6. 02 rad. is the value of conversion of the angle 0 = 345° to radians.
Here, we have,
given that,
Convert the angle theta = 345° to radians.
To convert from degrees to radians, multiply the number of degrees by π/180.
This will give you the measurement in radians.
If you have an angle that's 90 degrees, and you want to know what it is in radians, you multiply 90 by π/180. This gives you π/2.
here, angle = 345°
We convert degrees to radian by multiplying by (π/ 180)
=(345)×(π/ 180)
=( 345/180)×(π)
=1.9166π
=1.9166×3.14
=6.018 rad
≈6.02 rad .
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The quantity R, in grams, of a certain radioactive substance decreases according to the exponential decay model dRdt=−0.05R, where t is measured in seconds. During an experiment, a scientist determines that the rate of decay of a second substance with the quantity S, in grams, can be represented by a linear model dSdt=−4, where t is measured in seconds. If at time t=0, R(0)=100 and S(0)=125, at what time t, in seconds, will there be equal quantities of both substances?
Answer:
24 secondsExplanation:
1. Quantiy R
Decay model:
[tex]\dfrac{dR}{dt}=-0.05R[/tex]
That is a first order reaction, whose solution is:
[tex]R=R_0e^{-0.05t}[/tex]
The value at t = 0, R(0) = 100 is R₀.
Thus, the law is:
[tex]R(t)=100e^{-0.05t}[/tex]
2. Quantity S
Decay model:
[tex]\dfrac{dS}{dt}=-4[/tex]
That is a zero order kinetic, whose solution is:
[tex]S=S_0-4t[/tex]
The value at t = 0, S(0) = 125 is S₀
Thus, the law is:
[tex]S(t)=125-4t[/tex]
3. At what time will there ve equal quantities of both substances?
You must solve the system doing R(t) = S(t)
[tex]100e^{-0.05t}=125-4t[/tex]
That equation must be solved by graphing or by consecutive iterations
Note that when t = 0 R(t) = 100 and S(t) = 125. From, that the quantities decreases.
Subsitute with t = 10.
The left-hand side yields: 61 and the right-hand side yields 85.Then, the time is greater than 10.
Substitute with t = 15
Left-hand side = 47Right-hand side = 65t = 20
Left-hand side = 3745t = 25
Left-hand side = 29Right-hand side =25t = 24
Left-hand side =3 0Right hand side = 29Hence, 24 seconds is a satisfactory solution.
The graph attached shows that the intersection point is at t ≈ 23.548 seconds, confirming that 24 seconds is the best solution rounded to an integer number.
At t= 24 , in seconds, will there be equal quantities of both substances.
Given that,
The quantity R, in grams, of a certain radioactive substance decreases, according to the exponential decay model dR\dt=−0.05R, Where t is measured in seconds
The rate of decay of a second substance with the quantity S, in grams, can be represented by a linear model dS\dt=−4,
Where t is measured in seconds. If at time t=0, R(0)=100 and S(0)=125.
We have to determine,
At what time t, in seconds, will there be equal quantities of both substances.
According to the question,
Exponential decay model,
[tex]\dfrac{dR}{dt} = 0.05R[/tex]
The solution of first order reaction,
[tex]R = R_o.e^{0.05t}[/tex]
Substitute the value t = 0 ,R(0)= 100,
Then,
[tex]R(t) = 100.e^{0.05t}[/tex]
The decay model,
[tex]\frac{dS}{dt} = -4[/tex]
That is a zero order kinetic, whose solution is:
[tex]S= S_0-4t[/tex]
The value at t = 0, S(0) = 125 is S₀,
Therefore,
[tex]S(t) = 125-4t[/tex]
At what time will there +ve equal quantities of both substances,
Solve the system doing R(t) = S(t),
[tex]100.e^{-0.05t} = 125-4t[/tex]
The equation must be solved by graphing or by consecutive iterations
When t = 0 R(t) = 100 and S(t) = 125. From, that the quantities decreases.
Substitute with t = 10.
The left-hand side yields: 61 and the right-hand side yields 85.
Then, the time is greater than 10.
Substitute with t = 15
Left hand side = 47
Right-hand side = 65
t = 20
Left-hand side = 37
45
t = 25
Left-hand side = 29
Right-hand side =25
t = 24
Left-hand side =3 0
Right hand side = 29
Hence, 24 seconds is a satisfactory solution.
The graph attached shows that the intersection point is at t ≈ 23.548 seconds, confirming that 24 seconds is the best solution rounded to an integer number.
Hence, At t= 24 , in seconds, will there be equal quantities of both substances.
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Use grid paper to find the median of the data.
9,7,2,4,3,5,9,6,8,0,3,8
The median is....
The median of the data is 5.5.
Calculation of the median:Since the sequence is 9,7,2,4,3,5,9,6,8,0,3,8
We have to arrange the above sequence in the smaller to largerst number
i.e.
0,2,3,3,4,5,6,7,8,8,9,9
So since 5 and 6 are in middle
So, the median is
[tex]= (5 + 6)\div 2[/tex]
= 5.5
Therefore, The median of the data is 5.5.
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Sixty percent of what number is equal to 45 percent of 80?
Answer:
60
Step-by-step explanation:
60% * x = 45% * 80
Changing to decimal form
.60x = .45 *80
.60x =36
Divide each side by .60
.60x/.60 = 36/.60
x =60
Answer:
60
Step-by-step explanation:
Could someone please help me with this?
Answer:
18000
Step-by-step explanation:
What is the image of (4,-1) after a reflection over the line y=x
Answer:
(-4,1)
Step-by-step explanation:
(-1,4) is the image of (4,-1) after a reflection over the line y=x
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph
When a point is reflected across the line y = x, the x-coordinates and y-coordinates change their place.
So for the point (4,-1),the reflected image will be (-1,4)
Hence, (-1,4) is the image of (4,-1) after a reflection over the line y=x
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Calculate the exact lengths of segment e and segment f. Which is longer?
Answer:
Step-by-step explanation:
(We use the pythagorean theorem)
3-(-1) = 4
-2-1 = -3
4x4 + -3 x -3 = 16 x 9 = 144
line e: 12
2-(-1) = 3
2-(-1) = 3
3x3 + 3x3 = 9 x 9 = 81
line f: 9
Therefore, line e is longer!
Hope this helps! .ω.
Please give me brainliest :<
Without specific figures or numerical data, we cannot conclusively calculate the exact lengths of segments e and f. However, geometric principles suggest that segment f, if similar to a hypotenuse, would be longer. Accurate measurement or calculations based on the context (geometry, trigonometry, physical surveying) are required to determine the length of segments.
Explanation:To calculate the exact lengths of segment e and segment f, we need more specific information from the given figures. However, based on the information provided, we can infer certain principles that could lead us to a conclusion. The hypotenuse of a right-angle triangle, as mentioned, is always the longest side, which implies that the length of segment f, being akin to a hypotenuse, would be longer than segment e if these segments were sides of a right-angled triangle. Additionally, the concept of eccentricity described for an ellipse informs us about the ratio of distances and could be applied if the segments were part of an elliptical geometry. The surveyor's tapes information suggests that lengths must be measured accurately, taking into account environmental factors such as temperature, because this can affect the length measurements. Without specific numerical data or figures to reference, we cannot determine with certainty which segment is longer, but the principles outlined can guide us to make an educated conclusion once all data is available.
In general, when comparing two segments to determine which is longer, measurement tools or mathematical calculations are utilized based on the context, such as geometry, trigonometry, or physical measurement in the case of surveying. As per the given text, if the discussion revolves around visual illusions where segments appear different in length despite being the same, then careful measurement is necessary to establish their actual lengths.
The five-number summary suggests that about 75\%75%75, percent of salons in Jamesville have fewer than how many stylists employed?
Answer:
15
Step-by-step explanation:
khna academy
For the data set below which of the following measures is greatest? 3,3,4,5,6,8,16,20
In this question, the student is asked to compare mean, median, mode, and range for a given data set. Among these measures, the range, being 17, is the greatest.
The question given is asking for the greatest measure among the data set, which is 3,3,4,5,6,8,16,20. The measures being referred to are likely statistical measures such as mean, median, mode, and range.
The mean is the sum of all the numbers divided by the total count of the numbers, the median is the middle value when the numbers are arranged in order, the mode is the number that appears most frequently, and the range is the difference between the largest and smallest numbers.
To find the mean, we calculate (3+3+4+5+6+8+16+20)/8=7.875. The median is the average of the two middle numbers since we have an even count, (5+6)/2 = 5.5. This data set's mode is 3 since 3 repeats only. The range is 20 - 3 = 17.
Comparing these measures, we see that the range, with a value of 17, is the greatest.
An office building has the dimensions shown.
What is the volume of the building?
2. 50 m
10 m
110 m
90 m
70 m
-5(c-2)=20-5c+10
A. 4 B. Null Set C. 1 D. -1
For the angles shown in the diagram, which statements are true? Select all that apply.
A.The sum of m∠3 and m∠4 is 180°.
B.The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle.
C.∠3 is supplementary to ∠1.
D.m∠4 = m∠1 + m∠2.
E.m∠1 + m∠2 + m∠3 = 180
Answer:
A, D, E
Step-by-step explanation:
i just did it
The statements that are true include:
A.The sum of m∠3 and m∠4 is 180°.D.m∠4 = m∠1 + m∠2.E. m∠1 + m∠2 + m∠3 = 180°It should be noted that the sum of angles that are in a triangle equals 180°. Therefore, m∠1 + m∠2 + m∠3 = 180°.
Also, the sum of m∠3 and m∠4 is 180°. This is because the angle on a straight line equals 180°.
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Write a variable expression for 3 times the sum of a number and 5.
A) 5(x + 3)
B) 3x +5
C) 3(x + 5)
D) x + 15
Answer:
B) 3x+5
Step-by-step explanation:
Let's suppose that x is equal to the sum of a number. That means, that 3x needs to be somewhere in the variable equation. "And 5", means to add, so +5 also needs to be somehwere in the equation. Giving you 3x + 5 as the answer. Now you might be thinking, "But what about C? Isn't it basically the same answer as B?" The answer to THAT question is NO. For it to be the same as B, you would have to get rid of the parenthesis. This is because when there's a parenthesis, it means that it is the first thing you have to do in the equation. But that is not what we want. We do not want the sum of a number to be added to 5. We want it to be multiplied by 3. So that is why C is the not the same as B. B is yoir correct answer.
What’s the answer to this
Answer:
Slope = -2/3 (Answer choice "a.")
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
y = -2/3x +5
This is in the form y = mx+b where m is the slope and b is the y intercept
-2/3 is the slope
The line perpendicular has a negative reciprocal slope or - 1 over the slope
- 1 /(-2/3)
-1 * (-3/2)
3/2
The slope of the line that is perpendicular is 3/2
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 5 mm. What is
the volume of the composite figure? Use 3.14 for Round to the nearest hundredth.
5 mm
10 mm
Recall the formulas y-Bhand V-
376.80 cubic millimeters
847 80 cubic millimeters
1.177 50 cubic millimeters
1308 33 cubic millimeters
Rounded to the nearest hundredth the volume of the composite figure is:
1308 33 cubic millimeters
Explanation:Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:
[tex]V_{c}=\pi r^2 h \\ \\ r:radius \\ \\ h:height[/tex]
While the volume of half a sphere is:
[tex]V_{hs}=\frac{2}{3}\pi r^3[/tex]
Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:
[tex]V_{s}=\frac{4}{3}\pi r^3[/tex]
Then, the composite figure is:
[tex]V=\pi r^2 h +\frac{4}{3}\pi r^3 \\ \\ V=\pi r^2(h+\frac{4}{3}r)[/tex]
The radius of the cylinder is the same of the radius of each half sphere. So:
[tex]r=5mm \\ \\ h=10mm \\ \\ \\ V=(3.14) (5)^2((10)+\frac{4}{3}(5)) \\ \\ V=25(3.14)(10+\frac{20}{3}) \\ \\ \boxed{V\approx 1308.33mm^3}[/tex]
100 points and brainliest, need this quick
pplleeaassee
This sphere has a diameter of 5 m.
A sphere with diameter 5 meters.
What is the volume of the sphere?
V = StartFraction 9 Over 2 EndFraction pim3
V = StartFraction 125 Over 6 Endfraction pim3
V = StartFraction 500 Over 3 EndFraction pim3
V = StartFraction 4,000 Over 3 EndFractionm3
9514 1404 393
Answer:
(b) (125/6)π m³
Step-by-step explanation:
The formula for the volume of a sphere is ...
V = (4/3)πr³ . . . radius r
The radius is half the diameter, so is (5/2) m. Then the volume is ...
V = (4/3)π(5/2 m)³ = (4/3)(125/8)π m³ = (125/6)π m³
Y=-3x+3
Y=5x+19
Solve this system by substitution
Answer:
x=-2
Step-by-step explanation:
You can substitute the first equation into the second:
-3x+3=5x+19
Add 3x on both sides:
3=8x+19
Subtract 19 on both sides:
-16=8x
Divide 8 on both sides:
x=-2
Answer:
x = -2
y = 9
Step-by-step explanation:
to evaluate this system of equation we would say that
let
Y=-3x+3................................................. equation 1
Y=5x+19................................................... equation2
substitute equation 2 into equation 1
5x + 19 = -3x + 3
collect the like terms together
5x + 3x = 3 -19
8x = -16
divide both sides by the coefficient of x which is 8
8x/8 = -16/8
x = -2
put x = -8 into equation 1
Y=-3x+3................................................. equation 1
y = -3(-2) + 3
y = 6 + 3
y = 9
therefore the value of x and y is -2 and 9 respectively.
Find the area of the figure. PLEASSEEEEEEEE!!!!!!!!
Given:
side length = 6 ft
To find:
The area of the figure
Solution:
Area of the square = side × side
= 6 × 6
Area of the square = 36 ft²
Diameter of the semi-circle = 6 ft
Radius of the semi-circle = 6 ÷ 2 = 3 ft
Area of the semi-circle = [tex]\frac{1}{2} \pi r^2[/tex]
[tex]$=\frac{1}{2} \times 3.14 \times 3^2[/tex]
Area of the semi-circle = 14.13 ft²
Area of the figure = Area of the square - Area of the semi-circle
= 36 ft² - 14.13 ft²
= 21.87 ft²
Area of the figure = 21.9 ft²
The area of the figure is 21.9 ft².
helllloo plss help asap it would mean alottttt
plss helppp asap
Answer: The point will move across the Y- axis
Step-by-step explanation:
When the X coordinate's sign is changed, then the coordinate will be reflected over the Y-axis, becoming equidistant from the Y-axis.
A cylindrical bucket can hold approximately 301.44 in. The height of the bucket is about 6 inches. What is the diameter of the bucket to the nearest inch?
Answer:
The diameter is 8 inches
Step-by-step explanation:
This problem bothers on mensuration of solid shapes, this in particular a cylindrical
Given data
Volume of cylinder in inches v=301.44in^3
Height of the bucket h= 6 inches
Radius r=?
To solve for the diameter we neeed to solve for the radius and multiply It by 2 to get the diameter
We know that the volume of a cylinder is given as
v= πr^2h
301.44= 3.142*r^2*6
301.44= 18.85*r^2
r^2= 301.44/18.85
r^2= 15.99
r=√15.99
r=3.998in
We know that the
diameter d =2r
Therefore d= 3.99*2
d= 7.997in
≈ d = 8 inches
WILL MARK BRAINLIEST
In which quadrants do solutions for the inequality y>1/5x+3
A) l and ll
B) I,ll, and lll
C)l,lll, and lV
D) All four quadrants
Answer:B is your correct answer
Step-by-step explanation:
I TOOK THE TEXT AND GOT A HUNDRED
Prove: If a point on a circle is equidistant from two radii, then the radius from the point bisects the angle formed by the two given radii.
Answer:
see the explanation
Step-by-step explanation:
see the attached figure to better understand the problem
we have that
OA+OB=radii of circle O
Point P is equidistant from radii OA and OB ----> given problem
so
PA=PB
OP is a common side
Triangle OAP is congruent to Triangle OBP by SSS Postulate Theorem
Remember that
If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent
That means
[tex]m\angle POA=m\angle POB[/tex]
therefore
The radius from the point (PO) bisects the angle formed by the two given radii (angle ∠AOB)
I mark brainliest
please help me I suck at math
Answer:
A
Step-by-step explanation:
If you enter the inequality into a graphing calculator and line the points up you will know the correct answer.
Answer:
a
Step-by-step explana
graph a
WILL GIVE BRAINLIEST!!Which graph shows the following system of equations and its solution?
-4x-3y=4
4x-y=-4
Answer:
C, I believe?
Step-by-step explanation:
19.64851 2 s .f help please
Answer: 20
Step-by-step explanation:
19.64851 to 2s.f
To 2 significant figures
Looking at the digit behind the decimal
It is 6,meaning it is more than 5
So you round up to 1 and add to the digit in front
=20
Enter the slope-intercept equation of the line that has the same slope as y - 3 = (x + 3) and contains
the point (8,4). Complete the explanation of how you found the equation.
y= ;l used the general form of a line in slope-intercept form, or y=mx+
b w The
slope, m, is .Then, I substituted for x and fory into the standard form and solved
for b, which is
HELLPPP please
Given:
[tex]y-3=\frac{1}{2}(x+3)[/tex]
Point = (8, 4)
To find:
The slope-intercept form of the equation of the line.
Solution:
[tex]$y-3=\frac{1}{2}(x+3)[/tex]
Slope of this line = [tex]\frac{1}{2}[/tex].
Slope of the line is same as the slope of [tex]y-3=\frac{1}{2}(x+3)[/tex].
Slope of the line (m) = [tex]\frac{1}{2}[/tex]
General form of line:
y = mx + b
[tex]y=\frac{1}{2} x+b[/tex] ---------- (1)
It contains the point (8, 4). Substitute x = 8 and y = 4 in (1).
[tex]4=\frac{1}{2}( 8)+b[/tex]
[tex]4=4+b[/tex]
Subtract 4 from both sides, we get
b = 0
Substitute b = 0 in (1).
Equation of the line:
[tex]y=\frac{1}{2} x+0[/tex]
[tex]$y=\frac{1}{2} x[/tex]
Complete the sentence:
[tex]y=\frac{1}{2} x[/tex]; I used the general form of a line in slope-intercept form, y = mx + b. The slope, m is [tex]\frac{1}{2}[/tex]. Then I substituted 8 for x and 4 for y into the standard form and solved for b, which is 0.
What number between 18 and 22 is a prime number?
Answer:
I think
19 has no factors other than 1 and itself
Does it matter when finding if a slope is positive or negative if the line
goes through the origin?
Can three segments with length 4 cm, 6 cm, and 11 cm be assembled to form an acute triangle, a right triangle, or an obtuse triangle? Explain.
Answer:
No
Step-by-step explanation:
Three segments 4cm, 6cm, and 11cm cannot form a right triangle because if they could, then by Pythagorean theorem, 4^2 + 6^2 = 11^2, which is not true.
Moreover, the three segments cannot form an acute or obtuse triangle because by Triangle Inequality Theorem, the sum of two sides has to be greater than the third side. Here, (4cm + 6cm) is NOT larger than 11cm, and thus you cannot form a triangle.
Using triangle concepts, it is found that the sides with these lengths cannot form a triangle.
In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the larger side.
In this problem:
The smaller sides have lengths: 4 cm and 6 cm.The larger side has length: 11 cm.[tex]4 + 6 = 10 < 11[/tex]
Since the larger side length is greater than the sum of the lengths of the smaller sides, a triangle cannot be formed.
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At a school picnic, students can choose their dessert. The desserts include 8 ice cream sandwiches, 9 chocolate frozen bananas, 12 ice cream cones, 11 frozen pops, 16 push-up sticks, and 14 shaved ice cones. If desserts are chosen at random, what is the probability that the first person in line will choose an ICE CREAM CONE? Please select one answer.
Answer:
6/35
Step-by-step explanation:
8ice cream sandwiches
9 chocolate frosen banana
12 ice cream cones
11 frosen pops
16 push up sticks
14 shaved ice cones
So we will have to sum them up
8+9+12+11+16+14
70
So the probability for ice cream cones
12/70
Divide the two by 2
6/35
So the probability will be 6/35
q + 15 = 29???? what is it and can u also explain how...?