I NEED HELP WITH THIS !! PLS HELP!!

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer:

T=35X6.50

Step-by-step explanation:

Answer:

Sorry, I cant read whole problem. Edit your question and ill fix my answer

Step-by-step explanation:

equation= y-y¹=m(x-x¹)

= y-4= 3(x-3)

y-4= 3x-9

y= 3x-9+4

y=3x-5

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

7 × 1 = 7  7 × 10 = 70  7 × 12 = 84

Step-by-step explanation:

Answer:

C. Same shape

D. Similar

Step-by-step explanation:

All three angles in ∆ABC are congruent to all three corresponding angles in ∆DEF. However, the three corresponding sides of both ∆s are not the same but they are proportional to each other.

This implies that, both triangles are similar.

Similar triangles have the same shape but different size.

Thus, ∆ABC and ∆DEF can be referred to as being similar and also having the same shape.

Answer:

D. (x+8)^2=105 A P E X

Step-by-step explanation:

Answer:

The population of deer at any given time = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

Step-by-step explanation:

This is an example of logistic equation on population growth

carrying capacity, k = 200

Rate, r = 3% = 0.03

Initial Population, P1 =  80

P(t) =?

P(t) = (P1 (k)(e^rt)) ÷ (k- P1 + P1(e^rt))

P(t) = (80 (200)(e^0.03t)) ÷ (200 - 80 + 80(e^0.03t))

     = (16000(e^0.03t))  ÷ (120 + 80(e^0.03t))

      = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

The distance form the point A to point B is equal to 618.76 feet according to the trigonometric laws.

Given that beacon-light is 104 feet above the water.

Also ∠A = 7° and ∠B = 24° with respect to the ground and the light house.

Sketch part from the above information attached below.

Let's say that the lighthouse is "O".

According to the trigonometric laws:

Tan ∝ = opposite side / adjacent side

Now, we need to find accordingly.

⇒ Tan 7°=104/AO

A0 = 104/Tan 7°

AO ≈ 852.46

Similarly,

Tan 24°= 104/BO

BO = 104/ tan 24°

BO ≈ 233.7

Now, we need to find the distance from point A to point B.

AB = AO-BO

AB = 852.46-233.7

AB = 618.76 feet

Therefore, the distance from point A to point B is 618.76 feet.

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To factor the expression 54a⁶b²+ 9ab², you can use the fact that a common factor of 54a⁶b² and 9ab² is ab².

Thus, you can rewrite the expression as:

ab²(54a⁶ + 9)

You can then factor the expression inside the parentheses using the fact that 3 is a common factor of both 54 and 9:

ab²(3 * 18a⁶ + 3 * 3)

This can be simplified as:

ab²(6a⁶ + 9)

This expression is completely factored and cannot be further simplified. Therefore, the completely factored form of the expression is:

ab²(6a⁶ + 9)

The area, A, of the regular polygons found their side lengths, s and the length of their apothem, are;

4. A ≈ 2144.5 cm²

6. A = 12080 in²

8. A ≈ 1168.5 m²

A regular polygon is a polygon that have sides of the same length and that the sides are symmetric about a common central point.

The area of a regular polygon is given by the formula;

\( \displaystyle{A = \frac{n \times s\times a}{2} }\)

Therefore, we have;

4. The area of a regular pentagon is given by the formula;

\(\displaystyle{A = \frac{5 \times s\times a}{2} }\)

Where;

a = 24.3 cm, s = 35.3 cm, we have;

\(\displaystyle{A = \frac{5 \times 35.3 \times 24.3}{2} \approx 2144.5}\)

6. The area of a regular octagon is given by the formula;

\(\displaystyle{A = \frac{8 \cdot s\cdot a}{2} }\)

Where;

a = 60.4 in,

s = 50 in

Which gives;

\(\displaystyle{A = \frac{8 \times 50\times 60.4}{2} = 12080 }\)

8. The area of a regular decagon is given by the formula;

\(\displaystyle{A = \frac{10 \times s\times a}{2} }\)

Where;

a = 19 m

s = 12.3 m

Which gives;

\(\displaystyle{A = \frac{10 \times 12.3\times 19}{2} = 1168.5}\)

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Answer:

B.-3/2

Step-by-step explanation:

To find the slope, we need to take two points from a line. I am going to call them:

(x1,y1) and (x2,y2).

The slope is:

In this question:

(x1,y1) = (-2,5)

(x2,y2) = (4, -4)

So

So the correct answer is:

B.-3/2

Answer:

Step-by-step explanation:

Confidence interval for the difference in the two proportions is written as

Difference in sample proportions ± margin of error

Sample proportion, p= x/n

Where x = number of success

n = number of samples

For city 1,

x = 22

n1 = 155

p1 = 22/155 = 0.14

For city 2,

x = 12

n2 = 135

p2 = 12/135 = 0.09

Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Margin of error = 1.96 × √[0.14(1 - 0.14)/155 + 0.09(1 - 0.09)/135]

= 1.96 × √0.00138344086

= 0.073

Confidence interval = 0.12 - 0.09 ± 0.073

= 0.03 ± 0.073

C. Since the confidence interval does not include zero, there is evidence that the vacancy rates are different between the two cities.

Answer:

Option A

Step-by-step explanation:

90% CI for p₁ - p₂

\(x_1=22,n_1=155\\x_2=12,n_2=135\)

\(\hat p=\frac{22}{155} =0.141935 \approx 0.142\\\\\hat p_2=\frac{12}{135}=0.088889\approx 0.089\)

\((\hat p_1-\hat p_2)=(0.142-0.0889)=0.0531\)

\(SE_{(\hat p_1-\hat p_2)}=\sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2} } \\\\=\sqrt{\frac{0.142(1-0.142)}{155} +\frac{0.00889(1-0.00889)}{135} } \\\\=\sqrt{\frac{0.142(0.858)}{155} +\frac{0.00889(0.9111)}{135} } \\\\=\sqrt{\frac{0.1218}{155} +\frac{0.0080997}{135} } \\\\=0.037224\\\\\approx0.037\)

\(Z_{\alpha /2}=Z_{0.05}=1.645 (\texttt {from z table})\\\\\texttt {Margin of Error}=Z_{\alpha /2}SE_{p_1-p_2}=1.65\times0.0372=0.061234\\\\\texttt {CI is given by}:(\hat p_1- \hat p_2) \pm Z_{\alpha /2}SE_{p_1-p_2}\\\\\texttt {lower limit}=0.0531-1.645\times0.0372=-0.008187\approx-0.008\\\\\texttt {Upper limit}=0.053+1.645\times0.0372=0.114281\approx0.114\)

90% CI for p₁ - p₂ : (-0.008 , 0.114)

Therefore, Since the confidence interval does include zero, there is no evidence that the vacancy rates are different between the two cities.

Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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Answer: answer 40.

Step-by-step explanation:

Note : lets make x the missing denominator.

I would take the 4/5 and set it equals to 32/x

we then cross multiply

where it would be 4 * x = 32  * 5

it would then be 4x = 160

we would then divide 160 by 4

x = 160/ 4

and x would be 40

.... therefore the missing denominator is 40.

Answer:

Your fraction would be 32/40

Step-by-step explanation:

For it to be equivalent it has to be equal to 4/5. what i did was divided 32 by for and got 8. I then multiplied 4/5 and 8/8 and the answer was 32/40. I multiplied by 8/8 because for it to be equivalent i have to do the same thing to both the numerator and denominator.

I really hope this helps as much as it can

Have an amazing rest of the day or night : )

I will be glad to help if you have any more questions

If wheel on a scooter completes 124 revolutions and travels 22.4 meters then  diameter of the wheel is 57 mm

Each revolution of the wheel covers a distance equal to the circumference of the wheel.

The diameter of the wheel "d".

The distance covered in 124 revolutions is:

distance = 124 x circumference

= 124 x pi x d

= 124 x 3.14 x d

We know that this distance is equal to 22.4 meters, so we can set up an equation:

124 x 3.14 x d = 22.4

Simplifying and solving for d:

d = 22.4 / (124 x 3.14)

d = 0.057 meters

As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters

d = 57 millimeters

Therefore, the diameter of the wheel is approximately 57 mm.

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Chris' gross pay for the week after selling computer equipment worth $17,000 is $2,600.

The gross pay is the addition of the base pay and the sales commission.

The sales commission is graduated and computed as follows:

Chris' base pay = $300

Sales Commissions:

First $5,000 = 10%

Above $5,000 = 15%

Last week's sales = $17,000

10% Commission = $500 ($5,000 x 10%)

15% Commission = $1,800 ($17,000 - $5,000 x 15%)

Total Commission = $2,300

Gross pay = Base Pay + Commission

= $2,600 ($300 + $2,300)

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Answer:

15

Step-by-step explanation:

8x-3+4x+3=180

12x=180

x=180/12

x=15

Step-by-step explanation:

The Straight angle is an angle equal to 180 degrees.

So (8x - 3) + (4x + 3) = 180

8x - 3 + 4x + 3 = 180

12x = 180

x = 15

please give me a brainliest answer

Based on the annuities calculated, he should choose option 1.

Present value = $35,000 + (Annuity amount * Present value of an ordinary annuity of $1)

= $35,000 + ($9,400 * (5%,6))

= $35,000 + ($9,400 * 5.07569)

= $35,000 + 47,711

= $82,711

Present value = (Annuity amount * Present value of an ordinary annuity of $1)

= $17,700 * (5%,6)

= $17,700 * 5.07569

= $89,840

Alex should choose Option 1

Future value annuity = Annuity amount * Future value of an ordinary annuity of $1

= $180,000 * (6%,10)

= $180,000 * 13.1808

= $2,372,544

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The probability distribution of X is Binomial with parameter n = 3 , p = 0.5

a) X : The random variable denotes the number of heads observed over those three tosses.

b) n = number of tosses = 3 , p = probability of head = 0.5 ( as the coin is unbiased)

x P[X=x] = p(x) = (3)0.53\n

0 0.125

1 0.375

2 0.375

3 0.125

Total 1.0

c) The probability distribution of X is Binomial with parameter n = 3 , p = 0.5

d) We know mean of Binomial(n , p ) = np = 3 x 0.5 = 1.5

e) We know sd of Binomial np = \(\sqrt{np(1-P)} = \sqrt{3 * 0.5 * 0.5} = 0.867\)

f) P[Two or more heads] = P[ X= 2]+P[X=3]

= 0.375+0.125

=0.5

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Answer:

0.5944 = 59.44% probability that the team has at least 2 grade 11 students

Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

We have that:

6 + 8 = 14 students, which means that \(N = 14\)

6 grade 11 students means that \(k = 6\)

Teams of 4 members means that \(n = 4\)

What is the probability that the team has at least 2 grade 11 students?

This is:

\(P(X \geq 2) = 1 - P(X < 2)\)

In which

\(P(X < 2) = P(X = 0) + P(X = 1)\)

So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,14,4,6) = \frac{C_{6,0}*C_{8,4}}{C_{14,4}} = 0.0699\)

\(P(X = 1) = h(1,14,4,6) = \frac{C_{6,1}*C_{8,3}}{C_{14,4}} = 0.3357\)

Then

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0699 + 0.3357 = 0.4056\)

\(P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4056 = 0.5944\)

0.5944 = 59.44% probability that the team has at least 2 grade 11 students

Answer:

Maximum= (-2,15)

Minimum= (2,-15)

Answer:

option b : 90 sq. cm

Step-by-step explanation:

1) Area of circle with radius = 12cm

Area = π r^2

= 3.14 * (12) (12)

= 3.14 * 144

= approx 452.4

2) Circumference of circle with radius = 12cm

Circumference = 2πr

= 2 * 3.14 * 12

= approx 75 .4

3) Arc length = 15cm ......(given)

\( \frac{area \: of \: sector}{total \: area} = \frac{arc \: length}{circumference} \)

\( \frac{area \: of \: sector}{452.4} = \frac{15}{75.4} \)

\(area \: of \: sector \: = \frac{15 \times 452.4}{75.4} \)

\( = \frac{6786}{75.4} \)

\( = 90 {cm}^{2} \)

The true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

The expression is given as:

\(x^{2} -7x + 6\)

Expand;

\(x^{2} -6x - x +6\)

Factorize;

x(x-1) - 6 (x- 1)

Factor out x - 6

(x - 6) (x- 1)

This means that the factors of \(x^{2} -7x + 6\) are x - 1 and x - 6

Hence, the true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

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Answer: Answer is C

Step-by-step explanation:

Answer:

The conversation factor is 16.387604

The parametric equation that represents the same path as the given parametric equation is Option A.

A parametric equation is an equation where the value of x variable given in terms of theta is also expressed in y variable in terms of the same parameter theta.

Given that:

where;

The pair of (x and y) are called parametric equations.

At any given theta (θ), we can substitute it into the equation to determine the value of x and y.

Now, the cartesian form of the parametric equation will help us to determine if the parametric equation are represented in the same path.

The cartesian form is the equation with just x and y whereby the parameter is eliminated.

So, from the given equation;

x = 3 + cos θ

y = 2 sin θ

cos θ = x - 3

sin θ = y/2

We know from trigonometry identity that:

we can eliminate the parameter by saying:

From the given options, Option A represents the same path as the given parametric equation.

This is because:

x = 3 + cos 2 θ

y = 2sin 2 θ

cos 2θ = 3 - x

sin2θ = y/2

Eliminating the parameter, we have:

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