they are professional financial assistance when it comes to buying and selling of stocks.
Therefore the correct option is A.
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The complete question is:
Rod is looking for professional financial assistance. Rod has a solid grasp of how investing works, but needs a way to handle the actual buying and selling of stocks. Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. Recommend an appropriate financial professional for Rod.
a.Discount broker
b.Full-service broker
c.Financial planner
d.Investment Advisor
If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 4 volts
New current if the voltage is increased to 4 volts. = 0.1 A or 100 mA
What is a current simple definition?
The speed at which electrons go past a particular location in an electrical circuit is known as current. Current = flow, at its most fundamental level. The international unit for measuring current is an amp (AM-pir), sometimes known as an amp.amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit.
=> I ∝ V
=> I = V/R
R is a constant
and R is resistance
When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit.
=> 75 x 10⁻³ = 3 /R
=> R = 3 x 10³/75
=> R = 10³/25
=> R = 40
I = V/R
V = 4
R = 40
=> I = 4/40
=> I = 1/10
=> I = 0.1 A
or 100 mA
new current if the voltage is increased to 4 volts. = 0.1 A or 100 mA
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Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead?
Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.
Given statement;
Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.
→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.
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Michael is having party. He'll have 12 tables for every 32 guests. Complete the table below to find the number of guests he can seat with 3
tables.
Number of guests 32
Number of tables 3
In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia.
If Amelia scores 5 points, how many points did Bryce score?
Group of answer choices
A. 6
B. 10
C. 18
D. 5
Answer:
b
Step-by-step explanation:
b
Answer: Amelia 5, Keturah 10, Jordan 6, Bryce 18
Step-by-step explanation:
If Amelia scored 5 and Keturah scored 2 times of Amelia's score, then 5 x 2 is 10, so Keturah scored 10. If Keturah scored 10 and Jordan scored 4 points fewer than Jordan's score, then 10 - 4 is 6, so Jordan scored 6. If Jordan scored 6 and Bryce scored 3 times of Jordan's score, then 6 x 3 is 18, so Bryce scored 18. So C is the correct answer.
Find the slope of the line that contains the points:
(-6, 3) and (-4, 5).
1
-1
-5
-1/5
out of 150 coins, 90 are quarters. of the remaining coins, 40% are nickels and the rest are dimes and pennies. there are 5 dimes for every penny. how many pennies are there?
There are 6 pennies in a total of 150 coins.
Given that,
Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.
and also,
For every penny, there are five dime.
Total = 150 coins
Out of it, 90 are quarters so the remaining coins are 60
It is said that,
In that 60 coins 40% are nickels which means
40% of 60 is 24
So remaining coins are 36 (by subtracting 24 from 60)
It is said that there are 5 dimes for every penny which means
Using Algebra,
x + 5x = 36
6x= 36
x= 6
Therefore, there are 6 pennies in a total of 150 coins.
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Summary Consider the exponent properties (an)m = anm and an bn = (ab)". What is the main difference in these properties? When simplifying an exponential expression, how would you decide which one to use?
The difference between exponents [tex](a^n)^m = a^{mn}[/tex] and [tex]a^nb^n = (ab)^n[/tex] has been described below
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times....... \times a[/tex] (m times), a is the base and m is the index.
The laws of index are-
[tex]a^m \times a^n = a^{m + n}\\a^m \div a^n = a^{m-n}\\a^0 = 1\\a^{-n} = \frac{1}{a^n}\\\\a^m b^m = (ab)^m\\(\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]
In case of [tex](a^n)^m = a^{mn}[/tex], the base is single but in case of [tex]a^nb^n = (ab)^n[/tex], the base is a product of two numbers
If the base can be expressed as a product of different numbers,
[tex]a^nb^n = (ab)^n[/tex] is used
If the base cannot be expressed as a product, then [tex](a^n)^m = a^{mn}[/tex] is used
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The solution of the quadratic equation will be;
⇒ x = - 1 ± √5 / 8
⇒ x = –1 Plus or minus Start Root Start Fraction 5 Over 8 End Fraction End Root.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The quadratic equation is,
⇒ 8x² + 16x + 3 = 0
Now,
Solve the equation as;
⇒ 8x² + 16x + 3 = 0
⇒ 8x² + 16x = - 3
⇒ 8 (x² + 2x) = - 3
Now, Using completing the square as;
⇒ 8 (x² + 2x + 1) = - 3 + 8
⇒ 8 (x + 1)² = 5
⇒ (x + 1)² = 5 / 8
⇒ (x + 1) = ±√5 / 8
⇒ x = ±√5/8 - 1
⇒ x = - 1 ± √5/8
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make y the subject of the formula
k= y^2 + a
Answer:
y = [tex]\sqrt{(k-a)}[/tex]
Step-by-step explanation:
k= y^2 + a
k-a= y^2
y^2 = k-a
y = (k-a)^(1/2)
y = [tex]\sqrt{(k-a)}[/tex]
Answer:
[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]
Step-by-step explanation:
To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².
[tex]\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}[/tex]
Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)
Then square root both sides to get rid of the exponents of y-term:
[tex]\displaystyle{\sqrt{k-a}=\sqrt{y^2}}[/tex]
If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:
[tex]\displaystyle{\pm \sqrt{k-a}=y}[/tex]
Therefore, the new equation written in term of y is:
[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]
What is -900+16-2^3 ?
Answer: -893
Step-by-step explanation: -900 -(+16) = 884 +(-8) = -893
Answer:
-892
-900+16-2^3=-900+16-8=-900+8=-892
2. The lengths of a certain species of fish was
found to be normally distributed. The mean
length is 78 cm with a standard deviation
of 14 cm. In a school of 370 of these fish,
how many would be longer than than
92 cm
So, approximately 59 fish in the school would be longer than 92 cm.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.
Here,
We can solve this problem using the normal distribution formula, which states:
z = (x - mu) / sigma
where z is the standard score, x is the raw score, mu is the mean, and sigma is the standard deviation.
To find the number of fish longer than 92 cm, we need to find the proportion of fish in the population with lengths greater than 92 cm. We can then multiply this proportion by the total number of fish in the school to get the number of fish longer than 92 cm.
First, we calculate the standard score for 92 cm:
z = (92 - 78) / 14
z = 1
Next, we look up the proportion of the standard normal distribution that corresponds to a z-score of 1. We can use a standard normal distribution table or calculator to find this value. The proportion of the distribution that is greater than z = 1 is approximately 0.1587.
Therefore, the proportion of fish in the population with lengths greater than 92 cm is 0.1587. To find the number of fish longer than 92 cm, we multiply this proportion by the total number of fish in the school:
370 * 0.1587 = 58.8
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If you rotate point A(-3,4) 180 degrees clockwise and then rotate it again 90 degrees counter clockwise what would be the coordinates of A"?
(3,-4)
(4,3)
(-4,-3)
(-3,-4)
The coordinates of A'', applying the two rotations, are given as follows:
A'' (4, 3).
What is a rotation?A rotation is one example of transformation that a function can undergo, in which the congruence and similarity of the images are kept but the orientation of the image changes.
The rules for each possible rotation are given as follows:
90° clockwise rotation: (x,y) -> (y,-x).90° counterclockwise rotation: (x,y) -> (-y,x).180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y).270° clockwise rotation: (x,y) -> (-y,x).270° counterclockwise rotation: (x,y) -> (y,-x).The original coordinates are given as follows:
A(-3,4).
After the first 180º clockwise rotation, the coordinates are:
A'(3,-4).
(signals exchanged)
After the final rotation, the 90º counterclockwise rotation, the coordinates of A'' are given as follows:
A'' (4, 3).
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In triangle ABC, side AB is one-third of the length of side AC. Side BC is 5 more than the length of side AC. The perimeter is 19. What is the length of side AC?
Answer:
AC = 6 units===========
GivenAB = AC/3BC = AC + 5P = 19AC = ?SolutionP = AB + AC + BCSubstitute and solve for ACAC/3 + AC + AC + 5 = 192 1/3 AC = 147/3 AC = 14AC = 14*3/7AC = 6Note:
Other sides are 2 and 11. This is not a correct question as sum of two smaller sides (2 + 6) is less than the longest one (11), hence there is no such possible triangle.
Find the area of each trapezoid.
1)
8 in
6 in
4 in
The area of the given trapezoid is 24 square inches.
Area of trapezoid:
Area of the trapezoid is referred as the total space covered by its sides.
The formula to calculate the area of the trapezoid is
A = ½ (a + b) h
where
(A) is the area of a trapezoid,
'a' and 'b' are the bases that are parallel sides,
and 'h' is the height that is the perpendicular distance between a and b
Given,
Here we have the values 8 in, 6 in, and 4 in
Through the given values we have to find the area of the trapezoid.
Let us consider the base values of the trapezoid are 8in and 6 in and the height as 4 in.
Now, we have all the side value of the trapezoid.
Then we have to apply it on the formula,
Then we get,
Area = 1/2 (8 + 6) x 4
Area = 2 x (12)
Area = 24
Therefore, the area of the trapezoid is 24 square inches.
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Find the total amount given the original price, tax rate, and tip rate.
Original price: $90.34
Tax rate: 3.5%
Tip: 20%
Answer: 5468.9
Step-by-step explanation:
Answer:
I think its $90.75
Hopefully its right :)
Write an equation in slope-intercept form of the line that passes through $\left(-5,\ 19\right)$ and $\left(5,\ 13\right)$ .
Answer:
hmmm say 5)13
Step-by-step explanation:
i can't explain it
The equation of the line is y = (-3/5)x + 16
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line is given by:
y = mx + c
The line passes through:
(-5, 19) and (5, 13)
So,
m = (13 - 19) / (5 + 5)
m = -6/10
m = -3/5
Now,
(5, 13) = (x, y)
13 = (-3/5) x 5 + c
13= -3 + c
13 + 3 = c
c = 16
Now,
y = mx + c
y = (-3/5)x + 16
Thus,
The equation of the line is y = (-3/5)x + 16
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how many ways are there to distribute seven identical apples and six identical pears to three distinct people?
In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.
There are 7 identical apples and 6 identical pears.
So total number of fruits here = 7+6 = 13 identical fruits
The number of ways to distribute 13 fruits in three distinct people is given by [tex]=^{13}C_3=286[/tex] ways.
Hence the number of ways is 286.
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Kyra ha a rock collection. When he put her rock into 2 equal pille , there are no rock left over. When he put her rock into 3 equal pile , there are till no rock left over. When he put her rock into 4 equal pile , there are till no rock left over. How many rock could Kira have ?
By applying the lowest common multiple approach, Kyra may have acquired up to 12 rocks.
What does common factor mean?
A common factor is a whole number that is a factor of at least two other numbers. The highest common factor is the largest factor that will divide into two or more numbers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).
The least common multiple of 2, 3, and 4 can be used to determine how much rock Kyra has.
Several of:
2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3 = 3, 6, 9, 12, 15, 18, 21
4 = 4, 8, 12, 16, 20
The smallest number that 2, 3, and 4 have in common is 12. There are therefore 12 rock piles in Kyra's possession.
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a train goes at a constant speed.it can travel 150 miles
in 2 1/2 hours. what distance will it travel in 2 hours.
PLEASE ANSWER
The distance traveled by the car in 2hours is 120miles
What is speed?Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
from the definition speed= distance/time
since the train has constant speed,therefore the speed of the car = 150/2 1/2
= 60miles/hour
Distance= speed×time
Therefore for a time of 2hours the train will cover
60×2= 120 miles
Therefore the distance covered in 2hours is 120miles
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y=4x^2-8x+3
find the vertex form
The vertex of the quadratic equations is at (1, -1), then the vertex form will be:
y = 4*(x - 1)^2 - 1
How to find the vertex form?For a quadratic equation with leading coefficient a and a vertex (h, k), the vertex form is:
y = a*(x - h)^2 + k
And for a equation: y = a*x^2 + b*x + c
The x-value of the vertex is at:
h = -b/2a
In this case, we have:
y = 4x^2 - 8x + 3
So the x-value of the vertex is at:
h = -(-8)/2*4 = 1
To get the y-value we evaluate in x = 1
y = 4*1^2 - 8*1 + 3
y = 4 - 8 + 3 = -1
The vertex is at (1, -1) and the leading coefficient is 4, then the vertex form is:
y = 4*(x - 1)^2 - 1
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kara, who lives in canada, plays a popular online video game where every round has a winner. her best streak is 212121 wins in a row, and she wonders how that compares to other players. the game's website has a worldwide leaderboard of players with the longest win streaks for each month. kara finds that the top 200200200 longest streaks in the world in june had an average of about 636363 wins in a row. for which population is 636363 wins a legitimate estimate of the average longest streak?
For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June
Mean = sum of data / Number of data
The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,
Only the top 200200200 longest streaks worldwide in June will win.
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Jordan saved $225 and continues to save $45 each week. RayAnn saved $150 and continues to save $60 each week. Write and solve a system of equations using any method for the given situation.
Equation for Jordan:
Equation for RayAnn:
Solution:
please help me with this! I need the answer a s a p and I also the the y and x axis in the last equation please!
The equations using any method for the given situation illustrated that:
Equation for Jordan: 225 + 45w
Equation for RayAnn: 150 + 60w
How to calculate the equation?Let the number of weeks be represented by w.
Jordan saved $225 and continues to save $45 each week. The equation for this will be:
= 225 + (45 × w)
= 225 + 45w
RayAnn saved $150 and continues to save $60 each week. The equation will be:
= 150 + (60 × w)
= 150 + 60w
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Mr. Williams is planting a garden. It measures 30 meter along one side. He makes a mark every 1/5 meter. What is the total number of marks that Mr. Williams will make?
Answer:
150 marks
Step-by-step explanation:
Every meter has 5 marks.
30 meters × 5 marks = 150 marks
Britney operates an orange juice stand. On Monday she used 3 bags of oranges. On Tuesday
she used 1/2 as many oranges as on Monday. How many bags of oranges did Britney use on
Tuesday?
Answer:
1.5
Step-by-step explanation:
3÷2=1.5
engineers measure angles in gradients, which are smaller than degrees. The table shows the conversion of some angle measures in degrees to angles in gradients. What is the slope of the line representing the conversion of degrees to gradients?
Express your answer as a decimal rounded to the nearest hundredth
The slope of the line is 1.11
What is the slope of a line?Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line.
Given that, engineers measure angles in gradients, which are smaller than degrees,
Slope = (-200+100)/(-180+90) = -100/(-90) = 10/9 = 1.11
Hence, The slope of the line is 1.11
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Answer:
1.11
Step-by-step explanation:
it's correct.
What is the quotient of 3.243 x 10^8 and 7.05 x 10^2
Answer:
4,600,000,000
Step-by-step explanation:
Don't forget the order of operations
3.243 × 10⁸/7.05
= 46,000,000 × 10²
= 4,600,000,000
or 4.6 × 10⁹
Answer:
4.6x10 to the power of 5
Step-by-step explanation:
7.05×10
2
3.243×10
8
Divide them.
\frac{3.243}{7.05}\times \frac{10^8}{10^2}
7.05
3.243
×
10
2
10
8
Divide numbers and 10's separeately.
0.46\times 10^6
0.46×10
6
Subtract exponents.
(4.6\times 10^{-1})\times 10^6
(4.6×10
−1
)×10
6
Rewrite as a number bigger than 1
4.6\times (10^{-1}\times 10^6)
4.6×(10 −1 ×10 6 )
Associate
4.6\times 10^5
4.6×10 5
Add exponents
Ben and Charlie had the same number of books at first. Ben gave away 16 of his books, Charlie gave away 28 books. The ratio of the number of books Ben had left to that of Charlie's is 3:1. How many books did each boy have at first.
The number of books each boy had based on the 3:1 ratio of the books remaining is 34 books
What is a ratio?A ratio is a quantitative expression of the relationship between two values that indicates the relative proportion of each amount.
The initial number of books Ben had = The initial number of books Charlie has
The number of books Ben gave away = 16 books
The number of books Charlie gave away = 28 books
The ratio of the number of books Ben and Charlie had left is 3:1
Let x represent the number of books each of them initially have. Representing the numbers as a ratio gives;
The number of books Ben had left = x - 16
The number of books Charlie had left = x - 28
[tex]\dfrac{x - 16}{(x - 16) + (x - 28)} = \dfrac{3}{3+1}[/tex]
Which gives; [tex]\dfrac{x - 16}{(2\cdot x - 44) } = \dfrac{3}{4}[/tex]
4 × (x - 16) = 3 × (2·x - 44)
6·x - 4·x = 3×44 - 4×16 = 68
2·x = 68
x = 68 ÷ 2 = 34
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