FIND THE INVERSE OF -5 + 7i

The stiffness of one short spring is 13500 N/m

Solution:

We are given a chain with number of spring N = 30 and linked end to end ( in series) and stiffness of this chain is 450 N/m

We have to find the stiffness of one short spring

The springs are identical, which means they have same stiffness

The stiffness of one spring in series is given as:

[tex]k_i = N \times k_s[/tex]

Where,

N is the number of springs

[tex]k_i[/tex] is the stiffness of one spring

[tex]k_s[/tex] is the stiffness of this chain

Substituting,

[tex]N = 30\\\\K_s = 450[/tex]

Therefore,

[tex]k_i = 30 \times 450\\\\k_i = 13500[/tex]

Thus the stiffness of one short spring is 13500 N/m

If a chain of 30 identical short springs linked end-to-end has a stiffness of 450 N/m , The stiffness of one short spring is 13500 N/m

Given : Stiffness = 450 N/m,

To find : the stiffness of one short spring

According to the given question,

We knows that,

The springs are identical, by which means they have the same stiffness

Hence, The stiffness of one spring will be given as:

              [tex]\rm k_i=N \times k_s[/tex]  

Where,

On substituting the values in the formula we will get,

        N = 30

        [tex]\rm k_s[/tex] = 450

Then,

           [tex]\rm k_i =30 \times450\\\\k_i = 13500[/tex]

Therefore, The stiffness of one short spring is 13500 N/m

Learn more about Logical questions here : https://brainly.com/question/14806757

Answer:

a) 21.2%

b)  $176.05 or more

c) 15.87%    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $155

Standard Deviation, σ = $25

We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) P(spends more than $175 per week on groceries)

P(x > 175)

[tex]P( x > 175) = P( z > \displaystyle\frac{175 - 155}{25}) = P(z > 0.8)[/tex]

[tex]= 1 - P(z \leq 0.8)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%[/tex]

b) P(X > x) = 0.2

We have to find the value of x such that the probability is 0.2

P(X > x)  

[tex]P( X > x) = P( z > \displaystyle\frac{x - 155}{25})=0.2[/tex]  

[tex]= 1 -P( z \leq \displaystyle\frac{x - 155}{25})=0.2 [/tex]  

[tex]=P( z \leq \displaystyle\frac{x - 155}{25})=0.8 [/tex]  

Calculation the value from standard normal z table, we have,  

[tex]P(z < 0.842) = 0.8[/tex]

[tex]\displaystyle\frac{x - 155}{25} = 0.842\\\\x = 176.05[/tex]  

A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.

c) My family spends on average $130 dollars on groceries.

P(less than $130)

[tex]P( x < 130) = P( z < \displaystyle\frac{130 - 155}{25}) = P(z < -1)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]

Thus, my family percentile is 15.87%

a) 21.2%
b)  $176.05 or more
c) 15.87%    

We are given the following information in the question:
Mean, μ = $155
Standard Deviation, σ = $25
We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_(score) = \displaystyle(x-\mu)/(\sigma)[/tex]
a) P(spends more than $175 per week on groceries)
[tex]P(x > 175)P( x > 175) = P( z > \displaystyle(175 - 155)/(25)) = P(z > 0.8)= 1 - P(z \leq 0.8)[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%\\[/tex]

b) [tex]P(X > x) = 0.2[/tex]
We have to find the value of x such that the probability is 0.2
[tex]P(X > x) \\P( X > x) = P( z > \displaystyle(x - 155)/(25))=0.2 \\= 1 -P( z \leq \displaystyle(x - 155)/(25))=0.2 \\=P( z \leq \displaystyle(x - 155)/(25))=0.8[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(z < 0.842) = 0.8\\\displaystyle(x - 155)/(25) = 0.842\n\nx = 176.05[/tex]
A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.

c) My family spends on average $130 dollars on groceries.
P(less than $130)
[tex]P( x < 130) = P( z < \displaystyle(130 - 155)/(25)) = P(z < -1)[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]
Thus, my family percentile is 15.87%

Answer:yes

Step-by-step explanation: the answer does represent a function because if you were to put points in the line wherever, and connect them by drawing a line vertically, it would not cross two points.

Final answer:

The statistic concerning the number of siblings would be the mean number of siblings for the randomly selected students, not the entire school population.

Explanation:

The question posed by the student pertains to determining the mean number of siblings for students in a school. Anna collected data by randomly selecting 75 students and recording the number of siblings for each student. The statistic in this context is d. the mean number of siblings for the randomly selected students. This is because the statistic refers to a summary measure that is calculated from a sample of data. Therefore, the statistic is the calculated average number of siblings from just those 75 students and not the entire school population.

When discussing sampling methods, one could use a completely random method or use systematic sampling with a tool such as a random number generator for selection. Regardless of the method, the primary criterion is that every member of the population has an equal chance of being included in the sample.

Final answer:

The statistic refers to the mean number of siblings for the randomly selected students, computed by dividing the sum of siblings reported by the 75 students by 75.

Explanation:

The statistic in this scenario is the mean number of siblings for the randomly selected students. The mean, or average, will be calculated by adding up the total number of siblings reported by the 75 students and then dividing that sum by 75. This statistic will serve as an estimate for the mean number of siblings for each student in the whole school. Although option b attempts a similar approach with systematic sampling by selecting every 50th student, the actual calculated mean from the 75 randomly selected students (which is the result of the random sampling method described in option a) is the statistic we are referring to. Option c is asking for a different kind of statistic related to stress scores.

The given statement "All occurrences of the letter u in "Discrete Mathematics" are lowercase" is true.

Here's why:

There are no occurrences of the letter "u" in "Discrete Mathematics" at all.

Therefore, the question of whether they are uppercase or lowercase becomes irrelevant due to the absence of the letter itself.

Because the statement involves a vacuous quantification, meaning it deals with an empty set, it automatically becomes true.

In such cases, it doesn't matter what property is being attributed to the empty set because there are no elements for that property to be true or false for.

Yo sup??

y=-3/x+4

cross multiply

x+4=-3/y

x=-3/y-4

f(y)=-3/y-4

or

f(x)=-3/x-4

=-4x-3/x

The correct answer is option 4

Hope this helps.

Answer:

It is -4x-3/x.

Answer:

The equation would be [tex]4x-15=21[/tex].

Step-by-step explanation:

Given;

Total Number of Video games = 21

Let the number of video game Nicholas has be 'x'.

Now Given:

Robert has 5 fewer games than Nicholas.

so we can say that;

number of video game Robert has = [tex]x-5[/tex]

Also Given:

Charlie has twice as many games as Robert.

so we can say that;

number of video game Charlie has = [tex]2(x-5)=2x-10[/tex]

we need to write the equation.

Solution:

Now we can say that;

Total Number of Video games is equal to sum of number of video game Nicholas has, number of video game Robert has and number of video game Charlie has.

framing the equation we get;

[tex]x+x-5+2x-10=21\\\\4x-15=21[/tex]

Hence The equation would be [tex]4x-15=21[/tex].

On Solving we get;

Adding both side by 15 we get;

[tex]4x-15+15=21+15\\\\4x=36[/tex]

Dividing both side by 4 we get;

[tex]\frac{3x}{4}=\frac{36}{4}\\\\x=9[/tex]

Hence Nicholas has = 9 video games

Robert has = [tex]x-5= 9-5=4[/tex] video games

Charlie has = [tex]2x-10 = 2\times9-10=18-10=8[/tex] video games

Answer:

The equation would be  [tex]4x-15=21.[/tex]

Step-by-step explanation:

Given:

Three brothers Charlie Robert and Nicholas have 21 video games Charlie has twice as many games as Robert. Robert has 5 fewer games than Nicholas.

Now, to find the equation.

Let the games Nicholas has be [tex]x.[/tex]

Robert has games [tex]x-5.[/tex]

And Charlie has [tex]2(x-5).[/tex]

Now, the equation is:

[tex](x)+(x-5)+2(x-5)=21.[/tex]

[tex]x+x-5+2x-10=21\\2x-5+2x-10=21\\4x-15=21[/tex]

[tex]4x-15=21.[/tex]

Therefore, the equation would be [tex]4x-15=21.[/tex]

Answer:

4%

Step-by-step explanation:

Let the stock be $10

A 20% decline = 80/100 * 10

= 8

A 30% increase = 30/100 * 8

= 2.4 + 8 = 10.4.

Overall increase = 10.4 - 10 = 0.4

Percentage overall increase = 0.4/10 * 100

= 4%

Answer:

Step-by-step explanation:

Ben's car gets between 18 and 21 miles per gallon of gas. If his car's tank holds 15 gallons, it means that the least distance that Ben can drive on one tank of gas would be

18 × 15 = 270 miles.

Also, the most distance that Ben can drive on one tank of gas would be

21 × 15 = 315 miles.

Therefore the the range of distance that Ben can drive on one tank of gas is between 270 miles and 315 miles. If d represents the distance, then the range is

270 ≤ d ≤ 315)

Juan does not have enough paint to cover shape of a right rectangle prism

Solution:

Given that,

Juan wants to paint something in the shape of a right rectangle prism

From given,

Length = 17 inches

Width = 11 inches

Height = 9 inches

The surface area of prism is given as:

[tex]A=2(wl+hl+hw)[/tex]

Where, "l" is the length and "w" is the width and "h" is the height

Substituting the values we get,

[tex]A = 2(11 \times 17 + 9 \times 17 +9 \times 11)\\\\A = 2(187+153+99)\\\\A = 2 \times 439 \\\\A = 878[/tex]

Thus surface area of prism is 878 square inches

Given that,

He had enough paint to cover 850 sq in

No he cannot paint since surface area is 878 square inches which is greater than 850 square inches

So, he does not have enough paint

The answer is in the attachment

Answer: the length if the ramp is 47.17 feet

Step-by-step explanation:

The wheelchair ramp makes an angle of 11 degrees with the ground and forms a right angle triangle. The length of the ramp becomes the hypotenuse of the right angle triangle.

The distance of the platform from the ground level forms the opposite side of the right angle triangle.

To determine the length of the ramp, h, we would apply the Sine trigonometric ratio. It is expressed as

Sin θ = opposite side/hypotenuse

Therefore,

Sin 11 = 9/h

h = 9/Sin 11 = 9/0.1908

h = 47.17 feet

The radius of the cone is found by comparing the ratios of heights and radii in a similar triangle. By applying the given values, the radius of the cone is found to be 9 cm.

In mathematics, problems related to finding the dimensions of cones and frustums are common. As the problem mentions, a frustum is created when a smaller, similar cone is removed from a larger cone. To calculate the dimensions of the frustum, we use the properties of similar triangles.

For similar triangles:

Therefore:

Applying the given values, it becomes:

Hence, the radius of the cone is 9 cm.

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Final answer:

The volume of a frustum can be calculated using the formula [tex]\(V = \frac{1}{3}\pi h (r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})\)[/tex]. Given the dimensions provided for the frustum with the larger cone having a radius of 4.5 cm, the frustum a radius of 3 cm, and height of 3 cm, the volume of the frustum is approximately 134.25π cubic centimeters.

Explanation:

To work out the volume of a frustum that is formed by removing a small cone from a larger, similar cone, you can make use of the formula for the volume of a frustum:

V = [tex]\(\frac{1}{3}\pi h (r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})\),[/tex]

where:

h is the height of the frustum,

r₁ is the radius of the larger base (radius of the original cone),

r₂ is the radius of the smaller base (radius of frustum).

Given:

Radius of the large cone (r₁) = 4.5 cm,

Radius of the frustum (r₂) = 3 cm,

Height of the frustum (h) = 3 cm.

The height of the original cone (9 cm) is not needed to calculate the volume of the frustum. Plugging the given values into the formula:

[tex]\(V = \frac{1}{3}\pi \times 3 \times (4.5^{2} + 3^{2} + 4.5 \times 3)\)[/tex]

[tex]\(V = \pi (20.25 + 9 + 13.5)\)[/tex]

[tex]\(V = \pi (42.75)\)[/tex]

[tex]\(V = 134.25\pi \text{cm}^{3}\)[/tex]

Therefore, the volume of the frustum is approximately 134.25π cubic centimeters.

Answer: the amount of money in the account that earns 10% interest is $500

the amount of money in the account that earns 12% interest is $900

Step-by-step explanation:

Let x represent the amount of money in the account that earns 10% interest.

Let y represent the amount of money in the account that earns 12% interest.

There is $400 more in the account that pays 12% than there is in the other account. This means that

y = x + 400

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the account that earns 10% interest.

P = x

R = 10

T = 1 year

I = (x × 10 × 1) = 0.1x

Considering the account that earns 12% interest.

P = y

R = 12

T = 1 year

I = (y × 12 × 1) = 0.12x

If the total interest for a year is $158, it means that

0.1x + 0.12y = 158 - - - - - - - - - - -1

Substituting y = x + 400 into equation 1, it becomes

0.1x + 0.12(x + 400) = 158

0.1x + 0.12x + 48 = 158

0.22x = 158 - 48 = 110

x = 110/0.22 = 500

y = x + 400 = 500 + 500

y = 900

Answer:

DC = 10.93 cm ,  AC = 9.8 cm

Step-by-step explanation:

From trigonometry;

⇒ Tan 60 = AB/BD

⇒AB = BD Tan 60 ( where BD = 4 cm )

⇒ AB = 6.93 cm

Also, AB=BC , therefore;

⇒ BC = 6.93 cm

⇒ Cos 60 = BD/AD

⇒ AD = BD/ Cos 60 = 4/Cos 60

⇒ AD = 8 cm

From Pythagoras theorem;

⇒ [tex]AC^{2}[/tex] = [tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex](6.93)^{2}[/tex] + [tex](6.93)^{2}[/tex]

⇒ AC = [tex]\sqrt{96.05}[/tex] = 9.80 cm

⇒ DC = BD + BC = 4 + 6.93

⇒ DC = 10.93 cm

Answer:

Aidan got 56% of votes.

Step-by-step explanation:

Given:

Aidan is running for student body president. In today's election, he received 462 votes out of a total of 825 votes cast.

Now, to find the percent of votes did Aidan get.

Total votes cast = 825 votes.

Votes he received = 462 votes.

Now, to get the percent of votes Aidan get:

[tex]\frac{Votes\ he\ received}{Total\ votes\ cast} \times 100[/tex]

[tex]=\frac{462}{825} \times 100[/tex]

[tex]=0.56\times 100[/tex]

[tex]=56\%.[/tex]

Therefore, Aidan got 56% of votes.

Answer:

56%

Step-by-step explanation:

Aidan got fifty-six percent of the votes.

To solve this problem, start by letting p represent the unknown percent and write the percent as the fraction p over one hundred.

Write a second ratio that expresses the part-whole relationship between the numbers four hundred sixty-two over eight hundred twenty-five.

Set up a proportion between the two ratios.

Write the cross product equation. Eight hundred twenty-five p equals one hundred times four hundred sixty-two, or eight hundred twenty-five p equals forty-six thousand two hundred.

Divide each side of the equation by eight hundred twenty-five to solve for p.

p equals fifty-six.

Aidan received fifty-six percent of the votes cast.

Answer:

The methods that are fair include __A, B and C__ because __D__ is flawed due to increased chances of winning based on one's skill, ___F___ is flawed due to poor randomization, and ___E___ is flawed due to unequal probabilities of winning and losing.

Step-by-step explanation:

A. Place both names in equal amounts into a hat and draw one without looking:

If you place both names in equal amounts into a hat, then the probability of picking any one of the names would be equal.

For example, if you put 20 pieces of paper containing each name in a hat, then,there will be 40 names in the hat. The probability of picking any one or the other randomly would be:

P = 20/40 =1/2

B. Ask a stranger to flip a coin:

A coin has only two faces, head and tail. Hence, if one person picks head and the other picks tail, the probability of landing on either head or tail is given as:

P = 1/2

C. Roll a die and evaluate the outcome as either even or odd:

A die has 6 faces with equal number of faces with equal number of even numbers and odd numbers, 3. Hence, the probability of rolling an even or odd number is given as:

P = 3/6 = 1/2

D. Throw a stone closest to an object:

This method is not fair because then it depends solely on who can throw the farthest i.e. the physical ability of the throwers.

E. Play a hand of blackjack

This method is flawed because it has unequal probabilities of winning and losing.

F. Ask a random stranger to select:

This method is unfair because it then depends solely on the random picker. The picker could have personal preferences or a bias based on maybe height, beauty, weight, basically anything characteristic. Hence, it is unfair.

Final answer:

Fair methods for deciding who gets the prize include placing both names in a hat, flipping a coin, and rolling a die as they provide equal chances of winning, while throwing a stone, playing blackjack, or asking a stranger can introduce bias or skill, making them unfair.

Explanation:

The methods that are fair include placing both names in a hat, asking a stranger to flip a coin, and rolling a die because these methods provide equal probabilities of winning or losing. Method D: Throwing a stone closest to an object is flawed due to increased chances of winning based on one's skill, which means it's not random. E: Playing a hand of blackjack is flawed due to poor randomization, as the cards dealt can create significantly different chances of winning. F: Asking a random stranger to select is flawed due to unequal probabilities of winning and losing if the stranger holds a bias, even if unintended.

Tossing a coin is a fair way to decide because both outcomes (heads or tails) have equal chances of occurring, which is a 50% chance each way. This is consistent with the principle of randomness and independent events, where the outcomes of past coin tosses do not influence the results of future tosses.

Answer: 623 inches

Step-by-step explanation:

We can model this escalator as a right triangle, in which its length is the hypotenuse and its vertical rise ([tex]x[/tex]) is on of the sides of the triangle (as shown in the figure).

So, if we want to find [tex]x[/tex] we have to use the trigonometric function sine:

[tex]sin(15\°)=\frac{opposite-side}{hypotenuse}[/tex] (1)

Here, the opposite side is [tex]x[/tex] and the hypotenuse is [tex]200 ft 9 in[/tex].

Now we have to transform  [tex]200 ft 9 in[/tex] to inches, in this case we only have to convert [tex]200 ft[/tex] to inches, knowing that [tex]1 ft=12 in[/tex]:

[tex]200 ft \frac{12 in}{1 ft}=2400 in[/tex]

[tex]200 ft + 9 in=2400 in+ 9 in=2409 in[/tex]

Substituting this value in (1):

[tex]sin(15\°)=\frac{x}{2409 in}[/tex] (2)

Isolating [tex]x[/tex]:

[tex]x=frac{sin(15\°)}{2409 in}[/tex]

Finally:

[tex]x=623.49 in \approx 623 in[/tex]

Answer:

The question continues ; Which of the following is true ;

Jaylan basis in the partnership is $12,00 and Caspers is 10,000

Jaylan and Casper each have a basis in the partnership of 12,000

Jaylan will have a larger share of the profits than Casper

The first and third answers are both correct

Answer ; Jaylan and Casper each have a basis in the partnership of 12,000

Step-by-step explanation:

Both Jaylan and casper will have a partnership basis of $12,000 , it was mentioned initially in the question that (Jaylan and casper are equal partners in J&C racoon hats), equal partners implies both Jaylan and casper with have equal profit and equal losses as the case maybe Irrespective of the amount each contributed. Hence Jaylan and Casper each have a basis in the partnership of 12,000.

Answer: A. Approximately 0.017 pounds

Step-by-step explanation:

Formula to find the margin of error :

[tex]E=z^*\dfrac{s}{\sqrt{n}}[/tex] , where z* = critical value for confidence interval , s= standard deviation , n= sample size.

As per given , we have

s= 0.15 pound

n= 300

Critical value for 95% confidence = 1.96

Then, Margin of error for 9%% confidence interval will be :

[tex]E=(1.96)\dfrac{0.15}{\sqrt{300}}\\\\=0.0169740979142\approx0.017[/tex]

Hence, they can expect a margin error of 0.017 pound (approximately.)

Thus , the correct answer is A. Approximately 0.017 pounds

Answer:

600 in^2.

Step-by-step explanation:

There are 6 faces on a cube so the area we need is:

6 * 10 * 10

= 600 in^2.

Answer: the cost of Parker's tuition is $17955

Step-by-step explanation:

Let x represent the cost of Parker's tuition.

Parker was able to pay 44% of his college tuition with his scholarship. This means that the amount that he was able to pay with his scholarship would be

44/100 × x = 0.44 × x = 0.44x

The amount that is remaining for him to pay would be

x - 0.44x = 0.56x

If he paid the remaining $10,054.52 with a student loan, it means that

0.56x = 10054.52

x = 10054.52/0.56

x = 17954.5

Rounding up to the nearest whole number, it becomes

x = $17955

Answer: The larger rug is 4 times larger

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

The small circular rug covers an area of approximately 67 square feet. This means that

67 = πr²

r² = 67/π = 67/3.14 = 21.34

r = √21.34 = 4.62

If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be

2 × 4.62 = 9.24

The area of the larger rug would be

3.14 × 9.24² = 268.06ft²

Therefore

268.06/67 = 4

The larger rug is 4 times larger

Answer:

Step-by-step explanation:

1.

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

       =cot x (sec²x)²

       =cot x (1+tan²x)²     [ ∵ sec²x=1+tan²x]

       =  cot x(1+ 2 tan²x +tan⁴x)

       =cot x+ 2 cot x tan²x+cot x tan⁴x

        =cot x +2 tan x + tan³x        [ ∵cot x tan x [tex]=\frac{ \textrm{tan x }}{\textrm{tan x}}[/tex] =1]

       =R.H.S

2.

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

 L.H.S =(sin x)(tan x cos x - cot x cos x)

          = sin x tan x cos x - sin x cot x cos x

           [tex]=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}[/tex]

           = sin²x -cos²x

           =1-cos²x-cos²x

           =1-2 cos²x

           =R.H.S

3.

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

         =[tex]1+\frac{{sin^2x}}{cos^2x}[/tex]                       [[tex]\textrm{sec x}=\frac{1}{\textrm{cos x}}[/tex]]

         =1+tan²x                        [tex][\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}][/tex]

         =sec²x

        =R.H.S

4.

[tex]\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}[/tex]

L.H.S=[tex]\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}[/tex]

       [tex]=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}[/tex]

      [tex]=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}[/tex]

     [tex]=\frac{\textrm{2sin x}}{sin^2 x}[/tex]

      = 2 csc x

    = R.H.S

5.

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

        = sec²x-tan²x

        =[tex]\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}[/tex]

        [tex]=\frac{1- sin^2x}{cos^2x}[/tex]

        [tex]=\frac{cos^2x}{cos^2x}[/tex]

        =1

Answer:

Step-by-step explanation:

The sum of the angles on a straight line is 180 degrees. Therefore,

Angle XYZ + angle MYZ = 180

Angle XYZ + 115 = 180

Angle XYZ = 180 - 115 = 65 degrees

The sum of the angles in a triangle is 180 degrees. It means that

Angle XZY + angle YXZ + angle MYZ = 180

Therefore,

4k + 5 + 6k + 10 + 65 = 180

4k + 6k + 5 + 10 + 65 = 180

10k + 80 = 180

10k = 180 - 80 = 100

Dividing the left hand side and the right hand side of the equation by 10, it becomes

10k/10 = 100/10

k = 10

Answer:

48 bags are needed by George to fill his sandbox.

Step-by-step explanation:

Given:

Total capacity of the sandbox (V) = 32 cubic feet

Capacity of each bag = (B) = [tex]\frac{2}{3}[/tex] cubic feet

Now, number of bags required (N) = ?

The formula to find the total number of bags required to fill the sandbox is given as:

[tex]Number\ of\ bags=\frac{Total\ capacity\ of\ sandbox}{Capacity\ of\ each\ bag}\\\\N=\frac{V}{B}[/tex]

Now, plug in the given values and solve for 'N'. This gives,

[tex]N=32\div\frac{2}{3}[/tex]

In order to multiply a whole number with a fraction, we replace the division sing by multiplication and take the reciprocal of the fractional number. This gives,

[tex]N=32\times \frac{3}{2}\\\\N=\frac{32\times 3}{2}\\\\N=16\times 3=48[/tex]

Therefore, 48 bags are needed by George to fill his sandbox.

George needs 48 bags of sand, each holding 2/3 cubic feet, to fill his sandbox that requires 32 cubic feet of sand.

To determine how many bags of sand are required to fill George's sandbox that has a volume of 32 cubic feet, when each bag holds 2/3 cubic feet of sand, we need to perform a division operation. We divide the total volume (32 cubic feet) by the volume each bag holds (2/3 cubic feet).

The calculation is as follows:

Find the inverse of 2/3 which is 3/2.

Multiply the total volume by the inverse. 32 × (3/2) = 32 × 1.5 = 48.

Thus, George would need 48 bags of sand to fill his sandbox.

Answer:

(1) ADB = CDB = 90°

(2) c sinA

(3) (sinA)/a = (sinB)/b

Step-by-step explanation:

1. ADB = CDB = 90°

2. c sinA

since,

sin A = x/c , sin C = x/a

so x = c sinA and a sinC

3. from reflective property of x,

since x = c sinA

and x = a sinC

we substitute each equivalently

that is,

c sinA = a sinC

dividing each sides of the equation by ac we have ,

(c sinA)/ac = ( a sinC)/ac

simplifying we have,

(sinA)/a = (sinB)/b

Therefore the above equation is referred to as the SINE RULE.

Answer:

Q1:  p = - 33

Q2: d = - 99

Q3: t = - 13

Step-by-step explanation:

Q1: [tex]$ \textbf{-} \frac{\textbf{p}}{\textbf{3}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{8} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{3}[/tex]

We solve this taking LCM.

We get: [tex]$ \frac{-p - 24}{3} = 3 $[/tex]

[tex]$ \implies - p - 24 = 9 $[/tex]

[tex]$ \implies \textbf{p} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 33} $[/tex]

Q4: [tex]$ \frac{\textbf{d}}{\textbf{11}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{4} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13} $[/tex]

Again we proceed like Q1 by taking LCM.

We get: [tex]$ \frac{d - 44}{11} = - 13 $[/tex]

[tex]$ \implies d - 44 = - 13 \times 11 = - 143 $[/tex]

[tex]$ \implies d = - 143 + 44 $[/tex]

[tex]$ \implies \textbf{d} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 99} $[/tex]

Q7: 5t + 12 = 4t - 1

We club the like terms on either side.

[tex]$ \implies 5t - 4t = - 1 - 12 $[/tex]

[tex]$ \implies (5 -4)t = - 13 $[/tex]

[tex]$ \implies \textbf{t} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13} $[/tex]

Hence, the answer.

Answer: the value of y is 180

Step-by-step explanation:

If y varies directly as x, then as y increases,x increases and as y decreases, x decreases.

We would introduce a constant of proportionality, k. Therefore,

y = kx

When y = - 18, x = - 2

Therefore,

- 18 = - 2 × k

Dividing the left hand side and the right hand side of the equation by

- 2, it becomes

- 2k/ -2 = - 18/-2

k = 9

The expression becomes

y = 9x

Therefore, when x = 20,

y = 9 × 20 = 180

Yo sup??

since y varies directly with x we can say

y=kx

at y=-18, x=-2 then

-18=k*(-2)

k=9

therefore

y=9x

at x=20

y=9*20

=180

Hope this helps.

Answer:

114.29 ft

Step-by-step explanation:

tan ∅ = Opp/Adj

tan 77 = x/25

x = 25 tan 77

x = 108.29ft

Plus 6ft = 114.29 ft

Answer:

A

Step-by-step explanation: