Could someone help me with this please? :D

The missing terms for the congruent angles are;

Complementary angles

m∠1 + m∠3 = 90°

Transitive property of equality

Subtraction property of equality;

Congruent angles.

Congruent angles are defined as the angles that have equal measure. Therefore, all the angles that have equal measure are called congruent angles.

We are given that;

∠1 and ∠2 are complementary

∠1 and ∠3 are complementary

Now, we are told that m∠1 + m∠2 = 90°. Complementary angles are defined as the 2 angles that sum up to 90 degrees. Thus, ∠1 and ∠2 are complementary by definition.

Similarly, m∠1 + m∠3 = 90°

By the transitive property of equality, we can say that;

m∠1 + m∠2 = m∠1 + m∠3

By the subtraction property of equality;

m∠2 = m∠3

Thus;

∠2 = ∠3 by definition of congruent angles.

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Answer:

149.25

Step-by-step explanation:

Man I did the question and i got it wrong so after the second time of getting it wrong it gave me the answer.

A symbol of inequality can be utilized to exhibit that one of the two variables exists greater than, greater than or equal to, less than, or equal to another value.

The online furniture store can ship not more than 36 pieces of chairs and tables each day.

An inequality in mathematics depicts the relationship between two values in an unbalanced algebraic expression. A sign of inequality can be used to show that one of the two variables is greater than, greater than or equal to, less than, or equal to another value.

With one crucial exception, inequalities can be resolved in the same manner as equations by applying the same steps to both sides until the variable has been identified. You must flip the inequality sign if you multiply or divide by a negative number.

The inequality equation can be written as follows if the number of tables they can ship each day is represented by t and the number of chairs they can ship each day is represented by c.

(c + t) ≤ 36.

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a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Answer:

Top Left: Acute Top Right: Acute Bottom Right: Obtuse Bottom Left: Right

Step-by-step explanation:

The top left and right have all angles less than 90 degrees which makes them acute. The Bottom right has an angle over 90 degrees which makes it obtuse, and the last one has a right angle 90 degrees.

Answer:

8 2-point shots and 4 3-point shots

Step-by-step explanation:

Anthony scored 28 points with 12 baskets. Saying that, (with x-y representing 2 point shots-3 point shots) any combination with a supermajority (at least 75% of) of either shot is out. This leaves just 5 possible combinations. 8-4, 7-5, 6-6, 5-7, and 4-8. Multiply the first number by 2 and the second by 3.

(4 * 2) + (8 * 3) = 8 + 24 = 32 points, so no.

(5 * 2) + (7 * 3) = 10 + 21 = 31 points, so no.

(6 * 2) + (6 * 3) = 12 + 18 = 30 points, so no.

(7 * 2) + (5 * 3) = 14 + 15 = 29 points, so no as well.

(8 * 2) + (4 * 3) = 16 + 12 = 28 points, so this is the combination we're looking for.

Answer:

Step-by-step explanation:

Given: AC is a bisector of ∠BCD

           DC ⊥ AD

           BC ⊥ AB

To prove : BC ≅ Dc

                       Statements                        Reasons

1). AC bisects ∠BCD                       1). Given

2)∠ACB ≅ ∠ACD                           2). AC is a bisector of ∠BCD

3). DC ⊥ AD                                    3). Given

4). m∠ADC = 90°                            4). DC is perpendicular to AD

5). BC ⊥ AB                                     5). Given

6). m∠ABC = 90°                            6). BC is perpendicular to AB

7). ∠ABC ≅ ∠ADC                          7). Right angles are congruent

8). AC ≅ AC                                    8). Reflexive property

9). ΔABC ≅ ΔADC                          9). AL property of congruence

10). BC ≅ DC                                  10). CPCTC

The sample standard deviation is approximately 0.83.

Sample size \(($n$)\) = 36

Population mean \(($\mu$)\) = 50

Population standard deviation \(($\sigma$)\) = 5

The sample standard deviation, denoted as \($s$\) can be estimated using the formula:

\(\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}} \]\)

where:

\($x_i$\) represents the individual data points in the sample

\($\bar{x}$\) is the sample mean

In this case, since we don't have individual data points, we can use the population standard deviation as an estimate for the sample standard deviation when the sample size is relatively large (as in this case \($n = 36$\)). This approximation is known as the standard error of the mean.

Therefore, the sample standard deviation can be approximated as:

\(\[ s \approx \frac{\sigma}{\sqrt{n}} \]\)

Substituting the given values:

\(\[ s \approx \frac{5}{\sqrt{36}} = \frac{5}{6} \] = 0.83\)

Hence, the sample standard deviation is approximately 0.83.

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The area of the parallelogram is given as follows:

421 and 7/8 ft².

The area of a parallelogram is given by the multiplication of the base of the parallelogram by the height of the parallelogram, that is:

A = bh.

The parameters for this problem are given as follows:

Hence the area is given as follows:

A = 45/2 x 75/4

A = 3375/8 ft².

A = 421 and 7/8 ft².

(3375 divided by 8 has a quotient of 7 and a remainder of 8, which is the reason for the mixed number notation).

Hence the second option is the correct option.

The parallelogram is given by the image presented at the end of the answer.

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Answer:

x=0, x=2, x=7

Step-by-step explanation:

The roots of graph are points with y = 0

All normal distributions extend out three standard deviations in both directions from the mean then end: A. True.

The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

In this context, we can infer and logically deduce that it is true that all normal distributions would extend out three (3) standard deviations in both directions from the mean then end.

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D is correct :)

The bunnies are multiplying by 5 each time. The exponent will have the growth be 5 times the product before.

Hope this helps :)

Answer:

the 4th answer is correct

Step-by-step explanation:

although technically, we don't have enough information, it's the only one that it could be.

The probability of getting 2 socks of the same color given by the following solution is 65/132.

Beginning with the first sock, we have three options: blue, white, or grey. If we wanted to know the likelihood of drawing only one blue sock, we might divide the number of blue socks in the drawer by the total number of socks (2 / 12).

We have three options for the second sock: blue, white, or grey. Keep in mind that we are drawing without replacement, so there is now one fewer sock in the drawer. Thus, with three alternatives for the first sock and three options for the second sock, the total number of combinations is three times three, or nine. The following are all of the potential combinations: (blue, blue), (blue, white), (blue, grey), (white, blue), (white, white), (white, grey), (white, blue), (white, white), (white, grey), (grey, blue), (grey, white) (gray, gray).

So the probability of 2 socks of the same color is, in equation form:

P(2 socks of same color) = P(blue sock first) * P(blue sock second) + P(white sock first) * P(white sock second) + P(gray sock first) * P(gray sock second).

= 2/12*1/11 + 4/12*3/11 + 6/12*5/11

= 65/132

Therefore, the probability of getting 2 socks of the same color 65/132.

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Complete question:

Mixed in a drawer are 2 blue​ socks, 4 white​ socks, and 6 gray socks. You pull out two​ socks, one at a​ time, without looking. Find the probability of getting 2 socks of the same color.

Answer:

Answer:

21.9

Step-by-step explanation:

Similarity Theorem

15/13=x/19

1.15384615=x/19

19*1.15384615=x

21.9230769=x

Final Answer

21.9

Proof answer

15/13=21.9/19

1.2= 1.2

Answer:

v = 22.5 miles/hour

Step-by-step explanation:

It is given that,

The speed of Penguins is 33 ft/s.

We need to convert the speed to miles per hour.

We know that, 1 mile = 5280 feet

Speed,

\(v=33\ \dfrac{ft}{s}\\\\=33\times \dfrac{\dfrac{1}{5280}\ \text{miles}}{\dfrac{1}{3600}\ \text{hour}}\\\\=22.5\ \text{miles/hour}\)

So, the speed of the Penguins is 22.5 miles/hour.

The solution is, a)Range

The range is the difference between the highest and the lowest value of a set, so it is sensitive to extreme values. That is, you can have two sets with the same mean, but with very different spacings.

For example, two grades:

set A = {40, 50, 50, 60}

set B = {0, 50, 50, 100}

The set B has a way higher range(100) than set A(20), that is, the range is sensitive to extreme values.

So the correct answer is:

a)Range

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Answer:

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56

Prime Factorization of 56: 56 = 23 × 7

Step-by-step explanation:

Okay, it seems like you want to analyze a sample of 16 babies based on their weight.

The information you provided states that the Center for Disease Control and Prevention reports that 25% of baby boys aged 6-8 months in the United States weigh more than 20 pounds.

However, you haven't mentioned the specific question or analysis you want to perform on the sample. Could you please clarify what you would like to know or do with the given information?

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Answer:

have calculated all the numbers that 2838 is evenly divisible by. The numbers that 2838 is divisible by are 1, 2, 3, 6, 11, 22, 33, 43, 66, 86, 129, 258, 473, 946, 1419, and 2838. You may also be interested to know that all the numbers that 2838 is divisible by are also known as the factors of 2838.

Answer:

See below.

Step-by-step explanation:

So first, we can separate the entire figure into a semi-circle and an isosceles triangle.

AREA:

The area for a semi-circle is \(\frac{1}{2}\pi r^2\).

The diameter is 8cm, so the radius is 4cm.

Area of the semi-circle is:

\(\frac{1}{2}(4)^2\pi=\frac{1}{2}(16\pi)=8\pi cm^2\)

The area for a triangle is \(\frac{1}{2}bh\).

The base is the same as the diameter (8), and we are given the height as 10. Thus:

\(\frac{1}{2} (8)(10)=8(5)=40cm^2\)

The total area is \((8\pi +40 )cm^2\)

PERIMETER:

The perimeter of a semicircle is: \(\pi r + 2r\) (this is derived from dividing the circumference by 2 and then adding on the diameter).

Thus, the perimeter is:

\(4\pi +8\)

However, we ignore the 8 since the 8 is not part of the perimeter.

The perimeter of the triangle is the two slant lengths. We know the base and the height, so we can use the Pythagorean Theorem:

\(a^2+b^2=c^2\)

\(4^2+10^2=c^2\)

\(c^2=116\)

\(c=\sqrt{116}=2\sqrt{29\)

Two of them will be \(4\sqrt{29}\)

Thus, the total perimeter is \(4\pi + 4\sqrt{29}\)

If one member of the swim team is chosen randomly, the probability that the chosen member is a novice swimmer is 0.1867 or 18.67%.

To find the probability that the chosen swim team member is a novice swimmer, we need to first find out how many members of the swim team are novice swimmers.

We know that there are 150 total members on the swim team, 75 of whom are advanced swimmers and 47 of whom are intermediate swimmers. Therefore, the number of novice swimmers can be found by subtracting the number of advanced and intermediate swimmers from the total number of members:

Novice swimmers = Total members - Advanced swimmers - Intermediate swimmers

Novice swimmers = 150 - 75 - 47

Novice swimmers = 28

So, there are 28 novice swimmers on the team.

Now we can find the probability that the chosen swim team member is a novice swimmer by dividing the number of novice swimmers by the total number of members on the team:

Probability of choosing a novice swimmer = Number of novice swimmers / Total number of members

Probability of choosing a novice swimmer = 28 / 150

Probability of choosing a novice swimmer = 0.1867 or 18.67%

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Answer:

4-5i

Step-by-step explanation:

Answer:

4-5i

Step-by-step explanation:

(5-2i)-(1+3i)

5-2i-1-3i

5-1-2i-3i

4-5i

The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.

Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.

So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:

(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons

Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be  approximately 6.58 gallons.

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The complete question is :

What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?

A) we would send Order A to Factory 3.

B) we would send both Order B and Order C to Factory 3.

B 7,000 Factory 3

C 30,000 Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

To make decisions about which factory to send the orders to on Monday and Tuesday, we need to compare the costs per unit for each factory and consider the total number of units to be produced. Let's go through each day's scenario and make the production decisions.

a) Monday: Order A for 15,000 units

To decide which factory to send the order to, we compare the costs per unit for each factory. We select the factory with the lowest cost per unit to minimize the average cost per unit for the company.

Let's assume the costs per unit for each factory are as follows:

Factory 1: $10 per unit

Factory 2: $12 per unit

Factory 3: $9 per unit

To calculate the total cost for each factory, we multiply the cost per unit by the number of units:

Factory 1: $10 * 15,000 = $150,000

Factory 2: $12 * 15,000 = $180,000

Factory 3: $9 * 15,000 = $135,000

Based on the calculations, Factory 3 has the lowest total cost for producing 15,000 units, with a total cost of $135,000. Therefore, we would send Order A to Factory 3.

b) Tuesday: Order B for 7,000 units and Order C for 30,000 units

We have two options: sending each order to a separate factory or sending both orders to the same factory. We need to compare the average cost per unit for each option and select the one that results in the lowest average cost per unit.

Let's assume the costs per unit for each factory remain the same as in the previous example. We will calculate the average cost per unit for each option:

Option 1: Sending orders to separate factories

For Order B (7,000 units):

Average cost per unit = ($10 * 7,000) / 7,000 = $10

For Order C (30,000 units):

Average cost per unit = ($9 * 30,000) / 30,000 = $9

Total number of units produced for the company today = 7,000 + 30,000 = 37,000

Average cost per unit for all production today = ($10 * 7,000 + $9 * 30,000) / 37,000 = $9.43 (rounded to two decimal places)

Option 2: Sending both orders to the same factory (Factory 3)

For Orders B and C (37,000 units):

Average cost per unit = ($9 * 37,000) / 37,000 = $9

Comparing the two options, we see that both options have the same average cost per unit of $9. However, sending both orders to Factory 3 simplifies the production process by consolidating the orders in one factory. Therefore, we would send both Order B and Order C to Factory 3.

Production Report for Tuesday:

Order # of Units Factory

B   7,000      Factory 3

C  30,000    Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

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Answer:

725.51

Step-by-step explanation:

The required value of y for the unit circle is: 2/3

The circle is defined as 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 coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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