The value of the sinθ is -3/5.
What is the Pythagorean identity?
The Pythagorean trigonometric identity, also known as the Pythagorean identity, is a trigonometric identity that expresses the Pythagorean theorem. It is one of the fundamental relationships between the sine and cosine functions, along with the sum-of-angles formulae.
We have,
cosθ = 4/5
sin θ = ?
We'll use the definition of cos to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
[tex]cos\theta = \frac{Adjacent}{hypotenuse} = \frac{4}{5}[/tex]
We know the hypotenuse and adjacent sides and we'll use the Pythagorean theorem to find the remaining side(opposite side).
opposite = √hypotenuse² − Adjacent²
opposite = √(5)² − (4)²
opposite = √25 - 16
opposite = √9
opposite = 3
[tex]sin\theta = \frac{opposite}{hypotenuse}[/tex]
sin θ = 3/5
In the fourth quadrant, the sine and tangent ratios are negative and the cosine ratio is positive.
Hence, the value of the sinθ is -3/5.
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The Tabel corresponds to which of the following scatterplots?
Answer :
Step-by-step
A clerk is marking up merchandise 32%. The original price of an item is $450. What will be the retail price?
Answer:
$594
Step-by-step explanation:
450x1.32=$594
450+32%=$594
Annie has 5 pets, Eve has 3 and Molly has 10. What is the
mean amount of pets?
Answer: 6
Step-by-step explanation: the mean is the average. 5+3+10 = 18 and then you divide by the people (3) to get 6.
a rock is thrown off a 200-foot cliff. the trajectory of the rock is modeled by the function h(t)=(-10t^2)+200, where h is the height in feet and t is the time in seconds. when will the rock hit the ground.
Answer:
4.47 seconds.
Step-by-step explanation:
Given function:
[tex]h(t)=-10t^2+200[/tex]
where:
h is the height (in feet).t is the time (in seconds).The rock will hit the ground when h(t) = 0.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t)&=0\\\implies -10t^2+200&=0\\10t^2&=200\\t^2&=20\\t&=\pm\sqrt{20}\\t&=-4.47, 4.47\;\; \sf (2\;d.p.)\end{aligned}[/tex]
As time is positive, t = 4.47 s only.
Solve the compound inequality.
3x -4 > 5 or 1 - 2x≥7
Answer:
3x -4 >5 = x > 3.
1 -2x>7 = x ≥ -3
Step-by-step explanation:
#9: A college student's bank account is losing the same amount of
money each week since the beginning of the semester according to
the table shown below. Determine the equation of the function that
inputs the number of weeks since the beginning of the semester and
outputs the money in his bank account.
On Number 10, fill in the missing values on the table.
(Use the variables "m" and "w")
The equation of the function that inputs the number of weeks since the beginning of the semester and outputs the money in his bank account is
Money = 5340 - 356X(weeks)
The table will be as follows:
Weeks Money
0 5340
3 4272
7 2848
11 1424
15 0
Define an account.
An account in banking is an arrangement whereby a company, typically a financial institution like a bank or credit union, accepts a customer's financial assets and holds them on the customer's behalf at the discretion of the customer.
A financial account, specifically one that covers financial asset claims or liabilities to nonresidents, is a part of a country's balance of payments in macroeconomics. Direct investment, portfolio investment, and reserve assets are broken down by sector and are all parts of the financial account.
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A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is.
A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is
Given n(sample size) = 84
Population mean(μ) = 180
Standard Deviation(σ) = 36
Standard error of the mean = σx-bar = σ/√n = 36/√84 = 36/9.165 = 3.927
Standardizing the sample mean we have
Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n
x-bar = 180
Z(x-bar=185 at point C) = (185 - 180)/3.927 = 5/3.927 = 1.273
Z(x-bar=181 at point D) = (181 - 180)/3.927 = 1/3.927 = 0.254
The area ABCD is the probability that the sample mean will lie between 181 and 185.
The shaded Area ABCD = (Area corresponding to Z = 2 or x-bar = 185) - (Area corresponding to Z = 1 or x-bar = 181)
Area corresponding to Z = 1.273 = 0.898
Area corresponding to Z = 0.254 = 0.598
The shaded Area ABCD = 0.898-0.598 = 0.300
Therefore the probability that the sample mean will lie between 181 and 185 is 0.300.
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Last year, Jacky's age was six times the age of his son. If Jacky's son was 5 years old last year, find the age of Jacky this year.
About 75% of the wate produced in the U. S i recyclable. Micah’ family ha 40 pound of trah. He want to etimate how much of thi trah i recyclable
Answer:
30 lb
Step-by-step explanation:
75% of trash is recyclable.
40 lb trash.
75% of 40 lb = = 40/100 × 75 lb = 0.40 × 75 lb = 30 lb
Answer: 30 lb
Use the given information to prove that SVR = SUT
The ΔSVR ≅ ΔSUT by side angle side property of triangle.
What is congruency in triangles?The size of the sides and angles determines whether two or more triangles are congruent. The three sides and three angles of a triangle define its size and shape, accordingly. Two triangles are said to be congruent if their respective side and angle pairs are the same.
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In triangle SVR and triangle SUT
SR = ST (given)
∠RSV = ∠TSU ( Common)
SV = SU (given)
So, the ΔSVR ≅ ΔSUT by SAS property.
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If a population of 1000 people were to increae by 5% every year, what would the population be in 20 year?
The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.
How to estimate future population?
The future population can be estimated by the following equation:
P = P₀ × (1 + i)ⁿ
Where
P = population in the expected yearP₀ = current populationi = growth raten = number of periodsIf the recent population is 1000 people and the growth rate is 5% per year, what would the population be in the next 20 years?
The population in the next 20 years would be
P = P₀ × (1 + i)ⁿ
P = 1000 × (1 + 0.05)²⁰
P = 1000 × (1.05)²⁰
P = 1000 × 2.6533
P = 2653 people
Hence, the population in the next 20 years would be 2653 people.
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115% = 38x + 161y
What is 100%?
Answer:
100% is 32.3x + 136.85y------------------------
Given115% = 38x + 161yFind 100%100% = 115% - 15% (38x + 161y) - 15% = (38x + 161y)*(1 - 0.15) = (38x + 161y)*0.85 =38x*0.85 + 161y*0.85 = 32.3x + 136.85yAnswer:
32.3x + 136.85y
Step-by-step explanation:
Let's take it as,
→ z = 100%
Forming the equation,
→ z + 15% = 38x + 161y
Now the value of z will be,
→ z + 15% = 38x + 161y
→ z = 38x + 161y - (1 - (15/100))
→ z = (38x + 161y) × (1 - 0.15)
→ z = (38x + 161y) × (0.85)
→ [ z = 32.3x + 136.85y ]
Hence, the answer is above.
find the volume of a frustum of a right circular cone with height 25, lower base radius 13 and top radius 5.
Volume of the frustum of right circular cone = 271.22 [tex]units^{3}[/tex]
Volume of frustum of right circular cone:
Formula for the Volume of Frustum of Cone (V)= 1/3 πH ([tex]R^{2}[/tex]+Rr+[tex]r^{2}[/tex] )
where,
H = Height of frustum
R = Radius of lower base
r = Radius of top base
According to given question,
Height of frustum(H) = 25 units
Radius of lower base(R) = 13 units
Radius of top base (r) = 5 units
Substituting all the given values in the formula of volume of frustum of cone we will get,
Volume of frustum of right circular cone(V) = 1/3 πH ([tex]R^{2}[/tex] + Rr + [tex]r^{2}[/tex] )
= 1/3 π ( 13x13 + 13x5 + 5x5)
= 1/3 π ( 169 + 65 +25)
= 1/3 π (259)
= 86.33 π
= 271.22 [tex]units^{3}[/tex]
Volume of the frustum of right circular cone = 271.22 [tex]units^{3}[/tex]
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Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
They must sample 385 subscribers to obtained this interval.
What do you mean by sample?
An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values.
According to the given question,
We have:
95% confidence interval for z-score is 1.96
Using this formula to find the number of subscribers they must sample to obtain this interval
n≥ (zσ/2 ÷ 2ME)²
Where:
n= Sample
zσ = Z-score
ME = margin of error
Let put in the formula,
n≥ [1.96 / 2(0.05)]²
n≥ [1.96 / 0.1]²
= (19.6)²
= 384.16
=385 (Rounded)
Therefore, they must sample 385 subscribers to obtained this interval.
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you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b, defined below, mutually exclusive? explain your answer.
you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b then A and B are exhaustive.
Given
A= { 1,2,4}
B= { 2,3,4,5,6}
C= { 3,4}
D= { 2,4,5}
Solving (a): The mutually exclusive events
These are events that have no common or mutual elements
Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.
Solving (b): Exhaustive events.
Two events X and Y are said to be exhaustive if:
S= P(X n Y)
i.e. if the sample space equals the intersection of X and Y
For events A to D, we have:
AnB= { 1,2,3,4,5,6}
and the sample space is:
S= {1,2,3,4,5,6}
By comparison;
A n B= S
Hence, A and B are exhaustive.
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10.4.3: lining up club members for a photo. help outline ten members of a club are lining up in a row for a photograph. the club has one president, one vp, one secretary, and one treasurer. (a) how many ways are there to line up the ten people? (b) how many ways are there to line up the ten people if the vp must be beside the president in the photo? (c) how many ways are there to line up the ten people if the president must be next to the secretary and the vp must be next to the treasurer?
A) number of ways in which president is not next to the VP =3628800-725760 =2903040
B) Number of ways =9*9!=3265920
C) number of ways VP is in one end =2*9!=725760
What is permutation and combination ?Permutations and combinations are ways of representing groups of objects by selecting them and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.
Calculationa)
number of ways to line up 10 members =10! =3628800
number of ways so that VP and president are next to each other =N(consider president and VP as 1 member which can interchange in 2 ways , and now we need to arrange 9 members) =2*9!=725760
therefore number of ways in whcih president is not next to the VP =3628800-725760 =2903040
b)
Number of ways =N(9 choices for left most posiition except VP and arrange rest of 9 persons)
=9*9!=3265920
c)
number of ways VP is in one end =N(choose 1 place out of 2 end for VP and then arrange rest of 9 )
=2*9!=725760
therefore number of ways VP is not at one end =3628800-725760 =2903040
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Out of 30 problems on a
test, Jose got 3 wrong.
What percentage did Jose
get correct?
Answer:
Step-by-step explanation:
3 is 10% of 30. Therefore, the other 27 is the resulting 90% of the whole number of 30.
What is a 3rd of 12/12
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Step 1: Simplify
[tex]\frac{12}{12} =1[/tex]
Step 2: Multiply by [tex]\frac{1}{3}[/tex]
[tex]1*\frac{1}{3}=\frac{1}{3}[/tex]
Hope this helps! :)
Solve each equation by taking square roots
3b² +5=-25
Answer:
b = -3.16
Step-by-step explanation:
3b² + 5 = -25
3b² = -30
b² = -10
b = -3.1623 (5 significant figures)
= -3. 16
pls help
How to express 5 x 5 x 5 using exponent?
(A) 103 (B) 53 (C) 23
The expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]
The given expression is
5 × 5 × 5
The expression is the mathematical statement that consist of different variables, numbers and mathematical operator.
The power of a number that consider of base number and the exponent.
Therefore the power of a number is the a base number raised to the exponent.
The exponent of the number is defined as the number of times a number is multiplied by itself.
Here the given expression is
5 × 5 × 5 = [tex]5^3[/tex]
Where 5 is the base number and 3 is the exponent
Hence, the expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]
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A tram moved downward 35 meter in 7 econd at a contant rate. What wa the change in the tram' elevation each econd?
If a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter
The total distance that tram moved downwards = 35 meters
Total time taken = 7 seconds
Here we have to use the unitary method
The change in the tram's elevation for each second = The total distance that tram moved downwards / Total time taken
Substitute the values in the equation
The change in the tram's elevation for each second = 35 /7
Divide the terms
= 5 meters
Hence, if a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter
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The length of a rectangle is 7 cm more than the width. If the perimeter is 58 cm, find the length and width.
Answer:
length = 32.5, Width = 25.5
Step-by-step explanation:
Let x rep the width. Let x plus 7 rep the length.
x + x + 7 = 58
2x=58-7
2x=51
2x/2 = 51/2
x= 25.5
x plus 7 =
= 25.5 + 7
=32.5
✨️Hope that helps✨️
Which equation represents the line that is
perpendicular to the graph of 4x + 3y = 9 and
passes through (-2, 3)?
A. 3x-4y=-18
B. 3x+4y=18
C. 3x-4y=-6
D. 3x+4y=6
The equation that represents the line that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2,3) is
[tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
Let us revise some rules
1. The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]
2. The slope of a line whose equation is ax + by = c is [tex]m = \frac{-a}{b}[/tex], where a is the coefficient of x and b is the coefficient of y
The equation of the given line is 4x + 3y = 9
[tex]m = \frac{-a}{b}[/tex]
whereas a is the coefficient of x and b is the coefficient of y
Therefore the coefficient of x = 4 and the coefficient of y = 3
a = 4 and b = 3
[tex]m = \frac{-a}{b}[/tex]
The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]
That means reciprocal the fraction and change its sign
The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]
The form of the equation is y = mx + b
- Substitute m by [tex]\frac{3}{4}[/tex]
y = [tex]\frac{3}{4}[/tex] x + b
To find b substitute x and y in the equation by the coordinates
of a point on the line
The perpendicular line passes through point (-2 , 3)
x = -2 and y = 3
3 = [tex]\frac{3}{4}[/tex](-2) + b
3 = [tex]\frac{-3}{2}[/tex]+ b
Add to both sides
[tex]\frac{9}{2}[/tex] = b
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Hence the answer is perpendicular to graph of 4x+3y=9 and passes through (-2,3) is [tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
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help me the pic is the queston
Ximena is going to invest in an account paying an interest rate of 2.2% compounded continuously. How much would Ximena need to invest, to the nearest ten dollars, for the value of the account to reach $5,100 in 6 years?
Ximena need to invest $2384 so that account value reach $5,100 in
6 years.
As given in the question,
We have to find Principal ' P'
Given interest rate R = 2.2%
Amount = $5100
time t = 6 years
Formula used
Amount = P + P( 1 + R%)^t
Putting values in the formula
5100 = P + P (1 + 2.2%)^6
5100 = P ( 1 + (1 + 2.2%)^6)
5100 = P (1 + (1.022)^6)
5100 = P (1 + 1.139)
5100 = P (2.139)
P = 5100/2.139
P = 2384.291 ≈ 2384
Therefore, Ximena need to invest $ 2384 to reach $5,100 in 6 years with interest rate 2.2%.
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Answer:
P=4470
Step-by-step explanation:
i did it
If shown, AB and CD are straight lines. Find x in each case.
NEED HELP ASAP
If AB and CD are straight lines. Then x is 45 degrees.
What is Angle?Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given,
AB and CD are straight lines
The angle at O is 360 degrees which makes complete circle.
Few of the angles are given.
x+x+4x+90=360
6x+90=360
Subtract 90 from both sides
6x=270
x=45 degrees.
Hence the value of x is 45 degrees.
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Jacob bought 5. 5 pounds of jelly beans for $14. 74. How much would 7. 25 pounds of jelly beans cost, to the nearest cent?.
Answer:
$19.43
Step-by-step explanation:
when 5.5 pounds cost $14.74 then 1 pound costs $2.68
because 14.74 divided by 5.5 equals 2.68
To calculate the price of 7.25 you multiply the price for 1 pund by 7.25
7.25 * 2.68 = 19.43
Two numbers have a sum of 139 and a difference of 31. What are the two numbers?
Answer:
Thus, one of the numbers is 85
Step-by-step explanation:
Answer:
Step-by-step explanation:
Solve the following system of equations algebraically:
y = x2 - 7x - 5
y = 2x - 5
Answer:
x = 0; y = -5
x = 9; y = 13
Step-by-step explanation:
y = x² - 7x - 5
y = 2x - 5
Use substitution to set the two right sides equal.
x² - 7x - 5 = 2x - 5
x² - 9x = 0
x(x - 9) = 0
x = 0 or x - 9 = 0
x = 0 or x = 9
Now for each x value, we find a corresponding y vlaue.
x = 0
y = 2x - 5 = 2(0) - 5 = -5
x = 9
y = 2x - 5 = 2(9) - 5 = 13
Answer:
x = 0; y = -5
x = 9; y = 13
Answer:
(0,-5) and (9,13)
Step-by-step explanation:
Step 1: Set up
You can solve system of equations algebraically either by elimination or substitution.You know there is going to be two solutions because of x²Step 2: Solve
Substitution:
[tex]y=x^{2} -7x-5[/tex][tex]y=2x-5[/tex]Since both equations have been solved for y, you can just set them equal to each other.[tex]2x-5=x^{2} -7x-5[/tex][tex]9x-x^{2} =0[/tex][tex]-x(x-9)=0[/tex][tex]x=0\\x=9[/tex]Then plug both x values into one of the equations to get their corresponding y values.[tex]y=2(0)-5=-5[/tex][tex]y=2(9)-5=18-5=13[/tex]Elimination:
[tex]y=x^{2} -7x-5[/tex][tex]y=2x-5[/tex]Since both equations have been solved for y, multiply one equation by -1 in order to cancel the y variable and solve for x.[tex]y=x^{2} -7x-5[/tex][tex]-y=-2x+5[/tex][tex]0=x^{2} -9x+0[/tex][tex]0=x^{2} -9x[/tex][tex]0=x(x-9)[/tex][tex]x=0\\x=9[/tex]Then plug both x values into one of the equations to get their corresponding y values.[tex]y=2(0)-5=-5[/tex][tex]y=2(9)-5=18-5=13[/tex]the spread of the sampling distribution of is the spread of the corresponding population distribution sampling distribution
The spread of the sampling distribution of x is smaller than the spread of the corresponding population distribution sampling distribution.
In the given question,
We have to find the spread of the sampling distribution of x is............... the spread of the corresponding population distribution sampling distribution.
As we know that,
The size of the sample as well as its dispersion affect the sampling distribution's spread. We calculate the sampling distribution's spread as the population's standard deviation divided by the sample size's square root.
So, the spread of the sampling distribution of x is smaller than the spread of the corresponding population distribution sampling distribution.
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The right question is
The spread of the sampling distribution of x is .......... the spread of the corresponding population distribution sampling distribution.
larger than
smaller than
the same as
exactly 1/2
