Noah tried to prove that cos(θ)=sin(θ) using the following diagram. His proof is not correct.

Hey there! I'm happy to help!

If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.

r=2b+6

We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.

2b+6+b=33

We combine like terms.

3b+6=33

We subtract six from both sides.

3b=27

We divide both sides by 3.

b=9

Now we just subtract 9 from 33 to see how many red ones there are.

33-9=24

So, there are 24 red marbles and 9 black marbles.

Now, let's see which of these options are correct.

The equation r+b=33 represents the total number of marbles.

This is true because r plus b is equal to the total, which is 33.

The equation r=2b+6 can be used to find the number of red marbles.

This is true because it we used this r-value to find how many black marbles there were.

The equation r=2b+6 represents the total number of marbles.

This is false because it does not have the total number, which is 33.

The equation r=b=33 can be used to find the number of red marbles.

This is true because we plugged in the r-value to solve for b with this equation.

There are 9 red marbles in the bag.

This is false. There are 24 red marbles.

There are 9 black marbles in the bag.

This is true.

There are 24 black marbles in the bag.

This is false. There are 9 black marbles.

There are 24 red marbles in the bag.

This is true.

Have a wonderful day! :D

Answer:

1,2,4,6,8

Step-by-step explanation:

Answer:

multiplying the equation A

Step-by-step explanation:

3c=d-8 ####### *4

+ c=4d + 8

After that you will get the value of c and d.

Answer:

Multiply equation A by -4

Step-by-step explanation:

3c = d - 8

c = 4d + 8

Multiply equation A by -4.

-12c = -4d + 32

c = 4d + 8

Add the equations.

-11c = 40

Variable d is eliminated.

Answer:

0.65463

Step-by-step explanation:

From the given question:

It is stated that 2% of the parts are defective (D) out of 50 parts

Therefore the probability of the defectives;

i.e  p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]

p(defectives) = [tex]\dfrac{2}{50}[/tex]

p(defectives) = 0.04

The probability of the failure is the P(Non-defectives)

p(Non-defectives) =  1 - P(defectives)

p(Non-defectives) =  1 - 0.04

p(Non-defectives) =  0.96

Also , Let Y be the number of non -defective out of the 52 stock parts.

and we need Y ≥ 50

P( Y ≥ 50) , n = 52 , p = 0.96

P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)

= P(Y = 50) + P(Y =51) + P(Y=52)    (disjoint events)

P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]

[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]

P(Y = 50) = 0.27557

P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]

[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]

P(Y = 51) = 0.25936

(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]

[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]

P(Y = 52) = 0.1197

∴

P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197

P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463

Answer:

2.28% of babies born in the United States having a low birth weight.

Step-by-step explanation:

The complete question is: In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.

We are given that in the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.

Let X = birth weights of newborn babies

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 3,500 g

            [tex]\sigma[/tex] = standard deviation = 500 g

So, X ~ N([tex]\mu=3500, \sigma^{2} = 500[/tex])

Now, the percent of babies born in the United States having a low birth weight is given by = P(X < 2500 mg)

   P(X < 2500 mg) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{2500-3500}{500}[/tex] ) = P(Z < -2) = 1 - P(Z [tex]\leq[/tex] 2)

                                                                 = 1 - 0.97725 = 0.02275 or 2.28%

The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

Answer:

The z-score for 2,500 is -2. According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g. 5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g. Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500 g.

Step-by-step explanation:

did the assignment on edge:)

Answer:

[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.

At the beginning the area is 2100

After one year the area will be

   2100*(1-3.5%)=2100*0.965

After n years the area will be

   [tex]2100\cdot0.965^n[/tex]

So after 5 years the area will be

   [tex]2100\cdot0.965^5=1757.34027...[/tex]

So rounded to the nearest square kilometer is 1757

Hope this helps

Answer: 1757 km²

Step-by-step explanation:

Because 3.5% = 0.035, first do 1-.035 to get .965.  Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.

Answer:

The probability that all three people on the subcommittee are men

= 20%

Step-by-step explanation:

Number of members in the committee = 15

= 8 men + 7 women

The probability of selecting a man in the committee

= 8/15

= 53%

The probability of selecting three men from eight men

= 3/8

= 37.5%

The probability that all three people on the subcommittee are men

= probability of selecting a man multiplied by the probability of selecting three men from eight men

= 53% x 37.5%

= 19.875%

= 20% approx.

This is the same as:

The probability of selecting 3 men from the 15 member-committee

= 3/15

= 20%

Answer:

12 and 7

Step-by-step explanation:

The area of the first  triangle is

A = 1/2 bh

A = 1/2 ( 14*6)

A = 42

The area of the second triangle must equal 42

Varying inversely means as the height increases, the base must decrease at the same rate

Lets try 12 and 7

A = 1/2 (12*7)

A = 42

The height of the new triangle increased and the base decreased

Answer:

[tex]\boxed{12 \: \mathrm{and} \: 7}[/tex]

Step-by-step explanation:

Solve for the area of first triangle.

[tex]\frac{bh}{2}[/tex]

[tex]b=base\\h=height[/tex]

[tex]\frac{14 \times 6}{2}[/tex]

[tex]\frac{84}{2} =42[/tex]

The area of second triangle is same as the first triangle.

The area of second triangle is 42 units².

The base varies inversely with the height.

[tex]b \propto \frac{1}{h}[/tex]

As the value of b increases, the value of h decreases.

[tex]\frac{12 \times 7}{2}=42[/tex]

The answer is b = 12 and h = 7.

Answer:

3rd

Step-by-step explanation:

i got it right on khan academy

Answer:

13.33

Step-by-step explanation:

As in the attached diagram,  we can see that the points belong to  [tex]\mu\pm \sigma[/tex] interval

Data provided in the question as per the details below:

[tex]\mu_{\bar x}[/tex] = 440

[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480

So,

[tex]\sigma_{\bar x}[/tex] = 480 - 440

= 40

Now the standard deviation of the population is

[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]

= 13.33

Hence, the standard deviation of the population for which the sample is drawn is 13.33

Answer:

Option b and d

Step-by-step explanation:

With the following data,

H0:p=0.11

Ha:p≠0.11

The p-value was determined to be 0.106 and significance level of 0.05.

Since the p value (0.106) is great than 0.05, then we will fail to reject the null hypothesis and conclude that There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%

Answer:

x = -1 and x = 4.

Step-by-step explanation:

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

x - 4 = 0

x = 4

x + 1 = 0

x = -1

Check your work...

(4)^2 - 3(4) - 4

= 16 - 12 - 4

= 4 - 4

= 0

(-1)^2 - 3(-1) - 4

= 1 + 3 - 4

= 4 - 4

= 0

So, x = -1 and x = 4.

Hope this helps!

Answer: -4/3

Step-by-step explanation:

Formula to find a slope of two given points is

y(sub2) - y(sub1) / x(sub2) - x(sub1)

Plug the values in to get the answer.

-2 - 2 / -1 - (-4)

-4/3

Answer:

you will start to ascend at the rate of 1.6

Step-by-step explanation:

Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)

We are told that the equation z = 1600 − 0.005x² − 0.01y²

Therefore, we have;

∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)

This gives;

∇z = -0.005(2x)i - 0.01(2y)j

∇z = <-0.01x - 0.02y>

coordinates are (120, 80, 1464).

Thus;

∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>

D_uf = <-1.20, -1.60> × <0, - 1>

D_uf = 0 + 1.6

D_uf = 1.6

So, you will start to ascend at the rate of 1.6

Answer:

1. 55 degrees, 2. 316 degrees

Step-by-step explanation:

When it shows interior angles on a triangle it adds up to 180 degrees

When it shows exterior angles on a triangle it adds up to 360 degrees

1. ? = 55 degrees

85 + 40 = 125

180 - 125 = 55

2. ? = 316 degrees

Inside of triangle:

14 + 30 = 44

180 - 44 = 136 degrees

Exterior of triangle:

360 - 14 = 346 degrees

360 - 30 = 330 degrees

360 - 44 = 316 degrees

Answer:

504 ways.

Step-by-step explanation:

In this case, order matters. If Amy were lead, Bob were record keeper, and Charles were researcher, that would be different than if Bob were lead, Charles were record keeper, and Amy were researcher. So, we will be using a permutation formula to compute.

The formula is n! / (n - k)!, where n is the total number of people (9), and k is the number you are selecting (3).

9! / (9 - 3)! = 9! / 6! = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 9 * 8 * 7 = 72 * 7 = 504 ways.

Hope this helps!

Step-by-step explanation:

It is given that,

Total length of a board is 65 inches

It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.

Let x is the length of other piece and y is the length of first piece such that,

y = 2x-7 ....(1)

Also,

x+y = 65 .....(2)

Put the value of y from equation (1) to equation (2) such that,

x+2x-7 = 65

3x=65+7

3x=72

x = 24 inches

Put the value of x in equation (1)

y = 2(24)-7

y = 41 inches

So, the length of first piece is 41 inches while the length of other piece is 24 inches.

Answer:

See Image Below.

Step-by-step explanation:

The Shaded region is the area of numbers that this equation satisfies.

Answer:

Please see attached image

Step-by-step explanation:

In order to graph the inequality, start from plotting the boundary line defined by the equality;

y = 3 x

You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:

for x = 0 then y = 3 (0) = 0

for x = 1 then y = 3 (1) = 3

Then use the points (0, 0) and (1, 3) to plot the boundary line.

After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.

When you use it in the inequality, you get:

(0)  [tex]\leq[/tex] 3 (3)

0   [tex]\leq[/tex] 9

which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.

Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.

Answer:

y = 4/3x+2

Step-by-step explanation:

We can use the slope intercept form of the equation

y = mx+b

Where m is the slope and b is the y intercept

y= 4/3 x +b

Substitute the point into the equation

6 = 4/3(3) +b

6 = 4 +b

Subtract 4 from each side

2 = b

y = 4/3x+2

Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Answer:

(12.141, 14.059)

Step-by-step explanation:

Explanation is provided in the attached document.

Answer:

As X → - ∞ , y → ∞ and as x→ ∞ , y → ∞

Step-by-step explanation:

let f(x) = y = 3x² - 5x + 2

y = 3x² - 5x + 2

= x ( 3x - 5 ) + 2

y = ∞ ( 3 ( ∞ - 5 ) ) + 2

= ∞ (∞ ) + 2

y = ∞

y → ∞ as x → ∞

Now,

as x → - ∞

y = x ( 3x - 5 ) + 2

= ∞ ( 3 ( - ∞ ) - 5 ) + 2

= - ∞ ( - ∞ ) + 2

∞² + 2 = ∞

Hence , Option C is the correct answer.

Answer:

Mathematically you can use the following V = ⁴⁄₃πr³

π = pi

r = radius

To do this you would need a set of scales, a jug, some water, a pen, a ruler and some paper.

ωα√

Answer:

[tex](x+4)^2+(y-4)^2=9[/tex]

Step-by-step explanation:

From the graph, we need to identify two things: the center of the circle and the radius of the circle.

From this graph, we find that the center of the circle is at (-4,4) and the radius of the circle is 3.

Recall that the format for the equation of a circle is [tex](x-x_1)^2+(y-y_1)^2=r^2[/tex]

Now, we can put our know information into this equation and simplify to get our answer

[tex](x-(-4))^2+(y-4)^2=3^2\\\\(x+4)^2+(y-4)^2=9[/tex]

Answer:

The answer is below

Step-by-step explanation:

Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

Answer:

Given:

Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]

The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)

The 90% confidence interval is from 7.3442 to 9.9278

Answer:

Statistical concepts are used in quality testing. Companies make many products on a daily basis and every company should make sure that they sold the best quality items.

Step-by-step explanation:

pls keep brainly questions only school related thank you!

Answer:

11

Step-by-step explanation:

Answer:

x = 11.

Step-by-step explanation:

9 less than twice a number is the same thing as twice a number minus 9. Let's say that the number is x.

2x - 9 = 13

2x = 22

x = 11

Hope this helps!

Answer:

5/16

Step-by-step explanation:

P(tails) = 1/2

P(>3) = 5/8

P(tails AND >3) = 1/2 × 5/8 = 5/16

Answer:

45

Step-by-step explanation:

Both angles (2x+45) and x together form a straight angle which measures 180 degrees.

Together should make you think of adding the angle measurements.

So we have that (2x+45)+x should be 180 degrees.

The equation we want to solve is:

(2x+45)+x=180

2x+45+x=180

(2x+x)+45=180

3x+45=180

3x=180-45

3x=135

x=135/3

x=45

Let's confirm that x is 45.

(2x+45) with x=45:

(2*45+45)

(3*45)

135

So (2x+45)+x at x=45 gives us:

135+45

180

Answer has been confirmed.

Answer:

[tex]\boxed{x = 45}[/tex]

Step-by-step explanation:

=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)

=> [tex]3x+45 = 180[/tex]

Subtracting 45 to both sides

=> 3x = 180-45

=> 3x = 135

Dividing both sides by 3

=> x = 45

Answer:

La escala utilizada en el mapa es 1 : 900000.

Step-by-step explanation:

El enunciado describe claramente una escala de reducción. El factor de escala se define como sigue:

[tex]n = \frac{s_{plano}}{s_{real}}[/tex]

Donde:

[tex]n[/tex] - Factor de escala, adimensional.

[tex]s_{plano}[/tex] - Distancia en el plano, medida en centímetros.

[tex]s_{real}[/tex] - Distancia real, medida en centímetros.

Si [tex]s_{plano} = 5\,cm[/tex] y [tex]s_{real} = 4500000\,cm[/tex], entonces el factor de escala es:

[tex]n = \frac{5\,cm}{4500000\,cm}[/tex]

[tex]n = \frac{1}{900000}[/tex]

La escala utilizada en el mapa es 1 : 900000.

Answer:

Step-by-step explanation:

First, you have to figure out how many words he types in one minute. Then, have to multiply by the number of minutes. So,

Number of words per minute:

742 = Total number of words in 14 min

14 = time given

742/14 = 53 words per minute

Number of Words in 1 hour:

53 = words per min

60 = number of minutes

53*60 = 3,180

Hope my answer helps,

Kavitha

Answer:

3180 words

Step-by-step explanation:

We can use a ratio to solve

742 words           x words

---------------  = -----------------

14 minutes          60 minutes

Using cross products

742 * 60 = 14x

Divide each side by 14

742*60/14 = x

3180 words