SOLUTION
Given the question in the question tab, the following are the solution steps to find the angle of least positive measure.
Step 1: Define the concept of least positive measure
Coterminal angles are those angles that share the terminal side of an angle occupying the standard position. The question is asking for the least positive coterminal angle, so you must add or subtract until you reach a positive angle that is between 0 and 360 degrees.
Step 2: Find the angle of least positive meausre of 1313
To find the coterminal angles to your given angle, you need to add or subtract a multiple of 360°. Since the given angle is positive, we can get the required angle by finding:
\(1313\mod 360\)Or we keep subtracting 360 from 1313 until we have a positive value less than 360.
Step 3: We use the modulo method
It can be seen that 1313 mod 360 will give 233. i.e,
\(\frac{1313}{360}=3\text{ remainder 233}\)This implies that 1313 contains 3 complete revolutions and additional 233 degrees.
Hence, 233 is the angle of least positive measure.
What is the mode of this set of data?
Answer:
The mode is 15
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).
Answer:
The mode of this set is 15.
Step-by-step explanation:
the mode is 15 bcoz 15 is repeated two times where as other numbers aren't repeated..
How to solve this?? (-4)-(-8)+(-4)
Translate this sentence into an equation. 43 is the sum of 11 and Carlos age. Use the variable c to represent Carlos age.
Answer:
c + 11 = 43
Step-by-step explanation:
C = Carlos age
11 = The number added
43 = The number added plus carlos' age
c +11 = 43
c = 43 - 11
c = 32
Carlos' age is 32 years.
Answer:
C+11=43
Step-by-step explanation:
C= Carlos age
11= added number
43= Carlos age +added number
C+11=43
C=43-11
C=32
Age of Carlos 32. :)
In a hardware store you must first go to server 1 to get your goods and then go to a server 2 to pay for them. Suppose that the times for the two activities are exponentially distributed with means six and three minutes. Compute the average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2.
The average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2 will be 16 minutes.
Let us assume that, T = the total amount of time Bob spends in the hardware store.
Let us assume that, T1 = the amount of time Bob spends waiting in line for Al to get his goods from server 1
Let us assume that, T2 = the amount of time it takes for Bob to get his goods from server 1
Let us assume that, T3 = the amount of time Bob spends waiting in line for Al to pay server 2 for his goods
Let us assume that, T4 = the amount of time it takes for Bob to pay server 2 for his goods
So, the value of total time T will be
T = T1 + T2 + T3 + T4 and E[T] = E[T1] + E[T2] + E[T3] + E[T4]
Now, E[T1] = 6 min. because of the memoryless property of the exponential distribution
E[T2] = 6 min.
To find E[T3], the condition on the availability of server 2 after Bob is done with server 1
So, the value of E[T3] will be
E[T3] = E[T3 | Server 2 is free] P(Server 2 is free) + E[T3 | Server 2 is not free] P(Server 2 is not free)
= 0 + 3 . P(Bob is done with server 1 before AI is done with server 2)
\($$=3 \cdot \frac{1 / 6}{1 / 6+1 / 3}$$\)= 3(1/3) = 1 min. and E[T4] = 3 min.
So, E[T] = E[T1] + E[T2] + E[T3] + E[T4]
or, E[T] = 6+6+1+3= 16 minutes
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A rectangular table surface has a length of (5x-2) meters and a width of (x+2) meters. Mr. Phillip wants to put a glass mirror on the table. The width of the table not covered by the mirror is (x-3) meters. Find the surface area of the table that is not covered by the mirror.
The surface area of the table top that is not covered by the mirror in the form of algebraic expressions is \(5x^2 - 17x +6\,\,m^2\) .
The length of the table top = 5x - 2 m.
The width of the table not covered by mirror is x-3 m.
The surface area of the table top not covered by the mirror is
\($(5x-2)(x-3) = 5x^2 -15x -2x +6 \,\,m^2\)
\($=5x^2 -17x +6\,\, m^2\) in the form of algebraic expressions.
What are the formulas for the surface area of some common solid figuresSurface area of cylinder of radius r and height h = \(2\pi r^2 + 2\pi rh\)
Surface area of a cuboid of side length a = \(6a^2\)
Outside area for a sphere of radius r = \(4\pi r^2\)
Surface area of a regular tetrahedron of edge length a = \(\sqrt{3}\,a^2\)
Surface area of a right angled cone of base radius r, and lateral height l = \(\pi r^2 + \pi r l\)
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What percentage of the data is between 4 and 9?
A: 25
B: 50
C: 75
D: 100
Answer:
its 25% meaning A is the answer
Step-by-step explanation:
Use factoring to solve the polynomial equation. Check by substitution or by using a graphing utility and identifying
x-intercepts.
8x4-32x² = 0
Rewrite the equation in factored form.
(Blank)=0
Then what is the solution pair?
The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2
Using factoring to solve the polynomial equationTo solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:
8x²(x² - 4) = 0
Now we can use the difference of squares identity to factor the quadratic expression:
8x²(x + 2)(x - 2) = 0
Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.
Therefore, we can set each factor equal to zero and solve for x:
8x² = 0 or x + 2 = 0 or x - 2 = 0
Solving for x, we get:
x = 0 or x = -2 or x = 2
So the solution set for the equation is {0, -2, 2}.
To check the solution, we can substitute each value into the original equation and verify that it equals zero.
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Anybody Know This Answer. ?
Inverse Questions. Pls Help give answer options. A,B,C, or D.
The Solution:
GIven:
Required:
Find the inverse of the function and its domain.
Step 1:
Let:
\(\begin{gathered} y=f(x)=\sqrt{x}-5 \\ \\ y=\sqrt{x}-5 \end{gathered}\)Step 2:
\(y+5=\sqrt{x}\)\(\begin{gathered} (y+5)^2=(\sqrt{x})^2 \\ \\ (y+5)^2=x \\ \\ x=(y+5)^2 \end{gathered}\)Replace y with x.
\(f^{-1}(x)=(x+5)^2=x^2+10x+25\)Answer: [option C]
\(\begin{gathered} Inverse:\text{ }f^{-1}(x)=x^2+10x+25 \\ \\ Domain:\text{ \lbrack0},\infty) \end{gathered}\)
Given the following information, find the equation in vertex form, factored form and standard form.
1. Vertex (1, 4) Point (2, -1)
Vertex form
Standard form
Answer:
Vertex:
\(f(x)=-5(x-1)^2+4\)
Standard:
\(f(x)=-5x^2+10x-1\)
Factored:
This is unfactorable.
Step-by-step explanation:
The parabola has a vertex at (1, 4) and it crosses a point at (2, -1).
We will start off with the vertex form, given by:
\(f(x)=a(x-h)^2+k\)
Where (h, k) is the vertex.
Therefore:
\(f(x)=a(x-1)^2+4\)
Since the function passes through (2, -1), f(x) = -1 when x = 2:
\(-1=a(2-1)^2+4\)
Solve for a:
\(-5=a(1)\Rightarrow a =-5\)
Therefore, vertex form is:
\(f(x)=-5(x-1)^2+4\)
To find the standard form, expand:
\(f(x)=-5(x^2-2x+1)+4\)
Distribute:
\(f(x)=-5x^2+10x-5+4\)
And simplify:
\(f(x)=-5x^2+10x-1\)
We can now factor. Which two values multiply to be 5 and add up to be 10?
Since this is no possible, the equation is unfactorable.
In 1980 a domino's pizza cost $5.99. What would be the cost of that pizza in 2000?
HELP ASAP !!!!!!!!!!!!!!!
Bradley and Blake went fishing Saturday and each caught a fish. Blake’s fish weighed 1.37 pounds more than Bradley’s fish. Select the values that could represent how many pounds each fish could weigh. Mark all that apply.
Blake’s fish: 7.85 lb, Bradley’s fish: 6.48 lb
Blake’s fish: 5.20 lb, Bradley’s fish: 3.83 lb
Blake’s fish: 6.36 lb, Bradley’s fish: 4.99 lb
Blake’s fish: 8.81 lb, Bradley’s fish: 7.54 lb
Answer: its the second one
Step-by-step explanation: 5.20 - 3.83 = 1.37
The area of a square porch is 81 square feet. Find the dimensions of the porch.
Answer:
9 feet
Step-by-step explanation:
Square root 81 as all the sides of the porch are the same length
‼️‼️‼️‼️‼️‼️im gonna fail this test I NEED HELP ‼️‼️‼️
stay on my page more questions are coming up
Answer:
B
Step-by-step explanation:
What are the roots of the function represented by the table?
From the table, the root of the function is a point where y = 0.
Therefore,
The root of the function are ( 4, 0 ) and ( -3, 0 )
Final answer
I and III only Option B
6.4 x 7.8 partial product
Answer: 49.92
Step-by-step explanation: I had that question on my Exam
Car, x. When researchers looked at the association of x and y, they found that the coefficient of determination was = 0.158. Select two conclusions that the researcher can make from this data.
a) About 40% of the variation in the age of the car is explained by a linear relationship with the value of the car.
b) The correlation coefficient, r, is 0.842.
c). The correlation coefficient, r, is 0.025.
d) The correlation coefficient, r, is 0.397
e) About 84% of the variation in the value of the car is explained by a linear relationship with the age of the car
f.) About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.
Answer:
D and f
Step-by-step explanation:
From the question,
Coefficient of determination r² = 0.158
D.
To get the correlation coefficient,
We take the square root of birth sides,
√r² = √0.158
r = 0.397
F.
The coefficient of determination = 0.158
When approximated, we get 0.16
0.16 x100
= 16percent
So 16% of this variation explains the linear relationship with age of car
So from the explanations for d and f above, it is evident that the answer options I chose are the correct answers to the question.
Which statement describes the relationship between x
and y?
As x increases, y decreases.
QAs x increases, y increases.
O As x increases, y increases and then decreases.
As x increases, y decreases and then increases.
Answer:
1.) inverse proportion : 1kx = y
2) direct proportion. y = kx
PLEASE HELP ME PLEASE ASAP!!! I WILL GIVE BRAINLIST PLEASE
ΔABC is rotated 90° clockwise about the origin.
By using the concept of rotation, it can be inferred that
New coordinate of C (C') = (12, -6)
What is rotation?
Rotation is a mathematical transformation in which an object is turned about a fixed point called the center of rotation. Rotation is a very important tool in mathematics, especially in coordinate geometry.
In this problem, 90° rotation clockwise about the origin has been applied.
We need to find the new coordinate of C after rotation.
Coordinate of C = (6, 12)
C is in the first quadrant
On rotating 90° clockwise, point C will go to fourth quadrant
New coordinate of C (C') = (12, -6)
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Model -2/4 + 3/4 on the number line
The model lies between 0 and 1 on the number line.We can find by dividing number and then add both of number.
How do we represent number on a number line?The real number line is a horizontal line with arrows on both sides. It consists of the origin “0”. All the positive numbers are represented on the right side of the origin and all the negative numbers are represented on the left side of the origin, with a definite scale.
What is a Number Line Model?A number line model is a representation of numbers plotted on an infinite line that extends at both ends.It is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.
Now we find
-2/4 =-0.5
3/4= 0.75
0.75- 0.5=0.25
which is lies between 0 and 1 on the number line.
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A store is having a sale. All items for sale are discounted 15%. If the regular price of a bedspread is $45, what is the sale price?
(I NEED THIS QUICK)
Answer:
$38.25
Step-by-step explanation:
45 × 0.15 = 6.75
45 - 6.75 = 38.25
The sale price of the item will be $38.25
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a store is having a sale. All items for sale are discounted by 15%. the regular price of a bedspread is $45,
The discounted price will be calculated as:-
45 × 0.15 = 6.75
45 - 6.75 = $38.25
Therefore, the sale price of the item will be $38.25
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An object projected upwards with a velocity of 96 feet per second from a height of 6 feet above theground is modelled by the function ℎ() = −162 + 96 + 6 .A. [3 pts] How many seconds after launch will the object reach its maximum height? Round your answerto one decimal place.B. [3 pts] Find the maximum height that the object reaches. Round your answer to one decimal place.C. [3 pts] Find the x-intercept and explain its meaning on the context of the problem.D. [3 pts] After how many seconds will the object be 100 feet above the ground?E. [2 pts] Find the y-intercept and explain its meaning on the context of the problem
Given:
\(h(t)=-16t^2+96t+6\)Find-:
(a) Maximum second after launch will the object reach its maximum height
(b) Find the maximum height that the object reaches.
(c) Find the x-intercept and explain its meaning in the context of the problem.
(d) After how many seconds will the object be 100 feet above the ground
(e) Find the y-intercept and explain its meaning on the context of the problem
Sol:
(a)
Maximum second after launch.
For maximum value derivative should be zero.
\(\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h^{\prime}(t)=-(16\times2)t+96 \\ \\ \end{gathered}\)\(\begin{gathered} -32t+96=0 \\ \\ 32t=96 \\ \\ t=\frac{96}{32} \\ \\ t=3 \end{gathered}\)After 3-second the object reaches maximum height.
(b)
For maximum height is at t = 3
\(\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(3)=-16(3)^2+96(3)+6 \\ \\ h(3)=(-16\times9)+(96\times3)+6 \\ \\ h(3)=-144+288+6 \\ \\ =150 \end{gathered}\)(c) x-intercept the value of y is zero that means:
\(\begin{gathered} h(t)=0 \\ \\ -16t^2+96t+6=0 \\ \\ -8t^2+48t+3=0 \\ \\ t=\frac{-48\pm\sqrt{48^2-4(-8)(3)}}{2(-8)} \\ \\ t=\frac{-48\pm48.98}{-16} \\ \\ t=6;t=-0.061 \end{gathered}\)The negative value of "t" is not considered so at
x-intercept is 6 and -0.061
(d) Object be 100 feet above grounded is:
\(\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ -16t^2+96t+6=100 \\ \\ -16t^2+96t-94=0 \\ \\ -8t^2+48t-47=0 \\ \end{gathered}\)So, the time is:
\(\begin{gathered} t=\frac{-48\pm\sqrt{48^2-4(-8)(-47)}}{2(-8)} \\ \\ t=\frac{-48\pm\sqrt{800}}{-16} \\ \\ t=\frac{-48-28.28}{-16},t=\frac{-48+28.28}{-16} \\ \\ t=4.76,t=1.23 \end{gathered}\)At t= 4.76 and t =1.23
(e)
For y-intercept value of "x" is zero.
\(\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(0)=-16(0)^2+96(0)+6 \\ \\ h(0)=6 \end{gathered}\)So, the y-intercept is 6.
There is a bag filled with 2 blue, 4 red and 3 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting 2 the same colour?
Answer:
9 to 2 = 2+4+3=9 2 picks all together you have 9 marbles and you have 2 picks this will give you a ratio of 9 to 2
Please help me! My teacher gave us this and has only taught us about rectangles, not rhombi. My classmates and I are very confused
Step-by-step explanation:
It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other . Opposite angles are equal and adjacen angles sum to 180 degrees .
Then remember alternate angles are equal and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one
What is the slope of the line that passes through the points (-2, 2), and (-4, -2)?
-1/2
2
-2
1/2
Answer:
The slope would be 2
Step-by-step explanation:
Please brainliest!
And hope this helped you!
I also answered first!
And tell me If I am wrong! :D
im sorry im very bad at math ;w; what is 1/5 + 2/15 = ???
Answer:
the answer is 1/3
Step-by-step explanation:
.........
\( = \frac{1}{5} + \frac{2}{15} \)
\( = \frac{(1 \times 3)}{15} + \frac{(2 \times 1)}{15} \)
\( = \frac{3}{15} + \frac{2}{15} \)
\(= {\frac{5}{15}}\)
\( = \frac{5 \div 5} {15 \div 5} \)
\(\color{hotpink}= \frac{1}{3} \)
Therefore :-
\(\color{olive}\bold{ \frac{1}{5} + \frac{2}{15} =\color{hotpink} \frac{5}{15} \: \: \texttt{or} \: \: \frac{1}{3} }\)
Convert .805 liters to millimeter s
Use slope formula, m= y2, - y1 over X2-X1 to find the slope of a line that passes through the points (-3, 8) and (4.-6).
m=
use the slope-intercept form, y=mx+b to find the y-intercept (b) of the line
b=
what is the new equation written in slope-intercept form y=mx+b
Answer:
m= -2
b= 2
y= -2x + 2
Step-by-step explanation:
Just did it
The slope of a line is m = -2 that passes through the points (-3, 8) and (4.-6), the y-intercept (b) of the line is 2, and the equation is y = -2x + 2.
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Given that the line that passes through the points (-3, 8) and (4.-6).
Let
x₁ = -3, y₁ = 8
x₂ = 4, y₂ = -6
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
m = (-6 - 8)/(4 -(-3))
m = (-14)/7
m = -2
y - 8 = m(x - (-3))
y - 8 = -2(x + 3)
y = -2x -6 + 8
y = -2x + 2
Since the slope-intercept form, y = mx+b
So the y-intercept (b) of the line,
b = 2
Thus, the slope of a line is m = -2 that passes through the points (-3, 8) and (4.-6), the y-intercept (b) of the line is 2, and the equation is y = -2x + 2.
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Two bells P and Q ring at intervals of 3hours and 4hours respectively. After how many hours will the two bells first ring simultaneously (at the same time)
Answer:
12 hours
Step-by-step explanation:
4 / 2
2/2
1
4 = 2²
2² x 3 = 4 x 3 = 12
Marla’s mom bought a 36-pack of water bottles at the supermarket. Each bottle has 500 mL of water. How many liters of water is this?
1,800
36
18
3,6000
____________________________________________________________________8.
The best unit of measure for the liquid in a tea cup is the liter.
True
False
____________________________________________________________________10.
Every week, Marla’s mom buys 24 bottles of water that each have 16 oz. How many pints of water is this?
32 cups
12 cups
16 cups
24 pints
Answer:
See below.
Step-by-step explanation:
First one is 18 liters.
Second is false.
Third is 24 pints.
1) B.
2) A.
3) A.
4) True.
5) B.
-hope it helps
Answer:
18 liters, false, 24 pints
Step-by-step explanation:
Hope this helps