Answer:
sin(01) = -32.70/13Step-by-step explanation:
Given cos(01) = -30/13 where angle 01 is located in quadrant III. In the third quadrant, both cos and sin are negative. only tan is positive.
To calculate sin(01), we will apply the trigonometry expression as shown below;
cos(01) = -30/13
According to SOH CAH TOA;
cos(01) = adjacent/hypotenuse = -30/13
sin(01) = opposite/ hypotenuse
To get the hypotenuse, we will use the pythagoras theorem
[tex]hyp^{2}=opp^{2}+adj^{2} \\opp^{2}= hyp^{2}-adj^{2}\\opp^{2}= 13^{2} -(-30^{2} )\\opp^{2} = 169+900\\opp^{2}=1069\\opp = \sqrt{1069} \\opp = 32.70\\[/tex]
sin(01) = 32.70/13
Since sin is also negaitve in the third quadrant, the value of
sin(01) = -32.70/13
[tex]01 = cos^{-1}- 30/13[/tex]
The base of a rectangular prism has an area of 13 2/3, and the height of the prism is 8 5/6. What is the volume of the prism? Be sure to use this format: whole number numerator/denominator.
Answer:
120 [tex]\frac{13}{18}[/tex]
Step-by-step explanation:
The formula for finding the volume of a prism is:
V = Bh
You have to convert 13 [tex]\frac{2}{3}[/tex] into an improper fraction, like so:
[tex]\frac{41}{3}[/tex]
Convert the other:
[tex]\frac{53}{6}[/tex]
Multiply:
[tex]\frac{41}{3}[/tex] · [tex]\frac{53}{6}[/tex] = [tex]\frac{2173}{18}[/tex]
Convert to mixed fraction:
120 [tex]\frac{13}{18}[/tex]
what does the numerator of the fraction 10/6 mean?
Answer:
6
Step-by-step explanation:
It costs Trevor $50 to have a security system installed in his house. He pays a monthly service fee plus tax of 6% of his monthly bill. After 6 months, Trevor had paid a total of $361.64 for his service fee, taxes, and his initial installation. Trevor’s monthly service fee, not including taxes, is ___.
Answer:
$49
Step-by-step explanation:
Cost of security system installation = $50
Let the monthly service cost be $x
In 6 month monthly service cost = 6*$x= $6xtax percentage = 6% of monthly service cost
hence if monthly service cost is $x
Then Tax value in terms of x is = 6% of $x = 6/100 * $x =$ 0.06x
In 6 month, Tax value in terms of x = 6 * $0.06x = $.36x_______________________________________________
Therefore total cost incurred by Trevor in 6 month including installation charges =
6 month monthly service cost + Tax value in 6 month + installation cost
Substituting value of 6 month monthly service cost , Tax value in 6 month , installation cost in above expression we have
Therefore total cost incurred by Trevor in 6 month including installation charges = $6x+ $0.36x+ $50 = $6.36x + $50
But it is given that After 6 months, Trevor had paid a total of $361.64 for his service fee, taxes, and his initial installation
Therefore total cost incurred by Trevor in 6 month including installation charges is also equal to $361.64
Hence,
$6.36x + $50 = $361.64
=> $6.36x = $361.64 - $50
=>$6.36x = $311.64
=> x = $311.64/6.36
=> x = 49.
Therefore , Trevor’s monthly service fee, not including taxes is $X which is equal to $49.
PLEASE HELP ME
I NEED IT
Answer:
[tex]\sqrt{24}[/tex]
Step-by-step explanation:
[tex]4\frac{4}{9}[/tex] cannot be correct because it equals 4.4.
[tex]\sqrt{20}[/tex] cannot be correct because it equals 4.5.
480% is 480/100 which equals 4.8 which is also not correct.
Therefore, [tex]\sqrt{24\\}[/tex] is correct because it is greater than 4.8 and less than 5.0.
need help again lol plz
Need help with this
Answer:
5 to the power of -2
Step by Step explanation:
Because you are diving, you need to subtract the powers.
For example, you subtract 10 from 12 to get -2
The 5 remains the same so the answer should be 5 to the power of -2
Hope this helps
Reasoning in a laboratory, the probability a bacterial colony thrives is 70%. The numbers 0 to 6 represent the outcome that a colony thrives. The numbers 7 to 9 represent the outcomes that a colony does not thrive. The list of random numbers simulates the out comes of 4 colonies . Based On the simulation in 6 trails . what is the probability that exactly half of the colonies will thrive.
4285 6903 3829 7871 2868 5137
Answer:
The probability that exactly half of the colonies will thrive = (1/3) = 0.3333
Step-by-step explanation:
The list of random numbers simulates the out comes of 4 colonies.
Based On the simulation in 6 trails, what is the probability that exactly half of the colonies will thrive?
The probability of an event is given mathematically as the number of elements in the event divided the total number of elements in the sample space.
Noting that the numbers 0 to 6 indicate that a colony thrives and the number 7 to 9 represent that a colony doesn't thrive.
The 6 trials are given as
4285; 3 colonies thrive, 1 doesn't.
6903; 3 colonies thrive, 1 doesn't.
3829; 2 colonies thrive, 2 don't.
7871; 1 colony thrives, 3 don't.
2868; 2 colonies thrive, 2 don't.
5137; 3 colonies thrive, 1 doesn't.
The number of trials where exactly 2 colonies thrive = 2
The total number of trials = 6
The probability that exactly half of the colonies will thrive = (2/6) = (1/3) = 0.3333
Hope this Helps!!!
Dustin works in a department store. He earned $89.00 for working 10 hours last week. At this rate, how much would Dustin earn for working 38 hours?
Answer:
$338.20
Step-by-step explanation:
Find out how much Dustin gets for one hour of work, since you are given how much Dustin earns in 10 hours, you divide it by 10 (the number of hours) to find one hour,
89/10=8.9
$8.9 per hour
So 38 hours would be
8.9 x 38= $338.20
Answer:
$338.20
Step-by-step explanation:
Select the equation that represents the graph below.
Answer:
D)
Step-by-step explanation:
The y intercept is at 3 and it goes up 3 over 2. and since its going up its positive. Remember rise over run.
Answer:
D
Step-by-step explanation:
Slope: 3/2
y-intercept:3
x,y
0,3
2,6
1) write down a different ratio equivalent to 12 : 3
2) write down a different ratio equivalent to 30 : 24
Answer: 1) 4:1 2) 60/48
Step-by-step explanation:
1. 12: 3 is the same as 12/3 so you can diving both side by 3.
12:3 ÷ 3/3=4/1
2. 30:24 is the same as 30/24 so you can divide both sides by 6 or multiply both sides by 2.
30/24 * 2/2= 60/48
Suppose f(x) =
[tex] {x}^{2} [/tex]
. What is the graph of g(x)=1/2f(x)?
Answer:
It's D.
Step-by-step explanation:
The 1/2 stretches the graph horizontally of x^2 by a factor 1/2.
Option-D will represent the required graph of the function [tex]g(x) = \frac{1}{2}f(x)[/tex].
What is a function?"A function is defined as a relation between a set of inputs having one output each."
The given function:
[tex]f(x) = x^{2}[/tex]
Therefore the required function is:
[tex]g(x)\\= \frac{1}{2}f(x)\\= \frac{1}{2}x^{2}[/tex]
By putting the values of 'x' as -2, -1, 0, 1, 2 etc. we get:
[tex]g(-2) = (-2)^{2} = 4\\ g(-1) = (-1)^{2} = 1\\ g(0) = (0)^{2} = 0\\ g(1) = (1)^{2} = 1\\ g(2) = (2)^{2} = 4[/tex]
By plotting this value, we get option-D is the graph that represents the function g(x).
Learn more about a function here: https://brainly.com/question/12251916
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Which is the longest length?
a 1 yd. 20 in.
b 1yd. 1 ft.
С
40 in.
d 3 ft.
Answer:
a-1yd20in
Step-by-step explanation:
a-4ft 8in
b-4ft
c-3ft 4in
d-3ft
Answer:
it's A, one yard and 20 inches
Step-by-step explanation:
If you convert them all to inches, a yard and a 20 inches are equal to 56 inches, so you can rule out the 40 inches answer. a yard and a foot are equal to 48 inches, so we can rule out that also. 3 feet is equal to 36 inches, because we know that a foot is equal to 12 inches. so you are left with A. 1 yard and 20 inches.
In the similar quadrilaterals below, what is the length of AB
10 cm
2.5 cm
8 cm
3 cm
Answer:
Side AB is 10 cm.
Step-by-step explanation:
The given quadrilaterals ABCD and EFGH are similar.
From the given figure, we can observe the following angles and sides are corresponding.
[tex]\angle A = \angle E=90^\circ\\\angle B = \angle F=63^\circ\\\angle C = \angle G=117^\circ\\\angle D = \angle H=90^\circ[/tex]
Ratio of corresponding sides will be equal:
AB:EF = BC: FG = CD:GH = DA:HE
We have to find the side AB.
Given the sides
EF = 5 cm
BC = 9 cm
DA = 8 cm
EH = 4 cm
So, ratio DA:EH = 8:4 = 2:1
We know that ratio of corresponding sides will be same:
AB:EF = DA:EH
[tex]\Rightarrow \dfrac{AB}{5} = \dfrac{2}{1}\\\Rightarrow AB = 10 cm[/tex]
So, side AB is 10 cm.
The one-to-one functions g and h are defined as follows.
=g, , −7 1, , −4− 8, , 6 7 , 7− 3
=hx−2x3
Find the following
Answer:
g^−1(7) = 6
h^−1(x) = x/2 + 3/2
(h^−1 ∘ h)(3) = 3
Step-by-step explanation:
If
g(6) = 7
Then
g^−1(7) = 6
h(x) = 2x - 3
Isolate x:
2x = h(x) + 3
x = h(x)/2 + 3/2
Replace x with h^−1(x) and h(x) with x:
h^−1(x) = x/2 + 3/2
We know that:
(h^−1 ∘ h)(x) = x
then:
(h^−1 ∘ h)(3) = 3
Given the line 2 x - 3 y - 5 = 0, find the slope of a line that is perpendicular to this line. A.3/2
B.2/3
C.- 3/2
Answer:
Step-by-step explanation:
2x - 3y = 5
-3y = -2x + 5
y = (2/3)x - 5
the perpendicular slope is -3/2
the answer is c
Answer:
the perpendicular slope is -3/2
Step-by-step explanation:
What is the surface area, in square inches, of the
sphere shown below? (SA = 4.0) (pi ≈ 1 3.14)
а. 530.7 sq in.
b. 2122.6 sq in.
с. 4245.3 sq in.
d. 9203 sq in.
Answer:
hey if you still need the i have them all just finished the test
Step-by-step explanation:
find the vertex of the parabola represented by the function f(x)= -2x^2
Find m Just trying to get my credit
Answer:
130
Step-by-step explanation:
2x+5x+5=180
7x+5=180
7x=175
x=25
5(25)+5=125+5=130
Answer:
∠ABC=130
Step-by-step explanation:
2x+5x+5=180
7x=180-5
7x=175
x=25
∠ABC=5*25+5=130
Which of these graphs represents a function
A.w
B.x
C.y
D.z
The correct option is D. The graph z is representing a quadratic function.
What is a quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
The general form of the quadratic functions is represented as below:-
y = ax² + bx + c
Where a,b, and c are the constants x and y are variables.
The graph of the quadratic functions will be parabolic on the x-y plane.
Therefore, the correct option is D. The graph z is representing a quadratic function.
To know more about a quadratic function follow
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5 CR
UTION
Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the
equations of the system is y = 3x – 1. Which could be the other equation?
y = 3x + 2
3x - y = 2
3x - y = 1
3x + y = 1
Done
Answer:
3x - y = 1
Step-by-step explanation:
The system:
[tex]$\left \{ {{y = 3x -1} \atop {y = 3x + 2}} \right. $[/tex]
There is no solution to this system of equations.
The system:
[tex]$\left \{ {{y = 3x -1} \atop {3x - y = 2}} \right. $[/tex]
[tex]$\left \{ {{y = 3x -1} \atop { y = 3x-2}} \right. $[/tex]
The is one solution to this system.
The system:
[tex]$\left \{ {{y = 3x -1} \atop {3x - y = 1}} \right. $[/tex]
[tex]$\left \{ {{y = 3x -1} \atop { y = 3x-1}} \right. $[/tex]
There are infinity solutions to the system.
The system:
[tex]$\left \{ {{y = 3x -1} \atop {3x + y = 1} \right. $[/tex]
[tex]$\left \{ {{y = 3x -1} \atop { y = 1-3x}} \right. $[/tex]
The is one solution to this system.
20 points! I need the answer ASAP! Thanks!
Answer: y=5/7x+2
Step-by-step explanation:
The y- intercept would be 2 since that is where the line goes through the y axis. Also if you use slope form you will see that the slope is 5/7.
complete the square to form a perfect-square trinomial.
2. x^2 - 4x + ?
4. x^2 + 12x + ?
6. x^2 + 18x + ?
(just tell me what the number is for the ? on each problem.)
Look at the attached picture
Hope it will help you.
Good luck on your assignment
I need help to get to 8.9 I need help to figure out the numbers for the empty boxes.
Answer:
Bottom row from left to right we have 0.4 0.3 0.3 0.1 0.5 0.5 Second row from right to left 0.7 0.6 0.4 0.6 1 On the Third row from right to left 1.3 1 1 1.6 On the Fourth row 2.3 2 2.6 On the Fith row 4.3 and 4.6 The last Row also the highest 8.9
Step-by-step explanation:
you take two numbers right and left add them and put the answer in the box above and in between
Write the number in standard form. 6.45×10^−4
Answer:
.000645
Step-by-step explanation:
.0006.45
move the decimal place 4 places to the Left because it is a negative.
If Kevin wants a 90 average in math after 5 tests and his first 4 tests are 76, 92, 89 and 97 what does he need on the fifth test for a 90 average?
please help me! thank you
Answer:
13 pounds happy to help mark me as brainliest pls!!!
Step-by-step explanation:
Simplify, using the distributive property and then combining like terms. 5c+2(10−c)
Answer:
3c +20
Step-by-step explanation:
5c+2(10−c)
Distribute
5c+ 20 -2c
Combine like terms
3c +20
Answer:3c+20
Step-by-step explanation:
Distribute
5c+(2)(10)+(2)(-c)
5c+20+-2c
Combine Like Terms:
(5c+-2c)+(20)
3c+20
Hope I helped:)
What is the solution to the equation sqrt5X-7= sqrt3X+5?
x = 1
x = 6
x = 12
x = 24
Answer:
X=6
Steps are in the picture
math question screen shot down below
Answer:
6
Step-by-step explanation:
If you plug 3 into x for the equation, you are left with:
y=-3(3)+15
Expanding the parentheses:
y=-9+15
Combining like terms:
y=6 miles remaining
Hope this helps!
6. Y is 6. He has 6 more miles left to go.
-3*3+15=6
Math question down below
Answer:
12 large books
Step-by-step explanation:
