The distance between the person and the shuttle is changing at a rate of 640 feet/sec when the shuttle is 4000 ft high and is rising at a rate of 800 ft/sec.
Considering x to be the height of the triangle and y to be the hypotenuse of the triangle, a right-angled triangle will be formed according to the given information having a base of 3000 feet which is the distance of the person from the launch pad.
In this right-angle triangle x will be the height of the shuttle and y will be the distance between the person and the shuttle.
Now we apply the Pythagorean theorem to the triangle;
y² = x²+(3000)²
Now differentiating this equation with respect to time,t :
2y (dy/dt) = 2x(dx/dt) + 0
dy/dt = x(dx/dt)/y
As the shuttle is rising at a speed of 800 ft/sec, (dx/dt)=800
Substitute 4000 for x into the equation, y²=x²+(3000)², to find y;
y² = (4000)²+(3000)²
y = 5000
Now we substitute 4000 for x, 5000 for y, and 800 for dx/dt in the equation, dy/dt = x(dx/dt)/y
dy/dt = 4000(800) / 5000
dy/dt = 640
Therefore, the distance between the person and the shuttle is increasing at a rate of 640 feet/sec.
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just need 8 thanks..
Answer:
8a)
D: [tex]1\leq x\leq 3[/tex].
R: [tex]0\leq y\leq 4[/tex]
8b)
D: [tex]x\geq 0[/tex]
R: [tex]y\geq 1[/tex]
Step-by-step explanation:
8a) The domain is the set of all possible numbers the x values could be. If there is no corresponding y value for an x value, that x value would not be considered part of the domain.
In the question, the function starts at x = 1 and continues until 3. The ends of the function are closed, so it is inclusive. This can be written as [tex]1\leq x\leq 3[/tex].
The range is all the possible y values. The function does not go below y = 0 and has a maximum of 4. The ends of the function are closed, so it is inclusive. This can be written as [tex]0\leq y\leq 4[/tex]
8b) We can do the same for this problem. The x has a minimum at 0 and continues to go on without an upper bound(as indicated by the arrow), is also includes the point where x=0. Therefore, the domain can be written as [tex]x\geq 0[/tex].
As for the range, the y minimum is 1 and the function continues to increase as shown by the upwards slope and arrow. The function also includes the point where y=1, so it can written as [tex]y\geq 1[/tex]
A normally distributed data set of 600 values has a mean of18.5 and a standard deviation of 3.25.What is the approximate number of values in the dataset expected to be 22 or greater?
Note the in such type of questions the term 'probability' and 'proportion' can be used in place of each other. It is because the probability gives the proportion of favorable outcomes to the total outcomes.
Let X be the random variable representing the number of data points greater than or equal to 22.
Given that the mean and standard deviation is 18.5 and 3.25, respectively.
Consider the formula for z-score as,
[tex]z=\frac{x-\mu}{\sigma}[/tex]So the probability is calculated as,
[tex]\begin{gathered} P(X\ge22)=P(z\ge\frac{22-18.5}{3.25}) \\ P(X\ge22)=P(z\ge1.08) \\ P(X\ge22)=P(z\ge0)-P(0\leq z\leq1.08) \\ P(X\ge22)=0.5-\emptyset(1.08) \end{gathered}[/tex]From the Standard Normal Distribution Table,
[tex]\emptyset(1.08)=0.3599[/tex]Substitute this value,
[tex]\begin{gathered} P(X\ge22)=0.5-0.3599 \\ P(X\ge22)=0.1401 \end{gathered}[/tex]Thus, there is 0.1401 or 14.01% probability that a data will be greater than or equal to 22.
So, the 14.01% of the data is expected to be 22 or greater.
please help ASAP
Brainliest
Answer:
Check-mark the ones with the number 7
Step-by-step explanation:
How is it 840g plsss help!
Step-by-step explanation:
Let's say first piece is x. First and third ratio is 1:4 so it would be
4x - x = 360
3x = 360
x = 120 Third piece is 120g. Now we just multiply the rest.
2 × 120 = 240g
4 × 120 = 480g, total 840g
Answer:
840 g
Step-by-step explanation:
Ratio:Ratio of weight of 3 pieces = 1 : 2 : 4
Weight of 3 pieces = x , 2x , 4x
Weight of third piece - weight of first piece = 360 g
4x - x = 360
3x = 360
Divide both sides by 3,
x = 360÷ 3
x = 120 g
Weight of first piece = x = 120 g
Weight of second piece = 2x = 2*120 = 240g
Weight of third piece = 4x = 4 *120 = 480 g
Weight of the whole cake = 120 + 240 + 480
= 840 g
Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina’s rate miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
What is the answer please…
Answer:
answer is T 25............
How would you write (a-b)^5 without simplifying it?
The way we can write the expression (a - b)⁵ without simplifying is by using Pascals' Triangle to get; a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵
How to use Pascals' Triangle of binomial coefficients?Pascal’s Triangle is a method that is used to know the binomial coefficients of terms of binomial expression (x + y)ⁿ, where n can be any positive integer and x,y are real numbers.
For the expression (x + y)⁵, the coefficients are;
1, 5, 10, 10, 5, 1
According to the binomial expansion, the power of m will be decreasing while the power of 5 will be increasing as shown below. Thus;
(a - b)⁵ = (a + (-b))⁵ = a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵
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Solve 3(2m + 1) − 3m = −12. m = −5 m equals negative 13 over 3 m equals negative 15 over 6 m = −0.33
The value of m from the given equation is -5. Therefore, option A is the correct answer.
The given equation is 3(2m+1)-3m=-12.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
A general rule for equation solving:
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The given equation can be solved as follows:
6m+3-3m=-12
⇒ 3m+3=-12 (Subtract the like terms)
⇒ 3m=-12-3 (Transpose 3 to other side of the equation)
⇒ 3m=-15
⇒ m=-15/3 (Transpose 3 to other side of the equation)
⇒ m=-5
The value of m from the given equation is -5. Therefore, option A is the correct answer.
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Answer:
m=-5
Step-by-step explanation:
Anton picks corn at a local farm. He is paid 80 cents per bushel for the first 50 bushels, 90 cents per bushel for the next 50 bushels, and 95 cents per
bushel for all bushels picked over 100.
Determine how much Anton would earn if "x" is 128 bushels. $
Anton would earn $111.6 if "x" is 128 bushels.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that Anton picks corn at a local farm.
Anton is paid 80 cents per bushel for the first 50 bushels, 90 cents per bushel for the next 50 bushels, and 95 cents per bushel for all bushels picked over 100.
Thus, First 50 bushels: 0.80 x 50 = 40
Next 50 bushels: 0.90 x 50 = 45
Remaining bushels: 0.95 x 28 = 26.6
Total = $40 + $45 + $26.6 = $111.6
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Write 56% as a fraction in simplest form.
Answer:
[tex]\frac{14}{25}[/tex]
Step-by-step explanation:
per cent means 'out of 100 ' , then
56%
= [tex]\frac{56}{100}[/tex] ( divide numerator/ denominator by 4 )
= [tex]\frac{14}{25}[/tex] ← in simplest form
A warehouse is 64 yards long, 28 yards wide, and 8 yards high. What is the area of the warehouse floor? If the warehouse is filled to half its height with tightly packed boxes, what is the volume of the boxes?
The volume should be 7168 yards
The area for the floor should be 14,336 yards
Warehouse details:
64 yds long
28 yds wide
8 yds high
---------------------------------------------------------------------------------------
What is the area of the warehouse floor?
the base of the warehouse is 64*28
which is 1792 yds squared
1792 yards squared
If the warehouse is filled to half its height with tightly packed boxes, what is the volume of the boxes?
half the height of the warehouse is 8/2=
4 yards
the volue of half the warehouse is
1792 * 4 = 7168 yds squared
I'm not quite sure how they want me to answer this but this is all that I got
(this part below can't be trusted)
either the boxes can be 1x1x1 which means 7168 boxes will fit
either the boxes can be 2x2x2 which means 896 boxes will fit
either the boxes can be 3x3x3 which means 265.481481 boxes will fit, which is definetly not it because they said "filled...tightly packed boxes".
plus, we don't know if the boxes are square or rectangle so I'm not sure
[PLS HELP I’LL RATE BRAINLIEST] What is the measure of (5y+5)
Answer:
5y + 5 = 80
Step-by-step explanation:
5y + 5 +6y + 10 = 180 A straight angel is 180 Combine like terms
11y +15 = 180 Subtract 15 from both sides
11y = 165 Divide both sides by 11
y = 15 Substitute 15 in for y
5y + 5
5(15) + 5 = 80
Answer:
80 THIS TOOK ME SO LONG LOL
Step-by-step explanation:
Add all like terms together:
11y+15=180
And then subtract 15:
11y=165
Then Divide by 11:
y=15
Then you input the Y and solve:
5(15)+5
75+5
80
This question is worth 2 extra credit points. You do not have to complete it if you do notwant to.EXm4 ---> possible beginning ---->2or ------>ma . m2 or ----->(m2)Give a possible beginning to the following expression. (see example above)moHTML EditoreВ
Simplify 3(8a – 4b + 5)
Group of answer choices
24a – 4b + 5
11a – 4b + 5
11a – 7b + 8
24a – 12b + 15
Answer:
24a -12b + 15
Step-by-step explanation:
Answer:
=24a - 12b + 15
Step-by-step explanation:
3(8a-4b+5)
Apply the distributive law: m(a+b+c) = ma + mb + mc
3 (8a - 4b + 5 ) = 3 · 8a + 3( -4b)+ 3 · 5
= 3 · 8a + 3( - 4b) + 3 · 5
Simplify 3 · 8a + 3( -4b) + 3 · 5 : 24a - 12b + 15
= 24a - 12b + 15
How do I simplify???
1. [tex]i^{23}[/tex] = - i
2. [tex]\sqrt{-128}[/tex] = 8i√2
Explanation:Steps to simplify complex numbers:
Write the division as a fraction when dividing complex numbers. Then multiply both the numerator and the denominator by the denominator's conjugate. Then, use FOIL or the Distributive Property to simplify.Understanding how complex numbers work in their various operations requires simplifying complex numbers.1. To simplify [tex]i^{23}[/tex]
We can rewrite [tex]i^{23}[/tex] as [tex](i^{4)^{5} } (i^{2} . i )[/tex]
write [tex]i^{4}[/tex] as [tex](i^{2} )^{2}[/tex]
[tex](i^{4)^{5} } (i^{2} . i )[/tex] = [tex]((i^{2} )^{2} )^{5} (i^{2} . i)[/tex]
we know [tex]i^{2}[/tex] = -1
((-1²))⁵ [tex](i^{2} .i)[/tex]
we know that -1² = 1
= 1⁵ [tex](i^{2} .i)[/tex]
= 1 [tex](i^{2} .i)[/tex]
= [tex](i^{2} .i)[/tex]
here [tex]i^{2}[/tex] =-1
-1 . [tex]i^{}[/tex]
= - i
so [tex]i^{23}[/tex] is -i
2. To simplify [tex]\sqrt{-128}[/tex]
= [tex]\sqrt{(- 1) . (128)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{128}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (64)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (8) . (8)}[/tex]
here [tex]}\sqrt{-1}[/tex] = i
substituting i we get
= i . 8 √2
= 8i√2
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Under her cell phone plan, Salma pays a flat cost of $55 per month and $5 per gigabyte. She wants to keep her bill under $75 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes she can use while staying within her budget.
What is 6/7 of 2/3 ? PLEASEE HELPPP-
Answer:
4/7
Step-by-step explanation:
6/7 of 2/3
= 6/7 * 2/3
= 12/21
= 4/7
about 5% of americans have blue eyes. suppose 3 people are selected at random from the us population. what is the probability that all 3 have blue eyes?
If about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.
About 5% of americans have blue eyes
The probability of a person having blue eyes = 5% = 5/100
Eyes colour of a person is an indepedent event, which means the eye colour of one individual is independent of the other. The probability of one individual having blue eyes or not is independent of another person.
In case of independent event the probability of A intersection B = probability of A multiplied with probability of B
P(A∩B) = P(A) x P(B)
P(A∩B∩C) = P(A) x P(B) x P(C)
The probability that all 3 have blue eyes = 5/100 x 5/100 x 5/100
= 125/1000000
= 1/8000
Therefore, if about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.
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A new health drink has 130% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 45 mg. How many milligrams of the vitamin are in the drink?
In the drink , there are 58.5 milligrams of vitamin .
In the question ,
it is given that
the recommended daily allowance for a certain vitamin is = 45 mg
we have to find the quantity of the vitamin in the drink ,
also given that the amount of vitamin that the new drink has is = 130% of RDA ,
on substituting the value of recommended daily allowance ,
we get
amount of vitamin in the drink is = 130% × 45
= 1.3 × 45 ... because 130% = 1.3
= 58.5 mg
Therefore , the drink has 58.5 milligrams of the vitamin .
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The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
From the linear model we can see that the height of the balloon after 15 seconds is 0 feet.
Depending on the context, the phrase "linear model" is used differently in statistics.
The word is frequently used interchangeably with a linear regression model since it occurs most frequently in relation to regression models. The phrase has a different connotation when employed in time series analysis, though. The term "linear" is used in each instance to denote a subclass of models for which a significant decrease in the complexity of the underlying statistical theory is feasible.From the linear model we can see that the water balloon is thrown from a height of 40 feet upwards.
Now the balloon reaches a height of 70 feet and then falls back down on earth due to gravity.
At about 10 seconds the balloon falls on the ground and splashes.
Hence for further time the balloon is always at the ground.
Therefore at time of 15 seconds the height of the balloon is always 0 feet as represented in the linear model.
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need help please
mrs dawson bought 6 new plants for her garden each plant cost $5 the store gave her a discont so she only paid 2/3 pf a ragular price for each plant
use the propertys of multiplation to find the total cost for all the plants
A. $3.33
B. $20.00
C $45.00
D. $30.00
Answer:
B
Step-by-step explanation:
6x5=30
30x2/3=20
Which choice shows 2-3-15 rewritten correctly using the commutative property and then simplified correctly?
According to the commutative property of addition, you can rearrange the addends without altering the result.
2 + (-3) +(-15) = (-3) +(-15) +2
What is commutative property? Commutative law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution. Division and subtraction do not work interchangeably.According to the commutative property of multiplication, the result will always be the same regardless of the sequence in which the numbers are multiplied.According to the associative property of addition, you can arrange the addends in several ways without changing the result. According to the commutative property of addition, you can rearrange the addends without altering the result.To learn more about : Commutative
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CAN SOMEONE HELP
BD//EF, BF//DE
AB=8cm BC=12cm
x=?
The value of x is 4.8cm.
Here BD // EF and BF // DE
So from this, we have ∠ABF = ∠EFC
Let's take two triangles ΔABC and ΔFCE
∠C =∠C (common angle)
∠ABC = ∠EFC
So ΔABC ≅ ΔEFC
So ∠BAC = ∠FEC
AB/ EF = BC/ FC
AB = 8cm, EF =x, BC = 12cm, FC= 12-x
8/x = 12/ 12-x
2/x = 3/ 12-x
24 - 2x = 3x
5x = 24
x = 4.8cm
Therefore the value of x is 4.8cm.
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Please do this for me .I need it as soon as possible
Note:This is grade 6 maths
Answer:
9.6 but the 6 is recurringAnswer:
9 [tex]\frac{3}{4}[/tex]
13[tex]\frac{2}{3}[/tex]
3[tex]\frac{4}{6}[/tex] or 3 [tex]\frac{2}{3}[/tex] simplified
Step-by-step explanation:
For the fraction part, could how many total spaces between the numbers then count how many spaced over to the pointer.
For #16, there are 4 spaced between 9 and 10. The pointer is pointing to 3 spaces from 9 so the fraction is 3/4.
For #18, there are 6 spaces and the pointer is at the 4th space. You can see that if you counted every 2 spaces as I unit, you would have a total of 3 spaces and the pointer is over 2 of those three spaces. That would get your simplified answer of 2/3.
What is .. 9x-4 = 2x +3
Answer:
X=1
Step-by-step explanation:
9x -4 = 2x+3 :
9x-4=2x+3
9x -4 + 4= 2x + 3+4
Simplify
subtract 2x from both sides
Simplify
Divide both sides by the same factor
simplify
X=1
Image to problem- https://postimg.cc/G8VnJLTq
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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Find an equation in the form y=mx + b
Answer:
A) [tex]y = \frac{1}{10}x + 28[/tex]
B) $116.5
Step-by-step explanation:
The data we are given is:
• for 440 minutes of usage, the total cost is $72
• for 940 minutes of usage, the total cost is $122
A)
In order to find an equation in the form [tex]y = mx + b[/tex], we must first express the given data as coordinates in the form [tex](x, y)[/tex].
We are told that [tex]x[/tex] is the number of monthly minutes, and [tex]y[/tex] is the total monthly fee. Therefore the first piece of data expressed as coordinates is (440, 72), and for the second piece of data, it is (940, 122).
Now that we have the coordinates, we can make an equation using the formula:
[tex]\boxed{\frac{y - y_1}{y_2 - y_1}= \frac{x - x_1}{x_2 - x_1}}[/tex],
where [tex](x_1, y_1)[/tex] is (440, 72) and [tex](x_2, y_2)[/tex] is (940, 122).
Substituting the values into the formula, we get:
[tex]\frac{y - 72}{122 - 72}= \frac{x - 440}{940 - 440}[/tex]
⇒ [tex]\frac{y - 72}{50} = \frac{x - 440}{500}[/tex]
⇒ [tex]50 \times \frac{y - 72}{50} =50 \times \frac{x - 440}{500}[/tex] [Multiplying both sides of the equation by 50]
⇒ [tex]y - 72 = \frac{x - 440}{10}[/tex]
⇒ [tex]10y - 720 = x - 440[/tex] [Multiplying both sides by 10]
⇒ [tex]10y = x +280[/tex] [Adding 720 to both sides]
⇒ [tex]y = \frac{1}{10}x + 28[/tex] (Answer)
B)
To find the total cost if 885 minutes are used, we have to replace [tex]x[/tex] in the above equation with 885:
[tex]y = \frac{1}{10}(885) + 28[/tex]
⇒ [tex]y = 88.5 + 28[/tex]
⇒ [tex]y = 116.5[/tex]
Therefore, the total cost will be $116.5. (Answer)
Can you please help with with this?
Thanks
Answer:
slope is 3
Step-by-step explanation:
8-5/-2-(-3)=3/1=3 3 is the slope
help asap pleaseee
What are the coordinates of the vertices of triangle A’B’C’ after a reflection across a line through point P with a y-intercept at y=-2, followed by a translation T<3,3>?
Answer:
Coordinate A would be (12,3)
Coordinate B would be (12,7)
Coordinate C would be (10,5)
HELP ASAP NEEDS TO BE DONE BY TONIGHT
Answer: y = (5x/4) + 2
Step-by-step explanation:
Answer:
y = 5/4x + 2
Step-by-step explanation:
First, we convert 4x + 5y = 15 to slope intercept form (y=mx+b):
5y = -4x + 15
Divide both sides by five
y = -4/5 (x) + 3
The slope is -4/5
A perpendicular slope is the negative reciprocal of the other line. To find the negative reciprocal, you switch the numerator and denominator and switch the sign.
Slope = 5/4
Plug the slope and (-4, -3) into the slope-intercept form:
-3 = ( 5/4 · -4 ) + b
Isolate b (the y-intercept):
-3 = -5 + b
b = 2
y = 5/4x + 2