In the given figure, △ADE ∼ △ABC. Which triangle similarity theorem justifies
this similarity? Show proof toyour answer.

a. Using the figure below, name the three similar triangles.

b. Write the proportions that exist among corresponding parts of similar

\(\\ \sf\longmapsto f(2+h)\)

\(\\ \sf\longmapsto 4(2+h)-3\)

\(\\ \sf\longmapsto 4h+8-3\)

\(\\ \sf\longmapsto 4h+5\)

The labor force is the sum of those with full-time and part-time jobs, while the participation rate is the percentage of the labor force in relation to the adult population. Finally, the employment rate represents the percentage of the labor force that is employed.

(a) To calculate the adult or working age population (16 and older), we subtract the number of children under 16 (15) and retirees (10) from the total population of 100. Therefore, the adult or working age population is 100 - 15 - 10 = 75.

(b) The out-of-labor force refers to individuals who are not working or actively seeking employment. In this case, it includes full-time homemakers (10) and full-time students over age 16 (5). Thus, the out-of-labor force is 10 + 5 = 15.

(c) The labor force consists of those with full-time jobs (30) and part-time jobs (12). Therefore, the labor force is 30 + 12 = 42.

(d) The participation rate is calculated by dividing the labor force (42) by the adult or working age population (75) and multiplying by 100. The participation rate is (42 / 75) * 100 = 56%.

(e) The employment rate is calculated by dividing the number of employed individuals (full-time and part-time) in the labor force (42) by the labor force and multiplying by 100. The employment rate is (42 / 42) * 100 = 100%.

Learn more about percentage here:

https://brainly.com/question/30348137

#SPJ11

Answer:

Scalene, isosceles,

Step-by-step explanation:

Answer:

1,000

Step-by-step explanation:

The probability that at least one of them is not wearing a seatbelt is 0.5021.

Potential is described by probability. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of events. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

These concepts now have an axiomatic mathematical formalization thanks to probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, and philosophy.

Let X be the proportion of drivers who do not use a seat belt. It has a binomial distribution, as shown by,

n=4, p=1-0.84

p=0.16

The likelihood that at least one of them is not wearing seatbelt is:

P(X≥1)=1-P(X<1)

=1-P(X=0)

=1-{(4₀)(0.16)⁰(1-0.16)⁴⁻⁰

=1-0.4979

=0.5021.

Therefore, the probability that at least one of them is not wearing a seatbelt is 0.5021.

To know more about probability, visit:

https://brainly.com/question/15124899

#SPJ1

Answer:

a. $25

b. $2025

Explanation:

The profit the club makes is

profit = number of customers x amount charged per customer

Now, we are told that if we increase the price by $1, we will lose one customer.

Therefore, if we increase the price by $p then the number of customers we will have is

remaining customers = 70 customers - p = 70 - p

and the amount charged will become

amount charged per customer = 20 + p

Therefore, the profit will be

profit = ( 70 - p) ( 20 + p)

Now, the question is, for what value of p is the profit maximum?

Note that the equation for profit is a parabola (more precisely, a concave down parabola). Therefore, the vertex of the parabola gives the value of the maximum profit.

The parabola (70 - p)(20 + p) is graphed below.

As can be seen, the vertex of the parabola is at (25, 2025). This means that for p = 25, the profit is maximum.

In other words, if the club increases its price by $25, it will earn the maximum profit.

This maximum profit will be $2025.

Hence, to summarise.

a. $25

b. $2025

Answer:

√72=2⋅3√2

Step-by-step explanation:

Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

To know more about  logical reasoning refer here:

https://brainly.com/question/32269377?#

#SPJ11

The constant of  proportionality is 5 for the relation between x and y.

What is proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of the constant.

Given table is

x(days)         5    10   15   20

y(swings)      1      2     3    4

Since y is increasing with increase of days(x).

Thus the relation between y and x is in direct proportional.

Assume the relation be x ∝ y

x = ky, where k is constant proportionality.

Putting x = 5 and y = 1:

5 = k × 1

k = 5

Putting x = 10 and y = 2:

10 = k × 2

k = 5

To learn more about constant of proportionality, click on below link:

https://brainly.com/question/11205743

#SPJ1

Answer:

1/4

Step-by-step explanation:

Mrs. Lincoln has 15 girls and 10 boys in her homeroom. She randomly selects two students. The total number of students is 25.

The probability of choosing one girl is:

15 / 25 = 3 / 5

Now, 24 students are left.

The probability of choosing one boy is:

10 / 24 = 5 / 12

Therefore, the probability of choosing one girl and one boy is:

3 / 5 * 5 / 12

= 3 / 12

= 1/4

Answer:

676

Step-by-step explanation:

d1×d2/2

42×56/2

1352/2=676

please check it by doing again

Answer:

1176

Step-by-step explanation:

=a half the product of its diagonals

=1/2(42x56)

=1176

Could you please check the other question you put? Thanks!

Answer:

slope -intercept form

y = -328.275 x + 3142.15

Step-by-step explanation:

Step(i):-

Given that the points are (2, 2485.6) and (6,1172.5)

The slope of the line

               \(m = \frac{y_{2}- y_{1} }{x_{2}-x_{1} }\)

              \(m = \frac{1172.5-2485.6 }{6-2 }\)

            \(m = - 328.275\)

Step(ii):-

Equation of the straight line passing through the Point (2,2485.6)

\(y - y_{1} = m(x-x_{1} )\)

y - 2485.6 = (-328.275)(x-2)

y - 2485.6 = -328.275x+656.55

  y =  -328.275x+656.55 + 2485.6

y = -328.275 x + 3142.15

Final answer:-

slope -intercept form

y = -328.275 x + 3142.15

Answer:

hdhdhdhdhdhejnnxnhhhhhhhvwvavzvzvzvvz hhdhshs. eieiueudhd. ei

SOLVING

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

well  basically, the equation's already solved for t, almost, but we just need to subtract m from both sides:

T+m=R,

T=R-m

Here, it's solved for t.

Learn more;work harder

#Carryonlearning

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

Answer:

y- intercept = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

\(\frac{x}{3}\) + \(\frac{y}{2}\) = 1

Multiply through by 6 to clear the fractions

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide all terms by 3 )

y = - \(\frac{2}{3}\) x + 2 ← in slope- intercept form

with y- intercept c = 2

The probability that the number of sales is 2 or 3 is 0.50" is TRUE.

Sales (x) --> Probability (P(x))
0 --> 0.10
1 --> 0.15
2 --> 0.20
3 --> 0.30
4 --> 0.20
5 --> 0.05

To determine if the probability of making 2 or 3 sales is 0.50, we need to add the probabilities for 2 and 3 sales:

P(2 or 3) = P(2) + P(3) = 0.20 + 0.30 = 0.50

Since the sum of the probabilities for 2 and 3 sales is 0.50, the statement "Given this distribution,

the probability that the number of sales is 2 or 3 is 0.50" is TRUE.

To know more about Probability refer here:

https://brainly.com/question/30034780

#SPJ11

The definite integral of 0.2 * x^5 from 0 to 1, approximated to six decimal places using a power series, is 0.033333.

The definite integral of 0.2 * x^5 from 0 to 1 using a power series with an accuracy of six decimal places. To do this, we can use the power series representation of the integrand and then integrate term by term.

1. Find the power series representation of the integrand:
The integrand is a polynomial, 0.2 * x^5, so its power series representation is simply itself.

2. Integrate term by term:
Now, we integrate the power series term by term. In this case, we have only one term, which is 0.2 * x^5.
∫(0.2 * x^5) dx = (0.2/6) * x^6 + C = (1/30) * x^6 + C

3. Evaluate the definite integral:
Now, we can find the definite integral by evaluating the antiderivative at the given limits (0 and 1):
i = [(1/30) * (1^6)] - [(1/30) * (0^6)] = (1/30)

4. Convert to a decimal:
i ≈ 0.033333

Thus, the definite integral of 0.2 * x^5 from 0 to 1, approximated to six decimal places using a power series, is 0.033333.

To know more about integral refer to

https://brainly.com/question/18125359

#SPJ11

Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.

To find the rejected masses:

Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.

Know more about the range here:

https://brainly.com/question/26098895

#SPJ4

The correct question is given below:

A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?

Answer:

CCCC

Step-by-step explanation:

Answer:

.78q = 58

q = 74.4 = 74 questions

The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

For more questions like Minor axis click the link below:

https://brainly.com/question/29054958

#SPJ4

Answer: The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter of the wheels is 28 inches, so the circumference of each wheel is:

C = π(28) = 28π inches

To find how many revolutions the wheels need to make to travel 200 feet, we need to convert 200 feet to inches, and then divide by the circumference of each wheel. There are 12 inches in 1 foot, so 200 feet is equal to:

200 feet × 12 inches/foot = 2400 inches

Dividing 2400 inches by the circumference of each wheel, we get:

2400 inches ÷ (28π inches/revolution) ≈ 85.3 revolutions

Therefore, the car's wheels need to make approximately 85.3 full revolutions to travel 200 feet. Since the question asks for the number of full revolutions, we can round down to the nearest whole number to get:

Answer: D. 88 revolutions.

Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ1

Answer:

c or the third one

Step-by-step explanation:

when you flip one side over to the other it will look exactly alike which means it is symetricall so it cant be a or because it wont work like that

Answer:

C

Step-by-step explanation:

Think of the shapes as pieces of paper. If you fold them over the line, none of the others will be a perfect fit, and will have bits hanging over

The 95% confidence interval for the proportion of the population who prefer brand named items is:

CI = (0.102, 0.232)

What is confidence interval?

A confidence interval is a statistical tool used to estimate the range of possible values in which a population parameter, such as the mean or proportion, is expected to lie with a certain level of confidence based on the observed sample data.

To find the 95% confidence interval for the population proportion, we use the formula:

CI = p′ ± z*\(\sqrt{(p'q'/n)\)

where:

CI: confidence interval

p′: sample proportion

q′: 1 - p′

z: z-score from the standard normal distribution for the desired confidence level (95% in this case)

n: sample size

Substituting the given values, we get:

CI = 0.167 ± 1.96\(\sqrt{((0.1670.833)/180)\)

Simplifying, we get:

CI = 0.167 ± 0.065

Therefore, the 95% confidence interval for the proportion of the population who prefer brand named items is:

CI = (0.102, 0.232)

This means that we can be 95% confident that the true population proportion of people who prefer brand named items falls within this range.

To learn more about confidence interval visit:

https://brainly.com/question/15712887

#SPJ4

The cross section of a V-thread on a screw is an equilateral triangle. The distance p between successive threads is known as the PITCH of the thread, and the distance d is the DEPTH of the thread is 0.07.

To solve this problem, we can use the formula for the height of an equilateral triangle: h = √3/2 x s, where s is the length of one side (or the pitch, in this case).

Since the cross section of the V-thread is an equilateral triangle, the pitch (p) is equal to the length of one side of the triangle.

Therefore, s = p = 1/8. To find the depth (d) of the thread, we need to find the height (h) of the equilateral triangle. We know that the height is also equal to the distance from the top of one thread to the bottom of the next thread (i.e., the depth).

So: h = √3/2 x s h = √3/2 x 1/8 h = 0.0722 (rounded to nearest thousandth) Therefore, the depth of the thread (d) is approximately 0.07 (rounded to nearest hundredth).

Visit here to learn more about equilateral triangle:

brainly.com/question/17264112

#SPJ11

Answer:

A) 1/5>-1/5

Step-by-step explanation:

Answer:

Only n if 2n is/3 when 2nis divide by 3

Answer:3

Step-by-step explanation:

you could only divide 2n in 3 was there so it would be three