The slope Using the formula will be h = -100t + 4000
This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.
If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.
If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.
Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:
h = -100t + 4000 which appears to be choice a.
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a 61 mg of a vaccine is given to a patient to prevent measles. the vaccine leaves the body at a rate of 6.1% per hour. define a function g that gives the mass of the vaccine remaining in the body, v, in terms of the number of hours, n since the vaccine was administered. how much of the vaccine remains in the body 24 hours after it was administered? mg use your graphing calculator to determine how many hours passed before there were only 5mg of the vaccine remaining in the body.
The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.
What is rate?
A rate is a unique ratio where the two words are expressed in several units.
Given that the amount of vaccine is 61 mg.
The vaccine leaves the body at a rate of 6.1% per hour.
After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.
After n hour the body will consume 6.1%× n = 0.061n mg.
The remaining amount of vaccine is (61 - 0.061n).
The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.
Putting n =24 in the equation:
g = 61 - 0.061×24
g = 59.536 mg
The vaccine remains in the body 24 hours after it was administered 59.536 mg.
The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.
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What is 2/3 plus 4/8 equal to please let me know and please explain, and this is 5th grade.
5th grade
Answer: 7/6
Step-by-step explanation:
Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.
Hope this Helps :)
Write 30 000 000 in standard form.
Answer:
3×10^7
Step-by-step explanation:
Write 30 000 000 in standard form.
=3×10,000,000
=3×10^7
Step-by-step explanation:
this is
3.0 × 10⁷
as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).
and the first non-zero digit is 3.
an inverted cone is partially filled with water, as shown below. the radius of the inverted cone is 16 mm. the height of the inverted cone is 18 mm. if the volume of the water is increasing at a rate of 548 cubic mm per hour, what is the rate, in mm per hour, at which the height of the water is changing when the height of the water is 2 mm?
The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
Given data,
A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.
The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;
r/h = 16/18
= 8/9
r = 8h/9
The volume of the cone is;
v = [tex]\frac{1}{3}\pi r^2h[/tex]
v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]
v = [tex]\frac{64}{243}\pi h^3[/tex]
Now, differentiating concerning x;
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex] [tex]\frac{64}{243}\pi h^3[/tex]
[tex]\frac{dv}{dt}[/tex]= 64π/243*[tex]\frac{d}{dt}[/tex] h³
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]
We have;
[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm
[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 55.19
[tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.
Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
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A line passes through the point (-8,-3) and has a slope of -3/4
The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9
How to determine the equation of the line?From the question, we have the following parameters that can be used in our computation:
Slope, m = -3/4
Points, (x₁, y₁) = (-8, -3)
A linear equation can be represented as
y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = -3/4(x + 8) - 3
Open the brackets
So, we have the following equation
y = -3/4x - 6 - 3
Evaluate the like terms in the above equation
So, we have the following representation
y = -3/4x - 9
The above equation cannot be further simplified
Hence. the linear equation is y = -3/4x - 9
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Nadia and Sasha are measuring different lengths of ribbon.
Use the drop-down menus to complete the statements about Nadia's and Sasha’s measurements.
Nadia's
Measurement Actual
Length
4 cm 5 cm
Sasha's
Measurement Actual
Length
96 cm 100 cm
Nadia was(blank)
cm off the actual measurement of 5 cm.
That is a percent error of
(blank)%.
Sasha was
(blank) cm off the actual measurement of 100 cm.
That’s a percent error of(blank)
%.
Because Nadia’s ribbon is(shorter/longer)
than Sasha’s ribbon, each centimeter of error in measurement results in a(shorter/longer)
percent error.
Nadia was 1cm off the actual measurement of 5 cm. That is a percent error of 20%.
Sasha was 4 cm off the actual measurement of 100 cm. That’s a percent error of 4%.
How to calculate the percentage error?From the information, the measurement was 4cm and the actual measurement was 5cm. Therefore, the difference will be:
= 5cm - 1cm
= 4cm
The percentage error will be:
= Difference in measurement / Actual measurement × 100
= 1/5 × 100
= 20%.
The percentage error for Sasha will be:
= 4/100 × 100
= 4%
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there are 150 women who belong to a health club. The rest of the club members are men.3/5 of the members are men. How many members belong to the gym?
Answer:
3/5x 150
= 450/5
= 90
150+90
= 240 ans
The cost of a jacket j after a 5% markup can be represented
by the expression j+0.05j. Simplify the expression. Then
determine the total cost of the jacket after the markup, if
the original price is $35.
help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The object has fallen [tex] \boxed{\sf 289} [/tex] feet from ts intial position.
Step-by-step Explanation:
Given:
Formula:
[tex] \rm v = \sqrt{2gh} [/tex]
Where,
v = velocity (in feet per second)
h = Height fallen (in feet)
g = acceleration due gravity (in feet per second squared) = approximately 32 ft/s²
To find:
How far an object has fallen if its velocity (v) is 136 ft/s
Solution:
By substituting the value of g & v in the formula we get:
[tex]\rm \implies 136 = \sqrt{2 \times 32 \times h} \\ \\ \rm \implies 136 = \sqrt{64h} \\ \\ \rm \implies 64h = {136}^{2} \\ \\ \rm \implies h = \dfrac{ {136}^{2} }{64} \\ \\ \rm \implies h = \dfrac{18496}{64} \\ \\ \rm \implies h = 289 \: ft[/tex]
ben has 172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?
The number of months Ben can be a member of the fitness club is 7 months .
In the question ,
it is given that Ben wants to join a fitness club ,
initial membership fees for fitness club is = $49.50
monthly fees for fitness club = $17.50
let the number of months be [tex]=[/tex] x
the total fees that Ben paid = $172
So ,according to the question
the equation to represent the situation is
49.50 + 17.50x = 172
17.50x = 172 - 49.50
17.50x = 122.5
x = 122.5/17.50
x = 7
Therefore , Ben can be a member of fitness club for 7 months .
The given question is incomplete , the complete question is
Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?
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y=3x−15 in standard form please answer MY GRADES DEPEND ON IT
The equation, y = 3x - 15, written in standard form is 3x - y = 15
Writing an equation is standard formFrom the question, we are to write the given equation is standard form.
The given equation is
y = 3x - 15
The standard form of a linear equation is
Ax + By = C
Where A, B, and C are constants
x and y are variables
Now, we will write the given equation is the standard form of a linear equation.
y = 3x - 15
Substract y from both sides
y - y = 3x - y - 15
0 = 3x - y - 15
That is,
3x - y - 15 = 0
Add 15 to both sides of the equation
3x - y -15 + 15 = 0 + 15
3x - y = 15
Hence, the standard form is 3x - y = 15
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Use the formula for the area of a circle (A-ar) to find the area of the bull's-
eye.
12
20
100 mm 12 mm
180 mm
A. 101,736 mm2
B. 452.39 mm2
C. 22,686 mm2
D. 31,400 mm²
13
The area of a bull's eye is equal to: B. 452.39 mm².
What is the area of a circle?The area of a circle simply refers to the region enclosed or space occupied by a circle within its boundary, and in a two-dimensional plane.
How to calculate the area of a circle?Mathematically, the area of a bull's eye can be calculated by using this formula:
Area of bull's eye = πr²
Where:
r is the radius of a circle.
Note: The radius of the bull's eye is equal to 12 mm and π = 3.14159.
Substituting the given parameters into the formula, we have;
Area of bull's eye = π × (12)²
Area of bull's eye = 3.14159 × 144
Area of bull's eye = 452.39 mm².
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Nora is going to earn $300 from her summer job. Combined with her savings, Nora will then have $1,500 toward her music school. How much money does Nora have in her savings?
A. 1000
B. 1200
C. 1300
D. 1800
Answer:
1200
Step-by-step explanation:
1,500-300=1200
(1 point) a bit is a 0 or a 1. a bit string of length 5 is a sequence of 5 digits, all of which are either 0 and 1. (a) how many bit strings of length 5 are there?
A bit string of length 5 contains 2^5 = 32 potential values because each bit has two possible values.
The quantity of bits in a bit string determines its length. When the bit string is produced, this precise non-negative integer is fixed. The exact non-negative integers that are smaller than the bit string's length are the valid indexes. Bit strings can have zero bits or more. A series of bits is known as a bit string. Bit strings can be used to modify binary data or represent sets. In right to left order, a bit string's elements are numbered from zero to the number of bits in the string minus one.
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Sam has had five quizzes so far in his class. His average score is 74%. He
scored a 99% on his sixth quiz. What is his average now? Round to a whole
number.
Sam's average score based on the six quizzes is 78%.
What is the average?The average is the mean, a central tendency value.
We compute the mean by summing the values of a data set and dividing by the number of items in the collection.
In this situation, the average of 5 quizzes multiplied by 5 gives the total score in the 5 quizzes, which resulted in the average score.
This total is added to the score in the sixth quiz to get the total score for the six examinations before dividing the sum by 6, giving the overall average.
The average score in 5 quizzes = 74%
Total score in the 5 quizzes = 370% (74 x 5)
The score on the sixth quiz = 99%
Total score in six quizzes = 469% (370 + 99)
The average score in the 6 quizzes = 78.167% (469/6)
= 78%
Thus, Sam scored an average of 78% on the six tests.
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Suppose that a recent poll of american households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive. 25) what is the probability that all three randomly selected households own a dog? (round to the nearest hundredth)
There is a 0.091125 probability that all three randomly chosen houses have dogs.
In light of this, imagine that a recent survey of American homes regarding pet ownership revealed that 45% of households with pets were dog-owning, 34% were cat-owning, and 10% were bird-owning households.
• Three families are chosen at random, replaced, and with mutually exclusive ownership.
The calculation of probability is as follows based on the facts above:
=0.43^3
= 0.091125
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The emissivity of a surface coated with aluminum oxide can be approximated to be 0. 15 for radiation at wavelengths less than 5 μm and 0. 9 for radiation at wavelengths greater than 5 μm. Determine the average absorptivity of this surface at 1040. 00 K
For emission of a surface, the average absorptivity of this surface at 1040 K is 0.899705900025.
Knowing that ε1 =0.15 and ε2 = 0.9, we first solve for the average emission, e, as follows:
ε = ε1 [tex]f_λ[/tex] [ λT] + ε2 [1- [tex]f_{λ}[/tex](λT)]
is also solved for reference in calculating fλ
(λ*T) = (5 μm)(1040 K)
= 5200 μm K
[tex]f_{λ}[/tex]= 0.0003921333 when referencing this to a blackbody function.
Moving on, we solve for T1040 using the equation above:
ε = ε1 [tex]f_{λ}[/tex][λT] + ε2[1 -[tex]f_{λ}[/tex]( λT)]
=0.9 + (0.15-0.9)0.0003921333
=0.899705900025
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Use the Commutative and Associative Properties to find the expression
equivalent to (-3.3x + (-3.2)) + (5.7x + (−1)).
-3.3x + (-3.2) + 5.7x + (-1)
(-3.3x (-1)) + ((-3.2)x - 5.7)
(-3.3x + (-3.2)) + (5.7x- (-1))
(-3.3x + 5.7x) + ((-3.2) + (-1))
The expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is -3.3x + 5.7x) + ((-3.2) + (-1))
The commutative property of addition states that any change in the order of the numbers being added does not affect the sum.
a + b = b + a
The given expression is (-3.3x + (-3.2)) + (5.7x + (−1))
on simplifying we get, -3.3x - 3.2 + 5.7x - 1 = 2.4x - 4.2
Upon checking the options provided
-3.3x + (-3.2) + 5.7x + (-1)
= 2.4x - 4.2
(-3.3x (-1)) + ((-3.2)x - 5.7)
-9 - 6.7
-3.3x + (-3.2)) + (5.7x- (-1))
2.4x - 2.2
(-3.3x + 5.7x) + ((-3.2) + (-1))
2.4x - 4.2
Therefore, the expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is -3.3x + 5.7x) + ((-3.2) + (-1))
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A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 8 feet. The area of the logo must be less than 48 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use "b" for the base length of the triangular logo.
Answer:
Step-by-step explanation:
We know that the area of a triangle is given by :-
Let b be the base (in feet) of the triangle .
it is given that , The school wants the height of the triangle to be 6 feet.
Then, the area of triangle will be :-
(1)
The area of the logo must be at most (less than or equal to) 15 square feet.
i.e. Area ≤ 15 square feet (2)
Now, Substitute the value of A from (1) into (2) , we get
Divide both sides by 3 , we get
Question 4 (10 points)
(02.07 MC)
The figure shows triangle PQR and line segment AB, which is parallel to QR:
Triangle PQR has a point A on side PQ and point B on side PR. The line AB is parallel to the line QR.
Part A: Is triangle PQR similar to triangle PAB? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle PAB corresponds to line segment QR? Explain your answer. (3 points)
Part C: Which angle on triangle PAB corresponds to angle Q? Explain your answer. (2 points)
The location of the points A and B on side PQ and PR, and the information that segment AB is parallel to QR indicates;
Part A: Triangle ΔPQR is similar to ΔPAB by AA similarity postulate
Part B: The line segment on triangle ΔPAB that corresponds to line segment QR is segment AB
Part C: The angle on triangle ΔPAB that corresponds to angle ∠Q is angle ∠A
What makes two triangles similar?Two triangles are similar if two angles in one triangle are congruent to two angles in the other triangleThe lengths of all three sides of one triangle that is similar to other another triangle are proportional to the three sides of the other triangleTwo triangles are similar if two sides of on triangle are proportional to two sides of the other or second triangle and if the included angle between the two sides are congruent.Please find attached the drawing of triangles ΔPQR and ΔPAB created with MS Word
The in formation in the question are;
Line [tex]\overline{AB}{[/tex] is parallel to [tex]\overline{QR}[/tex], [tex]\left(\overline{AB} \parallel \overline{QR}\right)[/tex]
ΔPQR and ΔPAB overlap
Part A: Angle ∠PQR is congruent to angle ∠PAB (corresponding angles to parallel lines having a common transversal)
∠PRQ is congruent to ∠PBA (Corresponding angles formed by a common transversal to parallel lines)
ΔPQA is similar to ΔPAB (Angle-Angle, AA similarity postulate)
Part B: Corresponding sides of triangles are located on the same relative position within the triangle
Segment QR is the included segment to ∠PQR and ∠PRQ, which are each congruent to ∠PAB and ∠PBA, respectively in ΔPAB and segment AB is the included side to ∠PAB and ∠PBA, therefore, the line segment on triangle ΔPAB that corresponds to line segment QR is segment AB
Part C: Angle ∠Q on triangle ΔPQR is adjacent to segment QR on the right and angle ∠P on the left, while angle ∠A is adjacent segment AB on the right and ∠P on the right, segment AB in ΔPAB corresponds to segment QR on triangle ΔPQR, therefore, by the relative position of angle ∠A on triangle ΔPAB, it is the angle that corresponds to angle ∠Q
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1. A recipe for salad dressing calls for three parts oil for every one part vinegar. How many tablespoons of vinegar are needed to make 1/2 cup of salad dressing?
Answer: The answer is 8
Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup
Will give u brainliest!
Answer:6 is the correct answer
Step-by-step explanation:
Because 16 + 20 equals 36 and the sq root of 36 is 6. So you chose the correct answer.
Answer:
6
Step-by-step explanation:
[tex]\sqrt{16+20}[/tex]
[tex]\sqrt{36}[/tex]
6
What is 4.2x + 5.5y= 38
I hope this helps!
42x +55y =380
What is the amount of M
42 is value of ∠JNM because ∠JNM & ∠KNL are vertically opposite angles.
What is vertically opposite angles?
Angles that are opposite one another at a certain vertex and are produced by two straight lines intersecting are known as vertically opposite angles. Angles that are vertically opposed are equal to one another. These are also known as vertical angles.∠JNM = ∠KNL
4x + 6 = 7x - 21
7x - 4x = 21 + 6
3x = 27
x = 27/3
x = 9
∠JNM = 4 * 9 + 6 = 36 + 6
∠JNM = 42
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Suppose that y varies directly with .x, and y=-8 when x=2.
(a) Write a direct variation equation that relates x and y.
Equation:
(b) Find y when x = 5.
OC
Answer:
A. y = -4x
B. y = 20
Step-by-step explanation:
A. y = xk
Where k is constant
Substitute y for -8 and x for 2
-8 = 2k
Divide both sides by 2
-8/2 = 2k/2
-4 = k
k = -4
y = x(-4)
y = -4x
B. y when x = 5
y = 5(-4)
y = 20
Complete the statement. 48 cm = mm
Answer:
48cm = 480mm
Step-by-step explanation:
1cm = 10mm
48cm = 48 X 10 mm
48cm = 480mm
Answer:
480mm
When converting from cm to mm, multiply by 10.
48 x 10 = 480
Direct and Inverse Variations
The value of y is 24 when x is 7.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
There are direct variations
y= 24 when x=2
We need to find value of y when x =7
This can be found by forming an equation.
Let the value of unknown y be a
2/24=7/a
Apply cross multiplication
2a=24(7)
2a=168
We need to divide by 2 on both sides
a=24
Hence the value of y is 24 when x is 7.
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PL zz HELP WILL GIVE BRAINILIST
Answer:
n + 2
Step-by-step explanation:
If n is the smallest of three consecutive integers, the largest in the sequence must be only two integers greater.
Write equations of the horizontal and vertical lines that pass through (2,3) .
horizontal line:
vertical line:
A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.
Given that,
The point is (2,3).
We have to find the equation of the horizontal and vertical line that pass through point.
Take the point,
(2,3)
The value of x, in this example 2, will never change for a vertical line. This holds true regardless of y's value.
A vertical line passing through this point has the following equation:
x=2
The value of y, in this case 3, for a horizontal line will also never change. This holds true regardless of the value of x.
A horizontal line passing through this point has the following equation:
y=3.
Therefore, A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.
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What is the distance between (−1, 4) and (5, 4)?
Draw a line connecting the points. This is a
line.
The points have the same
.
To find the distance, use the expression
.
The distance between the points is
units.
The distance between points (-1, 4) and (5, 4) is 6 units.
Distance between two pointsFrom the question, we are to determine the distance between two points.
The given points are (-1, 4) and (5, 4)
Using the formula for calculating the distance between two points
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
From the given information,
x₁ = -1
x₂ = 5
y₁ = 5
y₂ = 4
Put the parameters into the equation
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(5 - (-1))² + (4 - 4)²]
d = √[(5 + 1)² + 0²]
d = √(6²)
d = 6 units
Hence, the distance is 6 units.
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Answer:
Step-by-step explanation: The distance between two points can be calculated using the formula:
d = √ ((x2 – x1)² + (y2 – y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the two points are (-1, 4) and (5, 4). Therefore:
d = √ ((5 - (-1))² + (4 - 4)²)
d = √ (6² + 0²)
d = √36
d = 6
Therefore, the distance between (-1, 4) and (5, 4) is 6 units.
I hope that helps! Let me know if you have any other questions!