Express the following ratio in the simplest form vii) 4.5km: 450m​

Answer:

Step-by-step explanation:

According to SOH in SOH, CAH TOA;

SOH means  sin theta = opposite/hypotenuse = 2/3

This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.

According to Pythagoras theorem; hyp² = opp²+adj²

adj² = hyp² - opp²

adj² = 3² - 2²

adj² = 9 - 4

adj² = 5

adj = √5

Hence the adjacent side is √5.

From the trigonometry identity above;

cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5

Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)

sec theta = hyp/adj = 3/√5

From the above calculation, the following are possible:

cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5

The correct options are C and D

Answer:

Significant figures are any digits that contribute to the number: In 02.400, only 2 and 4 are significant digits.  However, in 2.4001, 2, 4, 0, 0, and 1 are significant digits, because the number would not be the same without them.

Step-by-step explanation:

Hope it helps <3

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb

z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.

For 150 lb:

[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]

For 201 lb:

[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]

From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%

b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.

For 150 lb:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]

For 201 lb:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]

From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%

c) The probability from part C is more important

Answer:

The cosine of 86º is approximately 0.06976.

Step-by-step explanation:

The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:

[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]

The value of 86º in radians is:

[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]

[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]

Then, the cosine of 86º is:

[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]

[tex]\cos 86^{\circ} \approx 0.06976[/tex]

The cosine of 86º is approximately 0.06976.

Greetings from Brasil...

We know that the entire length of a circle its:

C = 2πR

C = 2π8

C= 16π      circumference length

now rule of 3:

 length              º

  16π   ---------  360

     X   ---------  135

360X = 135 · 16π

X = 2160π/360

Answer:

a. x = 36°, y = 36°, z = 34°

Step-by-step explanation:

X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°

The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°

Answer:

C. 15 centimeters

Step-by-step explanation:

The Triangle Midsegment Theorem

segment LM = 1/2 of AC

LM = 1/2 * 30

LM = 15 cm

Answer:

Step-by-step explanation:

Null hypothesis: u = 9.5hrs

Alternative: u =/ 9.5hrs

Using the t test

t = x-u/sd/√n

Where x is 10hrs, u is 9.5, sd is 1.6 and n is 15

t = 10-9.5 / (1.6/√15)

t = 0.5 / (0.4131)

t = 1.21

In order to make a conclusion, we have to find the p value at a significance level lot 0.1. The p value is 0.2263 which is greater than 0.1. This, we will fail to reject the null hypothesis and conclude that there is not enough statistical evidence to prove that the technique performs differently than the traditional method.

Answer:

18.03 inches

Step-by-step explanation:

The cardboard is cut as shown below.

The line c cuts the rectangle into 2 right angled triangles.

To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:

[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]

=> c = 18.03" = 18.03 inches

The length of c, the diagonal, is 18.03 inches.

Answer: 12-i

               12-(√-1)

Step-by-step explanation:

[tex]18-\sqrt{-25}[/tex]   Original Question

[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex]   Split

[tex]18-5*(\sqrt{-1} )[/tex]   Solve for square root

[tex]12-\sqrt{-1}[/tex]   Subtract

You can substitute [tex]\sqrt{-1}[/tex] for i

[tex]12-i[/tex]   Substitute

Answer:

18-5i

Step-by-step explanation:

Answer:

its b i got it right on edge

Step-by-step explanation:

Answer:

[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

Step-by-step explanation:

Hello,

"Find the sum of the following infinite geometric series"

infinite

   We will have to find the limit of something when n tends to [tex]+\infty[/tex]

geometric series

   This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.

The sum is something like

           [tex]\displaystyle \sum_{k=0}^{+\infty} a_k[/tex]

First of all, we need to find an expression for [tex]a_k[/tex]

First term is

   [tex]a_0=7[/tex]

Second term is

    [tex]a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}[/tex]

Then

   [tex]a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}[/tex]

and...

   [tex]a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}[/tex]

Ok we are good, we can express any term for k integer

   [tex]a_k=a_0\cdot (\dfrac{4}{9})^k[/tex]

So, for n positive integer

[tex]\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}][/tex]

And the limit of that expression when n tends to [tex]+\infty[/tex] is

   [tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

as

   [tex]\dfrac{4}{9}<1[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

From the information given:

For Adult Men

Mean [tex]\mu[/tex] = 69.5

Standard deviation [tex]\sigma[/tex] = 2.4

observed value X = 74

For Adult Women

Mean [tex]\mu[/tex] = 63.8

Standard deviation [tex]\sigma[/tex] = 2.6

observed value X = 70

Therefore ; the values for their z  scores can be obtained in order to determine who is more unusually tall within his or her respective sex

For Adult Men :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{74- 69.5}{2.4}[/tex]

[tex]z = \dfrac{4.5}{2.4}[/tex]

z = 1.875

For Adult Women :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{70- 63.8}{2.6}[/tex]

[tex]z = \dfrac{6.2}{2.6}[/tex]

z = 2.3846

Thus; we can conclude that , the women is more unusually tall within his or her respective sex

Answer:

12.04

Step-by-step explanation:

Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,

[tex]a^2 + b^2 = c^2[/tex]

We already have a and b which are 8 and 9 so we plug them in.

[tex](8)^2 + (9)^2 = c^2[/tex]

64 + 81 = c^2

145 = c^2

c = 12.04 rounded to the nearest hundredth.

Thus,

the unknown side is about 12.04.

Hope this helps :)

Answer:

well if you want my answer even though it could not be right so dont get mad at me if i am wrong but i think that it is all mostly based on how far they are from each other the further it is the more it will roll the closer it is the less it it will roll

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

rolling it shows its circumference and the other pennine has the ame circumference

Answer:

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220

The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.

Adult's ticket = [y]

Children's ticket = [x]

Student's ticket = [z]

and

y = 3x

Now -

x + y + z = 500

x + 3x + z = 500

4x + z = 500       ....[1]

and

12x + 18y + 15z = 8040

12x + 18(3x) + 15z = 8040

12x + 54x + 15z = 8040

66x + 15z = 8040     ....[2]

On solving [1] and [2], we get -

x = 90 and z = 140

and

y = 3x = 3 x 90 = 270

y = 270

Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Answer:

y=0.5x+40

Step-by-step explanation:

Copy the  equation.

x-2y=8

Subtract x from both sides.

-2y=-x-8

Divide both sides by -2.

y=0.5x+4

Now we know the slope is 0.5.

Any line with a slope of 0.5 will be perpendiculr to the original line.

One that you can use is y=0.5x+40.

=============================================

Work Shown:

x = speed of train A

y = speed of train B

"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y

distance = rate*time

d = x*7

d = (4/5)y*7 = (28/5)y represents the distance train A travels

d = y*7 = 7y represents the distance train B travels

summing those distances will give us 693

(28/5)y + 7y = 693

5*(  (28/5)y + 7y ) = 5*693

28y + 35y = 3465

63y = 3465

y = 3465/63

y = 55

Train B's speed is 55 mph

4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph

Train A's speed is 44 mph

Answer:

you need to have values for w and v

but u basically have to do

MOVE V TO THE OTHER SIDE

SO

W/V=P

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

              ✌ -ZYLYNN JADE ARDENNE

Answer:

0.3110

Step-by-step explanation:

This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.

The general formula for a binomial distribution is:

[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]

Where n is the sample size and k is the desired number of successes.

The probability of k=2 in a sample of n =6 is:

[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]

The probability is 0.3110

Step-by-step explanation:

a = 14.56231 cm

b(width) = 9 cm

a+b = 23.56231 cm

A(area) = 343.1215 cm

Sorry if this doesnt help

Answer:

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Step-by-step explanation:

In a golden rectangle, the width is a and the length is a + b.

The proportion of the lengths of the sides is:

(a + b)/a = a/b

Here, the width is 9 cm, so we have a = 9 cm.

(9 + b)/9 = 9/b

(9 + b)b = 81

b^2 + 9b - 81 = 0

b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)

b = (-9 +/- sqrt(81 + 324)/2

b = (-9 +/- sqrt(405)/2

b = -9/2 +/- 9sqrt(5)/2

Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2

Length = a + b = 9/2 +/- 9sqrt(5)/2

Since the length of a side of a rectangle cannot be negative, we discard the negative answer.

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Answer:

B. -3x

Step-by-step explanation:

A term is defined as either a constant or a variable with a coefficient.

-3 is incorrect because there is no constant -3 in the expression.

-3x is correct because there is a -3x in the expression

(x + 4) is incorrect because that is a linear binomial and has yet to be distributed.

-7 is incorrect because it has to be distributed.

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 13/3, 4 1/3, or 4.3

▹ Step-by-Step Explanation

x + 7 - 4(x + 1) = -10

x + 7 - 4x - 4 = -10

-3x + 7 - 4 = -10

-3x + 3 = -10

-3x = -10 - 3

-3x = -13

x = 13/3, 4 1/3, or 4.3

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x = 13/3

Step-by-step explanation:

x + 7 - 4(x + 1) = -10

x + 7 - 4x - 4 = -10

-3x + 3 = -10

-3x = -13

x = -13/(-3)

x = 13/3

Answer:

60

Step-by-step explanation:

x + 0.30x = 78

1.30x = 78

x = 60

Answer:

The answer is 60.

Step-by-step explanation:

here, let another number be x.

according to the question the number when increased by 30% will be 78. so,

x+ 30% of x =78

now, x+ 30/100×x =78

or, x+0.3x=78

or, 1.3x=78

Therefore the another number is 60.

Hope it helps...

Answer:

x=2

Step-by-step explanation:

3(x-2)-6x=4(x-5)

Distribute

3x -6  -6x = 4x -20

Combine like terms

-3x-6 = 4x-20

Add 3x to each side

-3x-6+3x = 4x-20+3x

-6 = 7x-20

Add 20 to each side

-6+20 = 7x-20+20

14 = 7x

Divide by 7

14/7 =7x/7

2=x

Answer:

Step-by-step explanation:

[tex]3(x - 2) - 6x = 4(x - 5)[/tex]

Distribute 3 through the parentheses

[tex]3x - 6 - 6x = 4(x - 5)[/tex]

Distribute 4 through the parentheses

[tex]3x - 6 - 6x = 4x - 20[/tex]

Collect like terms

[tex] - 3x - 6 = 4x - 20[/tex]

Move variable to L.H.S and change it's sign

[tex] - 3x - 4x - 6 = - 20[/tex]

Move constant to RHS and change it's sign

[tex] - 3x - 4x = - 20 + 6[/tex]

Collect like terms

[tex] - 7x = - 20 + 6[/tex]

Calculate

[tex] - 7x = - 14[/tex]

Divide both sides of the equation by -7

[tex] \frac{ - 7x}{ - 7} = \frac{ - 14}{ - 7} [/tex]

Calculate

[tex]x = 2[/tex]

Hope this helps..

Best regards!!

Answer:

g(2) =10x+6

Step-by-step explanation:

g(x) =5x+3

g(2)=5x+3

g(2)=10x+6

have a great day

Answer: i honestly dont know this seems very complicated

Step-by-step explanation:

Answer:

3x^3+12x

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

According to the given question, the calculation of number is shown below:-

Let the number be x.

[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.

[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]

Now we will solve the above equation

[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]

x = 5

Therefore the correct answer is 5

Hence, the number based on the given information provided in the question is 5

Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

How long will it take the projectile to hit the ground?

It happens when [tex]h(t) = 0[/tex]

So

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

[tex]-16t^{2} + 32t + 128 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]-16t^{2} + 32t + 128 = 0[/tex]

So [tex]a = -16, b = 32, c = 128[/tex]

[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]

[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]

[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

Answer:

The correct answer to this question is C: (72,24).

Step-by-step explanation:

We are given that:

The cost of 1 cap is $5 each

The cost of 1 t-shirt is $10 each

Let x be the number of caps sold

Let y be the number of t-shirt sold

In the context we are given that the drama club needs to raise at least $500 to go on the trip.

So based on this information we can create a inequality as:

the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500

Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.

Next we need to figure out how many caps and t-shirt were sold.

- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)

Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )

B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500

YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!

C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.

So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.

Answer: C

Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.

First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.

Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.

So, (8,5) is a valid solution in the context of the situation.