Use a Pythagorean Identity (not triangles) to find sin theta if you're given cos theta =
4/5 with theta in quadrant IV.

The ΔSVR ≅ ΔSUT by side angle side property of triangle.

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.

To know more about the congruency of a triangle, visit:

https://brainly.com/question/20521780

#SPJ13

Answer:

3x -4 >5 = x > 3.

1 -2x>7 = x ≥ -3

Step-by-step explanation:

If AB and CD are straight lines. Then x is 45 degrees.

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.

To learn more on Angles click:

https://brainly.com/question/28451077

#SPJ1

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.

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.

To learn more about sample, visit:

https://brainly.com/question/13287171?referrer=searchResults

#SPJ4

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

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.

a)

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

learn more about permutations and combinations here :

brainly.com/question/28720645

#SPJ4

Answer:

b = -3.16

Step-by-step explanation:

3b² + 5 = -25

3b² = -30

b² = -10

b = -3.1623 (5 significant figures)

= -3. 16

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%.

Learn more about interest rate here

brainly.com/question/1902400

#SPJ1

Answer:

P=4470

Step-by-step explanation:

i did it

Answer:

4.47 seconds.

Step-by-step explanation:

Given function:

[tex]h(t)=-10t^2+200[/tex]

where:

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.

Answer :

Step-by-step

Answer:

Thus, one of the numbers is 85

Step-by-step explanation:

Answer:

Step-by-step explanation:

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.

learn more about of dice here

https://brainly.com/question/24129793

#SPJ4

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]

Learn more about exponent here

brainly.com/question/15993626

#SPJ1

Answer:

------------------------

Answer:

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.

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

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! :)

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]

To learn more about linear equations click here https://brainly.com/question/2030026

#SPJ9

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

Step 2: Solve

 Substitution:

 Elimination:

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]

To learn more about Frustum of Cone visit: https://brainly.com/question/15437523

#SPJ4

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

Learn more about unitary method here

brainly.com/question/22056199

#SPJ4

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.

To learn more about Probability, click here https://brainly.com/question/25870256

#SPJ4

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.

To learn more about sampling distribution link is here

brainly.com/question/13501743

#SPJ4

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

Answer:

Step-by-step explanation:

3 is 10% of 30. Therefore, the other 27 is the resulting 90% of the whole number of 30.

The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.

The future population can be estimated by the following equation:

P = P₀ × (1 + i)ⁿ

Where

If 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.

Learn more about future population here:

brainly.com/question/15210976

#SPJ4

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.

To learn more about an account, use the link given
https://brainly.com/question/26690519
#SPJ1

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

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✨️

Answer:

$594

Step-by-step explanation:

450x1.32=$594

450+32%=$594