Answer:
a. The amount of caffeine left is 52.77 mg
b. It will take about 5.42 hours
Step-by-step explanation:
* Lets solve it as an exponential decay
- Exponential decay: If a quantity decrease by a fixed percent at
regular intervals, the pattern can be depicted by this functions
y = a(1 - r)^x
# a = initial value (the amount before measuring growth or decay)
# r = growth or decay rate (most often represented as a percentage
and expressed as a decimal)
# x = number of time intervals that have passed
* Now lets solve the problem
∵ The initial amount of caffeine is 100 mg
∴ a = 100 mg
∵ The caffeine decreases by about 12% each hour
∴ r = 12/100 = 0.12
* Lets solve a.
a. ∵ x = 5 ⇒ the time interval
∵ The amount of caffeine left = a(1 - r)^x
∴ The amount of caffeine left = 100(1 - 0.12)^5
∴ The amount of caffeine left = 100(0.88)^5= 52.77 mg
* To find the time x use the linear logarithmic function
b. ∵ The amount of caffeine is 50 mg
∴ 50 = 100(1 - 0.12)^x ⇒ divide both sides by 100
∴ 50/100 = (0.88)^x
∴ 0.5 = (0.88)^x ⇒ take ln for each side
∴ ln(0.5) = ln(0.88)^x
∵ ln(a)^n = n ln(a)
∴ ln(0.5) = x ln(0.88) ⇒ divide both sides by ln(0.88)
∴ x = ln(0.5)/ln(0.88) = 5.4 years
* It will take about 5.42 hours
After 5 hours, approximately 54.47 mg of caffeine would remain in your system. It would take approximately 3.72 hours for the caffeine level to reach 50 mg.
Explanation:To find the remaining amount of caffeine after 5 hours, we need to calculate the decreasing amount of caffeine each hour. The decrease in caffeine can be calculated by multiplying the previous amount of caffeine by 0.88 (1 - 0.12). So, after 5 hours, the remaining caffeine can be found using the formula:
Initial amount of caffeine: 100 mgRemaining caffeine after 5 hours: 100 mg * (0.88)5 = 54.47 mgTo find the time it takes to have 50 mg of caffeine remaining, we can set up an equation and solve for time:
Initial amount of caffeine: 100 mgRemaining caffeine: 50 mgDecay rate: 0.88 (1 - 0.12)Equation: 100 mg * (0.88)t = 50 mgSolving for t, we get:t = log0.88(50/100) ≈ 3.72 hoursTherefore, after 5 hours, approximately 54.47 mg of caffeine would remain in your system. It would take approximately 3.72 hours for the caffeine level to reach 50 mg.
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(5Q) Which is the graph of the given function?
Answer:
The graph of the given equation is letter A.
Step-by-step explanation:
I used the geogebra application to plot the graph of the equation.
You input the formula and the app will show you its graph.
Please help will mark brainliest (answer must be right)
True or false
The points on a line can be paired one to one with real numbers ?
Answer: TRUE
Step-by-step explanation: This is true, because there is an infinite amount of real numbers in both, and they are both countably infinite (so these infinities are equal). Hope this helps!
PLEASE HELP!!! 15 PTS!!
IF WOULD BE GREAT IF YOU COULD SHOW YOUR WORK SO I KNOW HOW TO DO IT MYSELF!!
Convert the rectangular coordinates (√2, -√2) into polar coordinates. Express all angles in degrees rounded to the nearest degree.
A. (2, 180°)
B. (2, 0°)
C. (2, -45°)
D. (2, 45°)
Answer:
[tex]\large\boxed{C.\ (2,\ -45^o)}[/tex]
Step-by-step explanation:
Regular coordinates (x, y)
Polar coordinates (r, φ)
[tex]r=\sqrt{x^2+y^2}\\\\\psi=\arctan\frac{y}{x}[/tex]
We have the point
[tex](\sqrt2,\ -\sqrt2)[/tex]
Substitute:
[tex]r=\sqrt{(\sqrt2)^2+(-\sqrt2)^2}=\sqrt{2+2}=\sqrt4=2\\\\\psi=\arctan\left(\frac{-\sqrt2}{\sqrt2}\right)=\arctan(-1)=-45^o[/tex]
Final answer:
The rectangular coordinates (√2, -√2) are converted to polar coordinates using formulas for radius and angle, resulting in polar coordinates (2, -45°), which matches Option C.
Explanation:
The question involves converting rectangular coordinates to polar coordinates. The given rectangular coordinates are (√2, -√2). To convert these to polar coordinates, we use the formulas r = √(x² + y²) and θ = arctan(y/x). First, calculate the radius r which is √((√2)² + (-√2)²) = √(2 + 2) = √4 = 2. Next, calculate the angle θ which is arctan((-√2)/(√2)) = arctan(-1). In degrees, arctan(-1) is -45°.
However, since polar coordinates represent angles positively in a counter-clockwise direction starting from the positive x-axis, we consider the equivalent positive angle which makes θ = 315°. However, to match the provided options more closely, we note that -45° is an equivalent way of expressing the direction taking the negative angle into consideration.
The correct polar coordinates are (2, -45°), which matches Option C.
At a game show, there are 6 people (including you and your friend) in the front
row
The host randomly chooses 3 people from the front row to be contestants.
The order in which they are chosen does not matter
There are 6C3 20 total ways to choose the 3 contestants
What is the probability that you a your friend are both chosen?
a. 3/20
b.4/20
c.2/20
d.2/3
Answer: 4/20
Step-by-step explanation:
Option b is correct. The probability that you and your friend are both chose is 4/20.
What is probability?The probability provides a means of getting an idea of likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.
Formula for probabilityP(E) = number of favorable outcomes/Total number of outcomes
Where,
P(E) is the probability of an event.
What is combination?An arrangement of objects where the order in which the objects are selected does not matter is called combination.
Combination Formula[tex]C_{n,k} = \frac{n!}{(n-k)!k!}[/tex]
Where,
n is total number of objects in set
[tex]C_{n, k}[/tex] is number of combinations
k is number of choosing objects from the set
According to the given question
We have
Total six people.
And,
There are total [tex]6C_{3}[/tex] ways to choose the 3 contestants.
⇒ [tex]6C_{3} = \frac{6!}{(6-3)!3!}[/tex] = [tex]\frac{(6)(5)(4)(3!)}{(3!)(3!)}[/tex] = 20
⇒ total number of outcomes = 60
⇒ There are 20 ways to select 3 contestant among 20 people.
Now, the number of ways that, you and your friend are chosen, along with 1 person from a set of 4 is given by
[tex]C_{4,1} = \frac{4!}{1!3!}= 4[/tex]
⇒ total number of favorable outcomes = 4
Therefore,
The probability that you and your friend are both chose = [tex]\frac{4}{20}[/tex]
Hence, option b is correct.
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The average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34. The data set has the following statistics:
x = 4.312
2 = 0.577
What is the standard deviation? Round to the nearest thousandth.
0.333
0.760
2.077
18.593
Answer: Second Option
[tex]\sigma=0.760[/tex]
Step-by-step explanation:
We have the average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009.
5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, 4.34
We know that the average [tex]{\displaystyle {\overline {x}}}[/tex] of the data is:
[tex]{\displaystyle {\overline {x}}}=\frac{\sum_{i=1}^{10}x_i}{10}=4.312[/tex]
We also know that the variance [tex]\sigma^2[/tex] is equal to 0.577.
So by definition the standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=\sqrt{\sigma^2}\\\\\sigma=\sqrt{0.577}\\\\\sigma=0.760[/tex]
Answer:0.760
just right by chance
Which is the factored form of x2(x-2)-3(x-2)?
From the equation, you can see that each value in the equation is multiplied (x - 2)
To get it into factored form, you can just factor out (x - 2) from the equation, and you would be left with:
x²(x - 2) - 3(x - 2)
(x - 2)(x² - 3) Your answer is A
What is the slope of the line?
1
-1
-1/3
1/3
Answer
m = 1
Explanation
Simple Method: Rise (go up) over Run (go left or right)
Start from a perfect point then rise and run.
Rise: 3, Run: 3 = 3/3 = 1
Alternatively, you could pick two points and use the formula y2 - y1/x2 - x1
Just as an example, I will choose (-2, -3) and (2, 1)
plug in:
1 + 3/2 + 2 = 4/4 = 1
ANSWER
1
EXPLANATION
The slope of the given line is obtained using the formula:
[tex]m = \frac{rise}{run} [/tex]
From the diagram the rise is 2 units and the run is 2 units.
This implies that,
[tex]m = \frac{2}{2} = 1[/tex]
Hence the slope of the given line is 1.
A rectangular painting has a diagonal measure of 26 inches and an area of 240 square inches. Use the formula for the area of a rectangle and the Pythagorean theorem to find the length and width of the painting
ANSWER
The length is 10 inches and the width is 24 inches
EXPLANATION
The diagonal of the rectangular painting is d=26 inches.
Let l and w be the length and width of the painting respectively.
From Pythagoras Theorem,
[tex] {l}^{2} + {w}^{2} = {26}^{2} [/tex]
[tex]{l}^{2} + {w}^{2} = 676..(1)[/tex]
Its area is 240 square inches.
This implies that,
[tex]l \times w = 240[/tex]
[tex]l = \frac{240}{w} ...(2)[/tex]
Put equation (2) into (1).
[tex]{( \frac{240}{w} )}^{2} + {w}^{2} = 676[/tex]
This implies that,
[tex] {w}^{4} - 676 {w}^{2} + 57600 = 0[/tex]
[tex]( {w}^{2} - 100)( {w}^{2} - 576) = 0[/tex]
[tex]{w}^{2} - 100 = 0 \: or \: ({w}^{2} - 576= 0[/tex]
[tex]{w}^{2} = 100 \: or \: {w}^{2} = 576[/tex]
Take positive square root to get,
[tex]{w} = 10\: or \: {w} = 24[/tex]
When w=24,
[tex]l = \frac{240}{24} = 10[/tex]
when w=10
[tex]l = \frac{240}{10} = 24[/tex]
Hence the length is 10 inches and the width is 24 inches.
The dimensions of the painting can be found by setting two equations, one for the area of the rectangle, and another based on the Pythagorean theorem, and solving for the length and the width. The key is to remember that these values must be positive, as they represent physical dimensions.
Explanation:First, let's recall what we know. The area of a rectangle is given by the formula length x width = area. Here, we know that the area of the painting is 240 square inches.
Next, remembering the Pythagorean theorem, which states that for any right-angle triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides. Here, we can write the Pythagorean theorem as length² + width² = diagonal² (26 inches).
Setting up these two equations, we would solve for length and width. Keep in mind that we're seeking positive and realistic solutions, as these represent the physical dimensions of the painting.
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Consider f and c below. f(x, y) = (7 + 8xy2)i + 8x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a function f such that f = ∇f. f(x, y) = (b) use part (a) to evaluate c f · dr along the given curve
c.
[tex]\dfrac{\partial f}{\partial x}=7+8xy^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=8x^2y[/tex]
The first equation gives
[tex]f(x,y)=7x+4x^2y^2+g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]8x^2=8x^2y+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=K[/tex]
for some constant [tex]K[/tex]. So
[tex]f(x,y)=7x+4x^2y^2+K[/tex]
and by the fundamental theorem of calculus,
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\vec r=f\left(3,\frac13\right)-f(1,1)=25-11=\boxed{14}[/tex]
To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. The function f(x, y) = 0 is such that ∇f = f. To evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f.
Explanation:To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. Let's start by finding the partial derivative of f with respect to x and y. ∂f/∂x = (7 + 8y2)i + 16xyj and ∂f/∂y = 16xyi + 8x2j. Equating both partial derivatives to f gives us the following equations:
7 + 8y2 = (7 + 8y2)i + 16xyj
8x2 = 16xyi + 8x2j
Simplifying these equations, we find:
i = 0
j = 0
Therefore, the function f(x, y) = 0 is such that ∇f = f.
In order to evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f. The tangent vector to c is given by dr/dt = (-1/t2, 1/t3). Evaluating f at (x, y) = (1, 1/t) gives us f(1, 1/t) = (7 + 8/t2)i + 8/t2j. Taking the dot product of this with (-1/t2, 1/t3) yields:
c·f · dr = ((7 + 8/t2)(-1/t2) + 8/t2/t3)dt = (-7/t4 + 8/t2/t3)dt = (-7/t4 + 8/t5)dt.
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Mary went to the circus. During the dog show, she counted 54 legs between the dogs and the trainers who were having
the dogs perform their amazing tricks. If there were a total of 15 dogs and trainers in the performance, how many of
each were there?
Select the correct response.
#1. 6 Trainers and 9 Dogs
#2. 13 Dogs and 2 Trainers
#3. 1 Trainer and 14 Dogs
#4. 3 Trainers and 12 Dogs
Answer:
d
Step-by-step explanation:
d is most likely
There are 3 trainers and 12 dogs. The correct answer would be an option (D).
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Let's assume the number of trainers would be x and dogs would be y
As per the given information, we can write the system of equations as
x+y=15 .....(i)
2x+4y=54 .....(ii)
From equation (i),
x = 15 - y
From equation (ii), and solve for y
2(15-y)+4y=54
30-2y+4y=54
2y=24
y = 12
Substitute the value of y = 12 in equation (iii), and we get the value of x = 3
Hence, there are 3 trainers and 12 dogs.
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Please help me with this:)
Answer:
55.4 in³
Step-by-step explanation:
The volume (V) of a triangular prism is
V = area of triangular face × length
note the triangle is equilateral with area (A)
A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is the length of the side )
= [tex]\frac{16\sqrt{3} }{4}[/tex] = 4[tex]\sqrt{3}[/tex] in², hence
V = 4[tex]\sqrt{3}[/tex] × 8 = 32[tex]\sqrt{3}[/tex] ≈ 55.4 in³
At the start of an experiment, the temperature of a solution was -12°C. During the expirament
Answer:
The final temperature of the solution was 5°C
Step-by-step explanation:
we know that
1) At the start of an experiment, the temperature of a solution was -12°C
In this moment the temperature is -12°C
2) During the experiment, the temperature of the solution rose 5°C each hour during 4 hours
so
5°C*4=20°C
In this moment the temperature is -12°C+20°C=8°C
3) The temperature changed by -3°C
In this moment the temperature is 8°C-3°C=5°C
Answer:
The final temperature of the solution was 5°C
Step-by-step explanation:
I ONLY GOT ONE SHOT SO PLS HELP, IM STUPID! ANSWER IF YOU KNOW IT. OR AT LEAST TAKE A LOOK!!!!!!!! ( 2 QUESTIONS)
1. A rectangular trampoline measures 15 meters by 18 meters. A pad of constant width is placed around the trampoline so that the total area is 340 square meters.
What is the width of the pad?
MY GUESS IS 1 METER
2.
Use the quadratic formula.
2x^2−5x−9=0
Enter the solutions, in simplified radical form, in the boxes.
x =
or x =
Answer:
Part 1) The width of the pad is [tex]1\ m[/tex]
Part 2) The solutions are
[tex]x=\frac{5(+)\sqrt{97}} {4}[/tex] and [tex]x=\frac{5(-)\sqrt{97}} {4}[/tex]
Step-by-step explanation:
Part 1)
Let
x----> the width of the pad
we know that
[tex](15+2x)(18+2x)=340[/tex]
Solve for x
[tex]270+30x+36x+4x^{2} =340\\ \\4x^{2}+66x-70=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=1\ m[/tex]
see the attached figure
Part 2) we have
[tex]2x^{2} -5x-9=0[/tex]
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2} -5x-9=0[/tex]
so
[tex]a=2\\b=-5\\c=-9[/tex]
substitute in the formula
[tex]x=\frac{5(+/-)\sqrt{-5^{2}-4(2)(-9)}} {2(2)}[/tex]
[tex]x=\frac{5(+/-)\sqrt{97}} {4}[/tex]
[tex]x=\frac{5(+)\sqrt{97}} {4}[/tex]
[tex]x=\frac{5(-)\sqrt{97}} {4}[/tex]
Helpppppppppppppppppp?????
The 3rd one. The number of 8 ounce glasses of milk in 1 gallon. If you read all the options carefully you can see that there’s no way that the other options could be “normally” distributed. The only on that could be “normal” is the 3rd one. Hope I helped!
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Use the probability distribution graph to answer the question.
P(X ≤ a) = 0.6
What is the value of a?
Answer:
a = 5.
Step-by-step explanation:
The graph here is a probability density graph. What will represent [tex]P(X\le a)[/tex] on the graph?
[tex]P(X\le a)[/tex] is the area
between the graph and the x-axis, to the left of [tex]a[/tex].The area under the graph between 0 and 9 is a trapezoid. Consider the trapezoid in three slices from left to right:
A right triangle of area [tex]\displaystyle \frac{1}{2}\times 0.2\times 4 = 0.4[/tex],A rectangle of area [tex]0.2 \times (5 - 4) = 0.2[/tex], andAnother right triangle of area [tex]\displaystyle \frac{1}{2} \times 0.2 \times (9 - 5) = 0.4[/tex].The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of [tex]a = 5[/tex] between the graph and the x-axis is [tex]0.6[/tex]. [tex]P(X \le 5) = 0.6[/tex]. [tex]a = 5[/tex].
As a side note [tex]a = 5[/tex] shall be the only answer to this question since the area under the graph to the left of [tex]a[/tex] can only increase or stay constant but not decrease as the value of [tex]a[/tex] increases.
Please help 20 points
Answer:
LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
Step-by-step explanation:
Determine the angle at the centre of a circle with radius 6.0 cm for an arc length of 8.0 cm.
3/4 radians
2/3 radians
4/3 radians
4π/3 radians
Answer:
Third option.
Step-by-step explanation:
You need to remember that the formula used to calculate the arc lenght is:
[tex]arc\ length=r C[/tex]
Where "r" is the radius and "C" is the central angle in radians.
You need to solve for "C":
[tex]C=\frac{arc\ length}{r}[/tex]
You know the radius and the arc lenght, therefore, you can substitute values to calculate the central angle in radians. Therefore, this is:
[tex]C=\frac{8.0cm}{6.0cm}[/tex]
[tex]C=\frac{4}{3}radians[/tex]
A triangle has side lengths 32, 45 and 18. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above
A triangle has side lengths 44, 36 and 30. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above
Answer:
Part A) Option C. obtuse
Part B) Option B. acute
Step-by-step explanation:
we know that
Applying the Pythagoras Theorem
if [tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle
if [tex]c^{2}>a^{2}+b^{2}[/tex] ----> is an obtuse triangle
if [tex]c^{2}<a^{2}+b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
Part A) A triangle has side lengths 32, 45 and 18. What type of triangle is it?
we have
[tex]c^{2}=45^{2}=2,025[/tex]
[tex]a^{2}+b^{2}=32^{2}+18^{2}=1,348[/tex]
therefore
[tex]c^{2}>a^{2}+b^{2}[/tex]
Is an obtuse triangle
Part B) A triangle has side lengths 44, 36 and 30. What type of triangle is it?
we have
[tex]c^{2}=44^{2}=1,936[/tex]
[tex]a^{2}+b^{2}=36^{2}+30^{2}=2,196[/tex]
therefore
[tex]c^{2}< a^{2}+b^{2}[/tex]
Is an acute triangle
Please help me with this pleaseee
Answer:
x = 88.2
Step-by-step explanation:
The angle at the top of the triangle = 90° - 10° = 80°
and the left side of the triangle is x ( opposite sides of a rectangle )
Using the tangent ratio in the right triangle
tan80° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{500}{x}[/tex]
Multiply both sides by x
x × tan80° = 500 ( divide both sides by tan80° )
x = [tex]\frac{500}{tan80}[/tex] ≈ 88.2
A carpenter's sketch of a room does not include a scale. She measures a wall that has been built and finds that it is 51.2 feet long. On the blueprint, this wall is 8 inches long. What is the scale for this blueprint?
Answer:
1 inch : 6.4 feet
Step-by-step explanation:
Since the wall is 51.2 feet tall, and then wall on the blueprint is 8 inches long, we can make a scale. So 8 in: 51.2 ft or 1 inch: 6.4 feet.
Answer is
1 inch:6.4 feet
Write an algebraic expression to represent the following verbal expression. the cube of the difference of a number and 43
Answer:
(n - 43)³
Step-by-step explanation:
Let the number be n.
Then the desired expression is (n - 43)³
Answer:
Algebraic expression = (x-43)^3
Step-by-step explanation:
Given , the verbal expression is the cube of the difference of a number and 43.
Let x be the number
Now, according to question
Difference means subtraction in which a number is subtracted from the other number
Difference of a number and 43
It means 43 is subtracted from x
Now , the algebraic expression =x-43
Cube of the difference of a number x and 43 =(x-43)(x-43)(x-43)
Cube of a number means multiply a number three times with self .
Therefore, Cube of the difference of a number x and 43=[tex](x-43)\times (x-43)\times(x-43)[/tex]
Cube of the difference of a number x and 43=(x-43)^3
Because in multiply when base same then power of the number added.
Hence,the algebraic expression =(x-43)^3.I
Max's T-shirt business uses the demand function P = -Q + 28 and the supply function P = Q - 12. According to these functions, what will the equilibrium point be for Max's T-shirt business?
A. (20,8)
B. (12,28)
C. (8,20)
D. (28,12)
A and c —————- Bc 20 +8 is 28
Answer:
The answer is (8,20) on APEX. just did the test. good luck!
Mike spent $7920 on his vacation, which was 11% of his monthly salary. What was his monthly salary
Answer: $72000
7290 divided by 11 = 720 720 times 100 = 72000The coordinates of Trapezoid EFGH are E(8, 8), F(8,10), G(1, 6), and H(4, 1). The image of EFGH under dilation is E’F’G’H’. If the coordinates of vertex E’ are (4, 4), what are the coordinates of vertex F’? A)(2, 6) B)(4, 6) C)(2, 5) D)(4, 5)
Answer:
D) (4,5)
Step-by-step explanation:
Vertex E was dilated by 1/2 because 8/2 = 4. Thus, you will divide all the other coordinates by the same scale factor.
2.04 miles
2.5 miles
2.22 miles
2.94 miles
Answer:
[tex]h=2.04\ miles[/tex]
Step-by-step explanation:
Let
h-----> the high of the balloon
we know that
In the right triangle of the figure
[tex]tan(63\°)=\frac{4}{h}[/tex]
[tex]h=\frac{4}{tan(63\°)}[/tex]
[tex]h=2.04\ miles[/tex]
The scatter plot shows the results of a survey in which 10 students were asked how many hours they spent studying for a test and the score they earned. How many students scored a 90 or above? Enter your answer in the box.
✔the answer was 5
Answer:the answer is 5
Answer:
answer is 5
Step-by-step explanation:
Given that the scatter plot shows the results of a survey in which 10 students were asked the number of hours they spent studying for a test and the score they earned.
The scatter plot shows
2 students got 100, 1 student between 90 and 100 and 2 students got 90.
Others got below 90
Hence no of students who scores 90 or above = 5
What is the volume of the cylinder below
the answer is 256π option B
Answer:
[tex]V = 256\pi \, u^{3}[/tex]
Step-by-step explanation:
The volume of the cylinder is determined by the following formula:
[tex]V = \pi\cdot r^{2}\cdot h[/tex]
Where:
[tex]r[/tex] - Radius of the cylinder's base.
[tex]h[/tex] - Height of the cylinder.
The volume of the cylinder is:
[tex]V = \pi \cdot (8\,u)^{2}\cdot (4\,u)[/tex]
[tex]V = 256\pi \, u^{3}[/tex]
To angle are supplementary. Measure of one angle is 56 degrees, what is the measure of the second angle
Answer:
124°
Step-by-step explanation:
Supplementary angles add to 180°.
56° + second angle = 180°
Subtract 56° from both sides of the equation:
second angle = 180° - 56° = 124°
An airplane is flying at an altitude of 2.7 miles and is 8.3 miles from the runway. Find the angle of depression that the airplane must make to land safely?
Answer:
[tex]18.98\°[/tex]
Step-by-step explanation:
Let
x-----> the angle of depression
we know that
The sine of angle x is equal to divide the altitude (opposite side to angle x) by the distance from the runway (hypotenuse)
[tex]sin(x)=\frac{2.7}{8.3}[/tex]
[tex]x=arcsin(\frac{2.7}{8.3})=18.98\°[/tex]
Answer:
18.02°
Step-by-step explanation:
Formula to find angle of depression is given as
tan y = opposite / adjacent
where y = angle of depression
Where opposite = height or altitude of a person or thing
adjacent = distance
In this question ,
opposite = altitude of the plane = 2.7 miles
adjacent = distance of the plane from the runaway = 8.3 miles
Angle of depression is calculated as
tan y = ( 2.7/8.3)
y = tan⁻¹ ( 2.7÷8.3)
y = 18.02°
Angle of depression that the plane must make to land safely = 18.02°
Standard form of a line passing through points (1, 3) and (-2, 5)
Answer:
2x + 3y = 33Step-by-step explanation:
As we move from (-2, 5) to (1, 3), x increases by 3 and y decreases by 2.
Hence, the slope of this line is m = rise / run = -2/3.
Start with the slope-intercept form y = mx + b.
Substitute 3 for y and 1 for x and -2/3 for m:
3 = (-2/3)(1) + b.
Remove fractions by mult. all three terms by 3:
9 = -2 + b, so b = 11, and y = (-2/3)x + 11
Again, mult. all three terms by 3:
3y = -2x + 33, or, in standard form,
2x + 3y = 33