The reference number for each value of t are;
(A) t = 4π/3: Reference number = 240 degrees
(B) t = 5π/3: Reference number = 300 degrees
(C) t = -7π/6: Reference number = 150 degrees
(D) t = 3.7: Reference number = 3.7 degrees
(A) How to find the reference number for given values of t?We need to determine the equivalent angle within one revolution (360 degrees) for each given value to find the reference number of t.
t = 4π/3:
To find the reference number for t = 4π/3, we need to convert it to degrees. Since 2π radians is equal to 360 degrees, we can set up a proportion:
2π radians = 360 degrees
4π/3 radians = x degrees
Solving for x, we have:
x = (4π/3) × (360 degrees / 2π radians)
x = (4/3) × 180 degrees
x = 240 degrees
Therefore, the reference number for t = 4π/3 is 240 degrees.
(B) How to find the reference number for t = 5π/3?t = 5π/3:
Using a similar process, we can find the reference number for t = 5π/3:
5π/3 radians = x degrees
x = (5π/3) × (360 degrees / 2π radians)
x = (5/3) × 180 degrees
x = 300 degrees
Therefore, the reference number for t = 5π/3 is 300 degrees.
(C) How to find the reference number for t = -7π/6?t = -7π/6:
Since t = -7π/6 is a negative angle, we can find the reference number by adding 360 degrees to the equivalent positive angle:
-7π/6 radians + 2π radians = x degrees
-7π/6 + 12π/6 = x degrees
5π/6 = x degrees
Therefore, the reference number for t = -7π/6 is 5π/6 or approximately 150 degrees.
(D) How to find the reference number for t = 3.7?t = 3.7:
Since t = 3.7 is given in degrees, it already represents the reference number.
Therefore, the reference number for t = 3.7 is 3.7 degrees.
To summarize:
(A) t = 4π/3: Reference number = 240 degrees
(B) t = 5π/3: Reference number = 300 degrees
(C) t = -7π/6: Reference number = 150 degrees
(D) t = 3.7: Reference number = 3.7 degrees
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Question 1
Which equation represents the relationship shown in the table
at the right?
Answer:
Option (4)
Step-by-step explanation:
When x = 0, y = -3.
Eliminate Option 1.Also, the slope is
[tex]\frac{-1-(-3)}{1-0}=2[/tex]
So, the equation is y = 2x - 3.
A group of restaurant owners surveyed a list of people to determine how preferences of meats compared to preferences of grains, and if they are related. The results are in the table above. Based on the table, is there evidence of association between chicken preferences and rice preferences
There is no association between the chicken preferences and rice preferences. Option C
What is association?There is an association between two variables when they both decrease or increase simultaneously. In many cases, the association between the variables can be shown using the correlation coefficient when the relationship is plotted on Cartesian coordinates.
If we look at the table, we can see that there is no association between the chicken preferences and rice preferences because because the proportion of chicken and rice eaters to all chicken eaters is lower than all rice eaters to all eaters; and because the proportion of chicken and rice eaters to all rice eaters is lower than all chicken eaters to all eaters.
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The mass of a proton is about 1.7 x 10^-24 g. The mass of a neutron is about the same as a proton. The nucleus of an atom of carbon has 6 protons and 6 neutrons. The mass of the nucleus is about 2 x 10^-26 units. Circle the best choice for the units this measurement is given in: g/kg/tons
The density of proton exists [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
How to estimate the density of proton?Given:
[tex]$r = 2 * 10^{-26[/tex] units.
[tex]mass = 1.7 * 10^{-24[/tex] grams
Formula, V [tex]= 4/3 * \pi * r^3[/tex]
Density = mass / Velocity
Put the givens into the formula.
Find the value for [tex]r^3[/tex]
[tex]V = (4/3) 3.14 * (1 * 10^{-13})^3[/tex]
To estimate the volume indicate divide by 3
[tex]V = (4/3) 3.14 * 1 * 10^{-39[/tex]
[tex]V = 1.256 10^{-38/3[/tex]
[tex]V = 4.1867 * 10^{-39[/tex]
Density = mass / velocity
Density = [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
Therefore, the density of proton exists [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
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A container is the shape of an inverted right circular cone has a radius of 4.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 2.00 inches deep, the surface level is falling at the rate of -2.00 in./s. Find the rate at which water is being drained.
The rate at which the water from the container is being drained is 24 inches per second.
Given radius of right circular cone 4 inches .height being 5 inches, height of water is 2 inches and rate at which surface area is falling is 2 inches per second.
Looking at the image we can use similar triangle propert to derive the relationship:
r/R=h/H
where dh/dt=2.
Thus r/5=2/5
r=2 inches
Now from r/R=h/H
we have to write with initial values of cone and differentiate:
r/5=h/5
5r=5h
differentiating with respect to t
5 dr/dt=5 dh/dt
dh/dt is given as 2
5 dr/dt=5*-2
dr/dt=-2
Volume of cone is 1/3 π[tex]r^{2} h[/tex]
We can find the rate at which the water is to be drained by using partial differentiation on the volume equation.
Thus
dv/dt=1/3 π(2rh*dr/dt)+([tex]r^{2}[/tex]*dh/dt)
Putting the values which are given and calculated we get
dv/dt=1/3π(2*2*2*2)+(4*2)
=1/3*3.14*(16+8)
=3.14*24/3.14
=24 inches per second
Hence the rate at which the water is drained from the container is 24 inches per second.
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What is the range of the function graphed below?
y
-8 -6
B.
C.
+
O D.
-2
8
6+
4+
2+
-2-
-4-
-6+
OA -∞0 < y < 2
-∞ < y < ∞
-2 < y < ∞
-∞0 < y < -2
-8-
N
10
--00
Y
+x
Answer:
D
Step-by-step explanation:
Range is the 'y' values a graph can have
you can see that the 'y' values can be anythig from - inf to + 2
The range of the function is [2, -∞].
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
We see that the function line y values are from 2 to negative infinity.
This means,
The range is [2, -∞].
Thus,
The range of the function is [2, -∞].
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Javid travels to work by bus or by train.
The daily bus fare is £2.50
The daily train fare is £3.50
In 5 days he spends a total of £14.50
On how many days did he travel by bus?
Javid travelled by bus for 3 days using a simultaneous equation
What is simultaneous equation?
This refers to equations that are solved together in order to determine the values of unknown variables.
In this case, the total amount spent on daily bus or train can be determined as the fare price multiplied by the number of days
Let X be the number of days that Javid took bus
total spent on bus=2.50X
Let Y be the number of days that Javid took train
total spent on train=3.50Y
Total spent=2.50X+3.50Y
14.50=2.50X+3.50Y
Secondly, X plus Y gives 5 days
5=X+Y
multiply the second equation by 2.50 and the first by 1
14.50=2.50X+3.50Y
12.50=2.50X+2.50Y
subtract the second equation from first
2=Y
substitute for Y
5=X+Y
5=X+2
X=5-2
X=3
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The number of days that he travelled by bus is; 3 days
How to Solve Simultaneous Equations?Let x be the number of days that Javid travelled by bus.
Let y be the number of days that Javid travelled by train.
Thus;
Total spent on bus = 2.50x
Total spent on train = 3.50y
Overall total spent is;
2.5x + 3.5y = 14.50 -----(1)
Total number of days is 5 days and so;
x + y = 5 -----(2)
Making x the subject in eq 2 gives us;
x = 5 - y -----(3)
Put eq 3 in eq 1 to get;
2.5(5 - y) + 3.5y = 14.50
12.5 - 2.5y + 3.5y = 14.5
y = 14.5 - 12.5
y = 2 days
Thus;
x = 5 - 2
x = 3 days
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In the figure shown, line AB is parallel to line CD. Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points) A 65⁰ P 120⁰ R B O
a) ∠PQR=65° (alternate interior angles theorem)
∠PRQ = 60° (linear pair)
x = 55° (angles in a triangle add to 180°)
b) ∠APQ and ∠PQR are congruent alternate interior angles.
v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
A: Identify the function type in the graph, and then describe a relationship that could be modeled by the function represented by the graph.
B: Identify and interpret the key features of the function in the context of the situation you described in part A.
The function type in the graph is a decreasing function.
What is a function?It should be noted that a function is simply used to illustrate the relationship between variables.
In this case, the function type in the graph is a decreasing function. As the number in X axis increases, the value in the y axis is decreased.
This illustrates a decreasing function.
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Volume =
Help me please thanks
Step-by-step explanation:
Volume of the right circular cone=31πr2h=31×π×6×6×10=120πcm3
Answer:
Volume = 405π unit^3
which is
1272.35 unit^3 to nearest hundredth.
Step-by-step explanation:
Volume of the given cone
= 1/3 πr^2 h
= 1/3π(6)^2*10
= 120π unit^3.
The cone similar to it with radius 9 will have a volume equal to
(9/6)^3 times the given cone
= 120π * 729/216
= 405π unit^3.
Answer fast in steps
What is the missing number in the synthetic division problem below? NEED HELP FAST!
Answer:
9
Step-by-step explanation:
3 + 0 = 3
-2 + 6 = 4
2 + 18 = 20
From this:
1 + 8 = 9
Answer:
A.9
Step-by-step explanation:
✓3 + 0 = 3
✓ -2 + 6 = 4
✓ 1 + 8 = 9
✓ 2 + 18 = 20 beacuse of this the answer is 9
Use the drawing tool(s) to form the correct answer on the provided number line. Consider the given functions. Function 1 Function 2 Graph shows a polynomial function plotted on a coordinate plane with vertical axis g of x. A curve enters quadrant 3 at (minus 5, minus 40), goes through (minus 4, 0), (minus 2, 32), (0, 15), (2, 0), and exits quadrant 1 at (4, 30). Represent the interval where both functions are decreasing on the number line provided.
Both functions decrease at (-1, 2)
How to determine the decreasing intervals of the function?The complete question is added as an attachment
The polynomial function f(x) is represented by the graph.
From the graph, the polynomial function decreases at (-2, 2)
The absolute function is given as;
f(x) = =5|x + 1| + 10
The vertex of the above function is
Vertex = (-1, 10)
Because a is negative (a= -5), the vertex is a maximum.
This means that the function decreases at (-1, ∞)
So, we have
(-2, 2) and (-1, ∞)
Combine both intervals
(-1, 2)
This means that both functions decrease at (-1, 2)
See attachment 2 for the number line that represents the interval where both functions are decreasing
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PLEASE HELP FAST!
The question is below:
The transformation that produces same image are:
Translate 3 units right and 5 units down. Then rotate 90 degrees about the origin.Translate 2 units up and 4 units left. Translate 6 units down and 4 units rightThe transformation that produces different image are:
Rotate 90 degrees about the origin. Then Dilate using a scale factor of 1/2Dilate using a scale factor of 5. Translate 4 units left and 2 units upWhat is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation, reflection and rotation are rigid transformation which produces same image while dilation produces similar shapes.
The transformation that produces same image are:
Translate 3 units right and 5 units down. Then rotate 90 degrees about the origin.Translate 2 units up and 4 units left. Translate 6 units down and 4 units rightThe transformation that produces different image are:
Rotate 90 degrees about the origin. Then Dilate using a scale factor of 1/2Dilate using a scale factor of 5. Translate 4 units left and 2 units upFind out more on transformation at: https://brainly.com/question/4289712
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Desiree opens an account with one deposit of $6500. she receives a statement twice a year, just after the interest is applied. which type of account is desiree most likely using?
From Longman Dictionary of Contemporary English opens an account to start an account at a bank or other financial organization by putting money into it Mary was in the bank to ask about opening a current account.
Step 1: Visit the official website of the bank in which you wish to open an account. Step 2: Fill in the application form online along with a digital copy of address proof, identity proof, age proof, income/employment proof, and photographs.
You need to be at least 18 years old to open an account. However, you can open a joint account as a minor with a parent or legal guardian as an account co-owner. Some banks do offer accounts tailored for minors.
Please check the attached file for a complete answer.
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Suppose the number of residents within five miles of each of your stores is asymmetrically distributed with a mean of 19 thousand and a standard deviation of 7.6 thousand. What is the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores
The 95th percentile for the average number of residents within five miles of each store is 20219.86.
Given mean of 19000 , sample size of 75 stores and standard deviation of 7600.
We have to find the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores.
We have to first find the margin of error to calculate the upper level of confidence interval.
Margin of error is the difference between the real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of z at given confidence level.
σ is standard deviation
n is the sample size.
z value at 95% confidence level is 1.39. (one tailed)
Put the values in the formula to get margin of error.
Margin of error=1.39*7600/[tex]\sqrt{75}[/tex]
=10564/8.66
=1219.86
Upper level=19000+1219.86
=20219.86
Hence the 95th percentile is 20219.86 for the average number of residents within five miles of each store in a sample of 75 stores.
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How many terms are in the sequence shown?
38, 36, 34, ..., -20
Answer:
30 terms
Step-by-step explanation:
In the sequence, the value of each term decreases by 2.
38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20.
1+ (38 - (-20))/2 = 1+ 29 = 30
Geometry question need explanation on finding the answer
Sample Response: First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller. Which did you include in your answer? Check all that apply. Write the ratios as fractions. Find a common denominator. Compare the numerators to see that 4:10 is the smaller ratio
In the case above, the option that one need to include in your answer is to Find a common denominator.
What is Fraction in lowest terms?When the numerator and denominator of a fraction are known to not have common factor other than 1, then a person can say that the fraction in its simple form or say its in its lowest term.
Since there is a common numerator and the common denominator will be between 10 and 20. Since 10 is less that than 20, the common denominator will be 20 as both can divide it.
Hence, In the case above, the option that one need to include in your answer is to Find a common denominator.
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A client has just inherited a property. the deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. the shape is an irregular quadrilateral and the other three sides have distances of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. more importantly, it is known that the front left corner of the property is a right angle.
Answer:
sorry ❣️ bro you halp me
Which of the following steps would you perform to the system of equations
below so that the equations have opposite y-coefficients?
4x+2y = 4
12X - Y = 26
A. Divide both sides of the top equation by 3
•
B. Divide both sides of the bottom equation by 3
• C. Multiply both sides of the bottom equation by 2
• D. Multiply both sides of the top equation by 2
Answer: Choice C
Multiply both sides of the bottom equation by 2
Reason:
The y coefficient of the first equation is 2. For the other equation, that y coefficient is -1. We need these coefficients to be equal but opposite. One way to do this is to double everything in the bottom equation
The bottom equation 12x-y = 26 doubles to 24x - 2y = 52
At this point we have the equivalent system of
[tex]\begin{cases}4x+2y = 4\\24x-2y = 52\end{cases}[/tex]
And we can see that we have equal but opposite y coefficients (2 and -2). The y terms add to 0 since 2y + (-2y) = 0y = 0 meaning we've eliminated y.
help me please omg im in a rush
Answer:48
Step-by-step explanation:
Question 5(Multiple Choice Worth 5 points)
(05.05 LC)
PLEASE HELP!!!!
The base length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle?
2 square feet
4 square feet
6 square feet
8 square feet
Answer:
4 square feet
Step-by-step explanation:
A function is a relation where each input value is assigned to (1) ___ one output value.the (2) ___ of a function is the set of all input values, or x-values, for which the function is defined. the (3) ___ of a function is the set of all output values, or y-values, for which the function is defined. to write the equation y = ax + b in function notation, substitute (4) ___ for y. options for 1: a. exactly b. at least c. less than options for 2: a. range b. interval c. domain d. rate of change options for 3: a. range b. rate of change c. interval d. domain options for 4: a. f(x) b. a c. b d. x
The blanks can be filed by exactly, domain, range, and, f(x) respectively.
While we've got a feature in formulation form, it also includes a simple count to assess the function. For example, the feature f(x)=5−3x2 f ( x ) = 5 − 3 x 2 can be evaluated with the aid of squaring the enter cost, multiplying by means of three, and then subtracting the product from 5.
You write capabilities with the function name observed by way of the established variable, together with f(x), g(x), or maybe h(t) if the function depends upon time. You read the function f(x) as "f of x" and h(t) as "h of t". functions no longer need to be linear. The feature g(x) = -x^2 -3x + 5 is a nonlinear characteristic.
A user is an actual-valued feature on a vector area, usually of functions. as an example, the electricity practical at the unit disk assigns various to any differentiable feature, For the practical to be non-stop, it's miles necessary for the vector space. of capabilities to have the perfect topology.
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Given: ΔABC is a right triangle and CD ⊥ AB.
Prove: AC2 + BC2 = AB2
Which reason completes the proof?
A.
Corresponding sides of similar triangles are proportional.
B.
Corresponding parts of congruent triangles are congruent.
C.
Corresponding parts of similar triangles are congruent.
D.
Corresponding sides of congruent triangles are proportional.
Answer:
Corresponding parts of similar triangles are congruent.
Step-by-step explanation:
Help ASAP will give 20 points!!!!!
use six unit multipliers to convert 33 cubic feet to cubic centimeters
Converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
How to determine the conversionIt is important to note that conversion of units requires the appropriate equivalent values
For
I cubic foot is equivalent to 28316. 8 cubic centimeters
But we were given
33 cubic feet for the conversion
If 1 cubic foot = 28316. 8 cubic centimeters
Then 33 cubic feet = x
Cross multiply, we get
x = 28316. 8 × 33
x = 934454. 4 cubic centimeters
Thus, converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
A. y 2 and ys x
B. x>2 and yz x
C. x22 and y> x
D. y 22 and y
The system is:
y < x
y ≥ 2
So we conclude that the correct option is D.
Which system of inequalities is represented in the graph?On the graph, we can see two lines. One with a positive slope that is dashed.
And a solid line that is constant of the form y = c.
We can see that the shaded region is above the constant line and below the line with a positive slope, so the system of inequalities is of the form:
y < line.y ≥ constant line (≥ is used because this line is solid).The only option that has this form is option d:
y < x
y ≥ 2
So we conclude that the correct option is D.
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5. Jigsel has 6 more years of teaching experience than Wangmo, and the two of themhave 16 years of teaching experience altogether. How many years of teaching experience does Wangmo have?
Answer:
10 just find the difference between the two
Step-by-step explanation:
16-6=10
Wangmo have 6 years of teaching experience.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Let Wangmo has x years of experience.
Jigsel has 6 more years of teaching experience than Wangmo.
So, Jigsel has x + 6 years of experience.
According to the question,
the two of them have 16 years of teaching experience altogether.
That means,
we have the equation,
(x+6) + x = 16
2x = 16 -6
2x = 10
x = 10/2
x = 5
Therefore, Wangmo has 6 years of experience.
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Simplify :-
(3x-2y) (3x+2y) (9x²+4y²)
Answer:
[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]
Step-by-step explanation:
Given expression:= (3x - 2y)(3x + 2y)(9x² + 4y²)
Using formula:[tex](a+b)(a-b)=a^2-b^2[/tex]= [(3x)² - (2y)²] (9x² + 4y²)
= (9x² - 4y²)(9x² + 4y²)
Using the above formula again
= (9x²)² - (4y²)²
= 81x⁴ - 16y⁴[tex]\rule[225]{225}{2}[/tex]
Geometry question need help finding the answers to this
Answer:
L' (-1, 1)
M' (1, 2)
N' (1, -1)