[tex]\text{Given that,}\\\\~~~~~~~~\cos \theta = \dfrac 35\\\\\implies \cos^2 \theta = \dfrac 9{25}\\\\\implies 1-\sin^2 \theta = \dfrac{9}{25}\\\\\implies \sin^2 \theta = 1-\dfrac{9}{25}\\\\\implies \sin^2 \theta = \dfrac{16}{25}\\\\\implies \sin \theta = \pm\sqrt{\dfrac{16}{25}}\\\\\implies \sin \theta = \pm\dfrac 45\\\\\text{Given that,}~ 270^{\circ} \leq \theta \leq 360^{\circ}, \text{So}~ \theta ~ \text{lies in fourth quadrant.}\\\\[/tex]
[tex]\text{Which means that}~ \sin \theta ~ \text{will be negative.}\\\\\text{Hence,}~ \sin \theta = -\dfrac 45[/tex]
f(x) is a function.
A. True
B. False
Answer:
A. true
Step-by-step explanation:
"f(x) = ... " is the classic way of writing a function.
Match each fraction on the left with an equivalent fraction on the right. Some options on the right will be used more than once.
Answer:
4/7=12/21
18/20=9/10
6/5=30/25
81/90=9/10
Step-by-step explanation:
12 / 21 will be equal to 4/7 and is denoted in the simplest form.
What is an equivalent fraction?A fraction that possesses the same value as another fraction regardless of how it's denominators and numeric components could be different is said to be equivalent.
12 / 21 can be simplified with the help of 3. This will result in 4/7.
18/20 can be simplified with the help of 2. This will result in a 9/10.
30/25 can be simplified with the help of 5. This will result in 6/5.
81/90 can be simplified with the help of 9. This will result in a 9/10.
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X
23 25 26 31 34 38
P(X)
0.16 0.09 0.18 0.12 0.24 0.21
What is the mean of this discrete random variable? That is, what is E(X), the
expected value of X?
A. 31.29
OB. 30.47
OC. 29.5
OD. 28.5
Using it's formula, it is found that the mean of the discrete random variable is given by:
B. 30.47.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Hence, considering the table, the mean of the discrete distribution is:
E(X) = 23 x 0.16 + 25 x 0.09 + 26 x 0.18 + 31 x 0.12 + 34 x 0.24 + 38 x 0.21 = 30.47.
Hence option B is correct.
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What is the solution of the system of equations shown in the graph? On a coordinate plane, a line goes through (0, 4) and (2, 0) and another line goes through (0, negative 1) and (2, 0). The lines intersect at (2, 0). a. (0, 2) c. (0, 4) b. (2, 0) d. (0, -1)
Answer:
(2,0)
Step-by-step explanation:
The intersecting points of the two lines is the solution for the two equations.
(2,0) is the solution.
[tex] \large\frak{ \purple{ Question}}[/tex]
In a certain class, one-third of the students were absent. Half of the total strength attended the Maths test and one-fourth of the total strength attended the Physics test. If 6 students attended both the tests and every student who was present attended at least one of the two tests, then how many students were absent on that day?
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The number of students that were absent is; 24
How to find the Probability?
Let the total number of students be x .
The number of students which were absent = ¹/₃x.
Number of students which were present = ²/₃x
Thus;
Number of students who attended math's test = ¹/₂x
Number of students who attended physics test = ¹/₄x
No. of students who attended both tests = 6
A denotes number of students who attended math's test
B denotes number of students who attended physics test
Thus;
n(A) = ¹/₂x
n(B) = ¹/₄x
n(A ∩ B) = 6
n(A∪B) = number of students which were present
Thus;
n(A ∪ B) = n(A) + n(B) − n(A∩B)
²/₃x = ¹/₂x + ¹/₄x − 6
²/₃x = ³/₄x - 6
³/₄x - ²/₃x = 6
x = 72
Thus, number of students that were absent = ¹/₃ * 72
Number of students that were absent = 24
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If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days, what is the amountof her deposit to the
nearest dollar (zero decimal place). Use a 360-day year. Enter only the number without $ sign
Answer: 2556
Step-by-step explanation:
Let the amount of the deposit be x dollars
The amount of simple interest earned can be represented by the formula PRT/100
Where,
P is the amount of deposit
R is the annual rate of interest
T is the time in years
Therefore,
P=x
R=6
T=150/360 = 15/36 = 5/12
So,
Simple interest = x(6)(5)/1200
63.90 = 30x/1200
63.90= x/40
x= 63.90×40
x=2556
Therefore, amount deposited = 2556
Find the slope between :
(0,6
(8,-6)
This is for my hw.
Answer:
Exact form: -3/2
Decimal Form: -1.5
Step-by-step explanation:
Hello there!
We need to find out the slope of the given two coordinates/points, that are:
(0,6(8,-6)Solution:
We'll need to use the formulae that is used to find out the slope,that is:
[tex] \pink{\star}\boxed{\rm \: Slope = \cfrac{y_2 -y_1}{x_2 - x_1}} \pink{\star}[/tex]
According to this question,here:
[tex]\rm \blue{\star} (y_2 , y_1) = (-6 , 6) \blue{\star}[/tex][tex]\rm \blue{\star}(x_2 , x_1)= (8 , 0) \blue{\star}[/tex]So substitute them accordingly:
[Slope is denoted as m][tex] \rm \: m = \cfrac{ - 6 -( 6)}{8 - 0} [/tex]
Simplify using PEMDAS rule.
[tex] \rm \: m = \cfrac{ - 12}{8} [/tex]
-12/8 could be canceled.
[tex] \rm \: m = \cfrac{ - 6}{4} [/tex]
-6/4 could also be canceled.
[tex] \boxed{ \rm \: m = \cfrac{ - 3}{2} \: or \: - \cfrac{3}{2} }[/tex]
Or it could be represented as decimal:
[tex] \boxed{ \rm \: m = - 1.5}[/tex]
Hence , the slope m will be -3/2 or -1.5
[tex] \rule{225pt}{2pt}[/tex]
A boat is heading towards a lighthouse,
whose beacon-light is 113 feet above the
water. The boat's crew measures the angle of
elevation to the beacon, 7°. What is the
ship's horizontal distance from the
lighthouse (and the shore)? Round your
answer to the nearest tenth of a foot if
necessary.
Answer: 920.3 ft
Step-by-step explanation:
[tex]\tan 7^{\circ}=\frac{113}{x} \\ \\ x(\tan 7^{\circ})=113 \\ \\ x=\frac{113}{\tan 7^{\circ}} \approx \boxed{920.3 \text{ ft}}[/tex]
4x-6y=17 4x+2y=21 solua
help me pls dont write fake answers pls
Answer:
it’s C, 5.2
hope i helped
ur wlcm :)
correct me if im wrong
What is the perimeter of this triangle?
Answer: [tex]a+b+\sqrt{a^{2}+b^{2}}[/tex]
Step-by-step explanation:
The distance from (0,b) to (0,0) is b.
The distance from (0,a) to (0,0) is a.
Using the Pythagorean theorem, the distance from (0,b) to (a,0) is [tex]\sqrt{a^{2}+b^{2}}[/tex]
So, the perimeter is [tex]\boxed{a+b+\sqrt{a^{2}+b^{2}}}[/tex]
Polygon G H I J K has 5 sides.
Which statements are true about the regular polygon? Select three options.
The sum of the measures of the interior angles is 900°.
Each interior angle measures 108°.
All of the angles are congruent.
The polygon is a regular hexagon.
The sum of the measures of the interior angles is 180(5 – 2)°.
Answer:
Each interior angle measures 108°.All of the angles are congruent.The sum of the measures of the interior angles is 180(5 – 2)°.Step-by-step explanation:
(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.
(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.
(3) By definition, all angles of a regular polygon are congruent.
(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.
(5) This is true. (See statement (1)).
Answer:
Options B, C, E
Step-by-step explanation:
Determine a series of transformation that would map polygon ABCDE onto polygon A'B'C'D'E'
What is the value of x?
log 3x =4
A. 7 B. 27 C. 81 D. 12
Answer:
81
Step-by-step explanation:
for example log2 8=3 is the same as 2^3=8, so if you switch around the variables from your question, your able to do 3^4, which is 81
Beginning in the middle of summer, the average temperature for a certain year in Phoenix could approximately be modeled by the function f(x)=31cos(0.0055πx)+88, where x represents the number of days since the middle of the summer, and f(x) represents the average temperature in degrees Fahrenheit.
What was the lowest average temperature in Phoenix that year (approximately)?
A) 57∘F
B) 31∘F
C) 55∘F
D) 88∘F
By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.
What was the lowest average temperature in Phoenix that year?We know that the average temperature is given by the equation:
f(x)=31cos(0.0055πx)+88
And it is in Fahrenheit degrees.
To get the lowest average temperature, we just need to find the minimum of the above function.
Remember that the minimum of the cosine function is:
cos(x) = -1
Then the lowest value of the above function is:
f(x₀) = 31*(-1) + 88 = 57
From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.
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I AM MARKING BRAINLIEST TO CORRECT ANSWER!!! PLEASE HELP!
Answer:
135
Step-by-step explanation:
3b + B = 180
4b = 180. ÷4
b = 45
a = 135
Solve the Application.
In one week Tommy earns $476 in regular pay and $144 in overtime pay. A total of $197 is deducted from his paycheck for taxes and a company loan. What is his take-home pay?
$423
$413
$433
$533
ƒ(x) = 4x² + 5x – 3
g(x) = 4x³ - 3x² +5
Find (ƒ + g)(x)
(f+g)(x)
= f(x) + g(x)
= 4x^2 +5x -3 + 4x^3 -3x^2 +5
= 4x^3+x^2+5x+2
Select the correct answer.
Teams with varying numbers of players are playing a group card game. The time taken by each team to complete one game is given in the table.
What is the relationship between the two variables?
Number of Players on the Team Time Taken to Complete Game (in minutes)
32
2
26
3
20
14
5
8
OA positive linear association
OB. exponential relationship
OC. negative linear association
O D.
no relationship
Answer:
a negative linear association (C)
Re-Written Problem [Formatted]
Teams with varying numbers of players are playing a group card game. the time taken by each team to complete one game is given in the table. What is the relationship between the two variables?
Numbers of players on team are going to be 1, 2 , 3, 4, 5.
time taken to complete game (in minutes) 32, 26, 20, 14, 8
(Select the correct answer)
A. Positive linear association
B. Exponential relationship
C. Negative linear association
D. No relationship
----------------------------------------------------------------------------------
Step-by-step explanation:
Lower x values (numbers of players on team) are correlated with higher y values (time taken to complete game)
[note: I know which values are x and y because of a cause-and-effect relationship. x causes y. number of players causes a change in minutes {it wouldn't make sense for the number of time it took to cause the number of players} ]
So, if we were to graph this relationship, we would see a downward-slope / negative slope of a line, because greater x-values are associated with lower y-values.
So, you would see a negative line, showing a negative linear association.
One of the roots of the equation x^2-13x+q=0 is 12. Find the other root and the value of the coefficient q.
The other root is 1 and the value of the coefficient q is 12.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x. ax²+bx+c=0. with a ≠ 0 .
Given:
x²-13x+q=0
when x= 12
So, 12²-13*12+q=0
144-156+q=0
-12+q=0
q=12
Now, x²-13x+12=0
x²-12x-x+12=0
x(x-12) - 1(x-12)=0
(x-1)(x-12)=0
x=1, 12
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F. In what order should items weighing
51 pounds, 40 pounds, 48 pounds,
and 44 pounds be stacked if you want
them in order from heaviest to lightest?
Answer:
51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.
which number is equal to 4 half
Answer:
2
Step-by-step explanation:
4 halves=2
1 half=0.5
2 halves=1
3 halves=1.5
4 halves=2
When shopping for a baby doll for her daughter, Ms. Martin found that the price of four baby dolls was less than $102. Which
of the following inequalities represents this information?
OA. 4+ b≤ $102
OB. 4x b< $102
OC. 4x b≤ $102
OD. 4+ b< $102
If you help me I will give 100 points
Answer:
b
Step-by-step explanation:
because it is 4 dolls and x is the amount of dollars 1 doll is and 4x dolls are less then 102, the only answer that makes sense is b
The answer is B. I will choose to explain by process of elimination. It is not A because it is not less than or equal to, it is just less than. Therefore, we can also eliminate C. It is not D because it is four dolls that cost the same so it is 4x instead of 4+x. I hope I helped!
The question is in the image. I
Please Answer fast
Find the value of x°.
Answer:
X=60°
Step-by-step explanation:
Because the sum of angle of all side of a triangle is 180°
and
if that goes on
the equation become
x°+75°+45°=180°
x°+120°=180°
x°=180°-120°
x°=60° hence prove
Using the GCF factor the given expression: 21xy + 14y
7(3xy + 2y)
7y(3x + 2)
3(7xy + 14y)
7xy(3 +2)
Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
Greatest common factor of an expressionThe greatest common factor is the value that will divide an expression without leaving a remainder.
Given the expression 21xy + 14y
Find the factors
21xy = 7 * 3 * x * y
14y = 7 * 2* y
Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
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5 divided by 4/9
i need the answer in a fraction form please.
apples cost $3.99 for 3 lbs. Susan wants to buy 5 lbs. How much will it cost her?
Answer: $5.99 is the answer hope this helps!
Cool Down
Lesson 3: Reasoning about Equations with Tape Diagrams
Cool Down: Three of These Equations Belong Together
Here is a diagram.
X
1. Circle the equation that the diagram does not match.
06+3x=30
03(x+6)=30
0 3x-30-6
030-3x+6
2. Draw a diagram that matches the equation you circled.
Using the figure given, The one equation that matches with the diagram is 3x=30-6. The diagram that matches the equation circled is given in the image attached.
What is the Equations about?From the above, we can see that the equation that matches with the diagram are:
3(x+6)=3030=3x+66+3x=30Note that for 3(x+6)=30
3x + 18 = 30
3x = 30-18
3x = 12
x = 12/3
x = 4
Then fixing x into the equation =
3(x+6)=30
3(4+6)=30
Therefore , 12 + 18 will give us 30 and the answer is straight forward. The same applies for 30=3x+6 and 6+3x=30 as the answer is straight forward.
But the one equation that does not matches with the diagram is 3x=30-6 because its output is not straight forward.
3x =30-6
3x = 24
x = 24/3
x = 8
Fixing 8 into the equation
3x = 30-6
3(8) = 24
=24 is the answer and not 30
Therefore, Using the figure given, The one equation that matches with the diagram is 3x=30-6.
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PLEASE HELP BRAINLIEST how many small blocks of wood each of length 6cm, breath 4cm, and height 2cm can i cut out from a block of wood of length 2m, breadth 4cm and height 2cm WITH STEP BY STEP EXPLANATION
Answer:
33 blocks
Step-by-step explanation:
Given the length , breath and height for small block 6cm, 4cm, and 2cm an d for large 2m = 200cm, 4cm and 2cm.
volume is given by
V = Length x breath x height
Volume of small block = 6 x 4 x 2 = 48 cm^3
Volume of big block = 200 x 4 x 2 = 1600 cm^
No of blocks = Volume of big block/ volume of small block
= 1600/48
= 33.33
Therefore no of blocks formed = 33