Help! I am on the struggle bus! I dont know if my teacher put in the wrong awnser or what!
I just want to see what you guys come up with!!​

Answer:

M∠2 = 37°

M∠3 = 143°

M∠4 = 37°

Step-by-step explanation:

∠3 is the complete opposite of ∠1

143° + 143° = 286°

there is 360° in a full circle or a repeating angle (aka the scissors)

360°-286°=74°

since ∠2 and ∠4 is opposite of each other

74°÷2=37°

Answer:

\(m \angle 2= \boxed{37}\;^{\circ}\\\\m \angle 3= \boxed{143}\;^{\circ}\\\\m \angle 4= \boxed{37}\;^{\circ}\)

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠1 + m∠2 = 180°

⇒ 143° + m∠2 = 180°

⇒ m∠2 = 37°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

worked them out, hope this helps!

The width, labelled x in the figure is 162.5 meters

From the question, we have the following parameters that can be used in our computation:

Length = 650 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (650 - 2x) * x

Evaluate

A = 650x - 2x²

Differentiate and set to 0

650 - 4x = 0

So, we have

4x = 650

Divide by 4

x = 162.5

Hence, the width is 162.5 meters

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Part 0/5: Yes, it is appropriate to use the normal approximation to find the probability that less than 25% of the individuals in the sample are government employees.

Part 1/5: The probability of less than 25% of the individuals in the sample being government employees is approximately 0.513.

Part 2/5: The probability that more than 20% of workers in the new sample of 100 are government employees is approximately 0.495.

Part 3/5: The probability that the proportion of workers in the sample of 100 who are government employees is between 0.11 and 0.17 is X (the exact value is missing).

Part 4/5: The probability that less than 25% of workers in the sample of 100 are government employees is X (the exact value is missing).

Part 5/5: It would not be unusual if the proportion of government employees in the sample of 100 was greater than 0.23 (choose "would not").

Part 1 of 5 (a):

Yes, it is appropriate to use the normal approximation to find the probability that less than 25% of the individuals in the sample are government employees.

The normal approximation can be used when the sample size is large enough and the conditions for using the normal distribution are met.

In this case, the sample size is 55, which is considered relatively large.

To determine the probability, we need to calculate the mean (µ) and standard deviation (σ) of the binomial distribution, which can be approximated using the normal distribution.

Given that the proportion of government employees in the population is 15%, we can calculate the mean and standard deviation as follows:

\(\mu = n \times p = 55 \times 0.15 = 8.25\)

\(\sigma = \sqrt{(n \times p \times (1 - p))} = \sqrt{(55 \times 0.15 \times 0.85)} \approx 2.844\)

Now, we can use the normal distribution to find the probability. Since we are interested in the probability that less than 25% of the individuals in the sample are government employees, we calculate the z-score and use it to find the corresponding probability from the standard normal distribution table.

z = (x - µ) / σ = (0.25 - 0.15) / 2.844 ≈ 0.035

Using the standard normal distribution table or a statistical calculator, we find that the probability is approximately 0.513.

Therefore, the probability that less than 25% of the individuals in the sample are government employees is approximately 0.513.

Part 2 of 5 (b):

To find the probability that more than 20% of workers in the new sample of 100 are government employees, we follow a similar approach.

First, calculate the mean and standard deviation:

\(\mu = n \times p = 100 \times 0.15 = 15\)

\(\sigma = \sqrt{(n \times p \times (1 - p))} = \sqrt{(100 \times 0.15 \times 0.85)} \approx 3.674\)

Next, calculate the z-score:

z = (x - µ) / σ = (0.20 - 0.15) / 3.674 ≈ 0.014

Using the standard normal distribution table or a statistical calculator, we find the probability corresponding to this z-score.

Since we are interested in the probability of more than 20%, we need to find the complement of the probability.

The complement of the probability is 1 - probability.

Therefore, the probability that more than 20% of workers in the new sample of 100 are government employees is approximately 1 - 0.505 = 0.495.

Part 3 of 5 (c):

To find the probability that the proportion of workers in the sample of 100 who are government employees is between 0.11 and 0.17, we calculate the probabilities for both values separately and subtract the smaller probability from the larger probability.

Using the same mean and standard deviation as in part (b), we can calculate the z-scores for both values:

z1 = (x1 - µ) / σ = (0.11 - 0.15) / 3.674 ≈ -0.011

z2 = (x2 - µ) / σ = (0.17 - 0.15) / 3.674 ≈ 0.011

Using the standard normal distribution table or a statistical calculator, we find the probabilities corresponding to these z-scores.

Let's denote these probabilities as P1 and P2.

The probability that the proportion is between 0.11 and 0.17 is

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The sum of the parts 11/7 and 12/5 of pizza is 139/35.

It is given that the parts of pizza are:

\(1. 11/7\\2. 12/5\\\)

It is required to find sum of the parts of pizza.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.

Calculating the sum of the parts of pizza:

\(=\frac{11}{7}+\frac{12}{5}\)

\(=\frac{139}{35}\)    

Thus, the sum of the parts 11/7 and 12/5 of pizza is 139/35.

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Answer:

slope is 4

y-intercept is -7

x-intercept is 7/4

Answer:

  4.8 m

Step-by-step explanation:

The area of a rectangle is the product of length and width. This relation can be used to find any of the dimensions when the other two are known.

__

Here, we know area and length, so we can find width.

  A = LW

  W = A/L = (29.76 m²)/(6.2 m) = 4.8 m

Mariosol's bedroom is 4.8 meters wide.

Answer:

124

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180:

m<R + m<S + m<T = 180

11x + 3 + x + 15 + 2x + 8 = 180 add like terms

14x + 26 = 180 subtract 26 from both sides

14x = 154 divide both sides by 14

x = 11 to find m<R replace x with 11

11*11 + 3 = 124

Apply angle sum property

\(\\ \rm\rightarrowtail 11x+3+x+15+2x+8=180\)

\(\\ \rm\rightarrowtail 14x+26=180\)

\(\\ \rm\rightarrowtail 14x=154\)

\(\\ \rm\rightarrowtail x=11\)

Answer

I think you meant to wtite

80.4/d = 0.0804

the answer is d = 1000 or 10^3

Step-by-step explanation:

Answer:

619.5cm2

Step-by-step explanation:

Based on what you defined as the parallel sides been 26cm and 33cm and the height been 21cm.

Hence the are of trapezium is half sum of the parallel sides × height.

Expressed mathematically we have:

1/2( 26 +33) × 21 = 1/2 ( 59) × 21 = (59×21)/2= 619.5cm2

The probability that they are the 4 oldest people in the group = 4/9

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

the group of people = 9

you randomly select 4 of them

the probability that they are the 4 oldest people in the group?

According to the formula :

Probability = expected number of outcome/Total number of outcome

If there are group of 9 people, then the total outcome of events will be 9.

If we are to select 4 oldest people from the group, then the expected outcome is 4.

So,

The probability that they are the 4 oldest people in the group = 4/9

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Answer:

52 mph

Step-by-step explanation:

If 88 ft/sec = 60 mph

The 22 ft/ sec is 60/4 = 15 mph

This is so because 88/22 is 4

So we simply proceed to add this to the previous speed in mph

That gives a total of 15 + 37 = 52 mph

Answer:

angle TEA = 58 (which is 29 times 2) degrees

angle TEF = 37 (which is 74 divided by two 2) degrees

Step-by-step explanation:

The angle bisector divides a given angle into two equal parts

Answer:

6 and -8

-6 and 8

Step-by-step explanation:

___· ___ = (-48)

Is the same as:

___· ___ = -48

A positive number multiplied by a negative number has a negative product.

P * N = N

Two positive numbers and two negative numbers have a positive product.

P * P = P

N * N = P

6 and -8  and -6 and 8 would be the correct answers. Again, a positive and a negative number will have a negative product.

6 * -8 = -48

-6 * 8 = -48

Hope this helps.

Answer:

70 degrees

Step-by-step explanation:

The angle opposite x and x itself are vertical angles, meaning that they have the same angle measure. Since the sum of the interior angles of a triangle is 180 degrees:

x+55+55=180

x+110=180

x=180-110=70

Hope this helps!

The required area of Fiona's circle is49π. Option D is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

The radius of Fiona's circle is half of the diameter, which is 14/2 = 7 meters.

The formula for the area of a circle is A = πr², where A is the area and r is the radius.

Substituting the value of the radius in the formula, we get:

A = π(7)² = 49π

So, the area of Fiona's circle is 154 square meters, if we use the value of π as 3.14.

Therefore, the answer is 49.

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The amount of water that flows from the tank during the first 40 minutes is 10,000 liters.

During the first 40 minutes, the rate of water flowing from the tank can be determined by substituting t = 40 into the given equation r(t) = 400 − 8t. This gives us r(40) = 400 − 8(40) = 400 − 320 = 80 liters per minute. To find the total amount of water that flows from the tank during this time period, we need to calculate the integral of r(t) from t = 0 to t = 40.

∫(400 − 8t) dt from 0 to 40 equals ∫(400 − 8t) dt = 400t - 4t^2 evaluated from 0 to 40, which simplifies to (400 * 40 - 4 * 40^2) - (400 * 0 - 4 * 0^2) = 16,000 - 0 = 16,000 liters.

Therefore, the amount of water that flows from the tank during the first 40 minutes is 16,000 liters.

The given equation represents the rate at which water flows from the bottom of the storage tank. By integrating this equation over a specific time interval, we can determine the total amount of water that has flowed during that period. Integration involves finding the antiderivative of the function and evaluating it at the upper and lower limits of the interval.

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Step-by-step explanation:

Using the given formula, we can substitute x = 3 and solve for y:

y = 5 x 2^x

y = 5 x 2^3 (substitute x = 3)

y = 5 x 8

y = 40

Therefore, when x = 3, y = 40.

Answer:

y = 40

Step-by-step explanation:

Plug in 3 for x

\(\bf{y=5\times2^x}\)

\(\bf{y=5\times2^3}\)

Simplify

\(\bf{y=5\times8}\)

Simplify

\(\bf{y=40}\)

Hence, y = 40

The range of books that Kenneth can purchase is from 0 to 3 books, inclusive.

Range: 0 ≤ b ≤ 3 books.

The range of books that Kenneth can purchase with a total of $25, we need to find the maximum number of books he can buy.

Let's denote the number of books Kenneth can buy as "b". Since he will purchase exactly 1 music CD for $10, the remaining amount he can spend on books is $25 - $10 = $15.

Since each book costs $5, we can divide the remaining amount by the cost of a book to find the maximum number of books Kenneth can purchase:

Max number of books = $15 / $5 = 3 books.

Therefore, the range of books that Kenneth can purchase is from 0 to 3 books, inclusive.

Range: 0 ≤ b ≤ 3 books.

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Told to walk in first week = 5km

Told to walk in second week = 8km

Told to walk in third week = 11km

It is forming a pattern,

5km      8km      11km       ..........

     +3       +3        +3

5km      8km     11km     14km     17km     20km    23km     26km   29km     32km

    +3       +3        +3       +3        +3        +3        +3         +3      +3  

The patient has to walk 32km in the 10th week.

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Answer: c

Step-by-step explanation:

The correct answer is option C i.e. all of the options

Question : Why did I choose the answer as option C

Reason : To assure it we'll match all the options with the figure

First of all in the given figure all the sides and angles are equal hence, we can refer it as regular

Secondly, It is convex because all the parts are pointing outwards and inner ones are not more than 180°

Finally, As it has 8 sides it is an octagon

Now, we can see all the three options are matching leaving C which states all of these options, hence C is correct

1) What is Octagon ?

ans :- Octagon is an 8 sided polygon

2) What is a regular polygon ?

ans :- Any polygon which has equal angles and sides is known as a regular polygon.

3) What is convex ?

ans :- A convex is a shape where all the parts points outwards and interior angles are not more than 180°

The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.

Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.

Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.

Substitute x = 3y into the first equation:

11(3y) + 10y = $86

Expanding the first term we get,

33y + 10y = $86

Combining terms,

43y = $86

Dividing both sides by 43 we get,

y = $2

So, Natalie worked y = 2 hours of landscaping.

To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -

x = 3(2) = 6

So Natalie worked x = 6 hours babysitting.

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Answer:

one solution

An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.

Step-by-step explanation:

All the three statements given in the question are valid.

(a) Two real numbers satisfy a^2 < b^2 if and only if |a| < |b|. This is a valid statement, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 < b^2, then taking square roots of both sides yields |a| < |b|.

(b) Two real numbers satisfy a^2 > b^2 if and only if |a| > |b|. This is also a valid statement, and the justification follows from the fact that the square of any non-zero real number is positive, i.e., a^2 > 0 and b^2 > 0, and if a^2 > b^2, then taking square roots of both sides yields |a| > |b|.

(c) Two real numbers satisfy if and only if |a| ≤ |b|. This statement is also valid, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 ≤ b^2, then taking square roots of both sides yields |a| ≤ |b|.

Therefore, all three statements are valid.

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