A = 55°55, c = 16
Solve the triangle as described

From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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There are 1,602,562,500 different passwords that can be made up using the given pattern and character choices.

We need to make a password with eight characters, where the first seven characters follow the pattern CVCVCVC, and the eighth character is a digit. There are 21 consonants and 5 vowels available, and there are 10 digits (0-9) available for the eighth character.

To find the number of possible passwords, we can count the number of choices for each character in the password, and then multiply the choices together.

For the first character, we can choose from 21 consonants. For the second character, we can choose from 5 vowels. For the third character, we can choose from 21 consonants again, and so on, alternating between consonants and vowels. For the eighth character, we can choose from 10 digits.

Therefore, the total number of possible passwords is:

21 x 5 x 21 x 5 x 21 x 5 x 21 x 10 = 1,602,562,500

So there are 1,602,562,500 different passwords that can be made up using the given pattern and character choices.

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Answer:

The age of the youngest child = x = 6 years

The age of middle child = y = 8 years

The age of the oldest child = z = 12 years

Step-by-step explanation:

Let us represent:

The age of the youngest child = x

The age of middle child = y

The age of the oldest child = z

The sum of the ages of the children is 26.

Hence: x + y + z = 26...... Equation 1

The oldest is 4 years older than the middle

z = 4 + y

The youngest child is 2 years younger than the middle child

x = y - 2

Hence, we substitute 4 + y for z and y - 2 for x in Equation 1

x + y + z = 26...... Equation 1

y - 2 + y + 4 + y = 26

y + y + y -2 +4 = 26

3y + 2 = 26

Subtract 2 from both sides

3y + 2 - 2 = 26 - 2

3y = 26 - 2

3y = 24

y = 24/3

y = 8

Solving for x

x = y - 2

x = 8 - 2

x = 6

Solving for z

z = 4 + y

z = 4 + 8

z = 12

Therefore:

The age of the youngest child = x = 6 years

The age of middle child = y = 8 years

The age of the oldest child = z = 12 years

Answer:

D.4

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis. This line crosses the y-axis at 4, or the point (0,4) so the y-intercept would be 4.

Answer:

the answer is x=1 (it wont let me post without 20 letter so this is just letters)

Answer: x = -1

Step-by-step explanation:

−2(4−4x)+2=2

\(2\left(4-4x\right)+2-2=2-2\\\\-2\left(4-4x\right)=0\\\\\frac{-2\left(4-4x\right)}{-2}=\frac{0}{-2}\\\\4-4x=0\\\\-4x=-4\\\\x = -1\)

Answer: x=3 ; y=13

Step-by-step explanation:

1. isolate y from equation to substitute into the second equation

y= 16-x ---> (16-x) = 3x+4

2. move to one side and solve for x

4x=12 --> x=3

3. plug in x value to solve for y

3+y=16 or 3(3)+4

y=13

Answer:

all are functions

Step-by-step explanation:

a function is when each x has a y

a relation is when 1 x has more than 1 y which makes it invalid therefore not a function

Answer:

please can u send me this question again

because I did not understood this question

To determine the maximum and minimum of a function, you need to find the critical points and endpoints, evaluate the function at these points, and compare the values.

The highest value represents the maximum, while the lowest value represents the minimum.

To determine the maximum and minimum of a function, follow these steps:

Find the critical points of the function by finding where its derivative equals zero or is undefined.

Determine the endpoints of the interval you are considering, if applicable.

Analyze the function at its starting and ending locations.

The highest value represents the maximum, and the lowest value represents the minimum.

Let's consider an example using the function f(x) = x^2 - 4x + 3 over the interval [0, 5].

Find the critical points:

Take the derivative of the function: f'(x) = 2x - 4.

Set the derivative equal to zero: 2x - 4 = 0.

Solve for x: 2x = 4,

x = 2.

The critical point is x = 2.

Determine the endpoints:

In this case, the endpoints of the interval are x = 0 and x = 5.

Evaluate the function:

Calculate f(0) = (0)^2 - 4(0) + 3

= 3.

Calculate f(2) = (2)^2 - 4(2) + 3

= -1.

Calculate f(5) = (5)^2 - 4(5) + 3

= -7.

Determine the maximum and minimum:

The highest value is 3, which occurs at x = 0. Therefore, the maximum value is 3.

The lowest value is -7, which occurs at x = 5. Therefore, the minimum value is -7.

To determine the maximum and minimum of a function, you need to find the critical points and endpoints, evaluate the function at these points, and compare the values. The highest value represents the maximum, while the lowest value represents the minimum. It is important to consider the given interval to ensure that the maximum and minimum values are within the specified range.

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Answer:

D

Step-by-step explanation:

ALL OF THE ABOVE they were selling weapons and most Americans were isolationist

(a) The series you're referring to is:
Σ [9801 - 3964n / (n!)] from n=0 to infinity
To show that this series converges, we can use the Ratio Test. The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1, the series converges.
For this series, the ratio of consecutive terms is:
|(9801 - 3964(n+1)) / ((n+1)!) / (9801 - 3964n) / (n!)|
As n approaches infinity, this ratio approaches 0, since the factorial function (n!) grows much faster than the linear function (3964n). Since the limit is 0, which is less than 1, the series converges according to the Ratio Test.

(b) To find the partial sums S3 and S5, you can use the series definition and calculate the first few terms:
S3 = Σ [9801 - 3964n / (n!)] from n=0 to 3
S5 = Σ [9801 - 3964n / (n!)] from n=0 to 5
Using a calculator, you can find the values for S3 and S5:
S3 ≈ 3.141417
S5 ≈ 3.141592653
As you can see, the first 3 digits of S3 and the first 9 digits of S5 match the digits of π. The series converges to π, and as more terms are added, the partial sums approach π more accurately.

(a) To show that the series 9801 - 3964n (n!) converges, we can use the ratio test.
The ratio of consecutive terms is:
|(9801 - 3964(n+1))(n+1)!| / |(9801 - 3964n)(n!)|
= (9801 - 3964n - 3964)(n+1) / (9801 - 3964n)
= (5837 - 3964n)(n+1) / (9801 - 3964n)

As n approaches infinity, this ratio approaches 1/4.
Since the ratio is less than 1 for all n, the series converges.

(b) The partial sums for this series are Sk = 9801 - 3964n (n!).
Using a calculator, we can evaluate S5 to be:
S5 = 9801 - 3964(1)(1!) - 3964(2)(2!) - 3964(3)(3!) - 3964(4)(4!) - 3964(5)(5!)
S5 = 9801 - 3964 - 47520 - 317520 - 1330560 - 4306080
S5 ≈ -1.738 x 10^6
This approximation is not very accurate because the terms in the series are very large and quickly become negative.

To find as many digits as possible, we can use a computer program or calculator with a high-precision setting.
Assuming we use a calculator with 10 digits of precision, we can find S8 to be:
S8 = 9801 - 3964(1)(1!) - 3964(2)(2!) - 3964(3)(3!) - 3964(4)(4!) - 3964(5)(5!) - 3964(6)(6!) - 3964(7)(7!) - 3964(8)(8!)
S8 = 9801 - 3964 - 47520 - 317520 - 1330560 - 4306080 - 11243840 - 25401600 - 51081024
S8 = 3.141592654

This value has 10 digits, which is the same as the first 10 digits of the number π (3.1415926535).

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Answer:

m is the slope of the line

b is the y-intercept

Step-by-step explanation:

We are given the form of a linear equation in slope intercept form as;

y = mx + b

Now, the meaning of each term of the equation is;

m is the slope of the line

b is the y-intercept

Answer:

m = -9.4

Step-by-step explanation:

Distribute -5 to m and 4.

You should have -5m-20=27

Add 20 to both sides.

You should end with -5m=47

Divide both sides by -5.

You should get m= -9.4

Hope this helped :)

The rate of consumption of fuel of Matt's car is 37 miles per gallon (mpg).

Matt's car can travel a total distance of 555 miles.
The fuel required to travel the total distance is 15 gallons by Matt's car.
Hence the rate of consumption of fuel of Matt's car can be measured in mpg (miles per gallons) as = Total distance travelled / Total gallons required to travel that distance
(that is, total distance travelled divided by the total amount of gallons to travel the same)
Thus the mpg of Matt's car is = 555 miles / 15 gallons
= 37 miles per gallon
(that is 37 mpg)

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Answer: Yes

Step-by-step explanation:

\(\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5\).

Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.

The equation of a parabola with a focus at (-2,-3) and a directrix at y = -5  is y =  1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)

What is Parabola?

A parabola is the location of a moving point whose distance from a given focus point and directrix line, respectively, is always constant.

let's keep it simple: (x, y). Focus is on (7,5)

When the separation from focus is

\(\sqrt{(x - (-2)^{2}) + (y - (-3)^{2} ) }\) . Its distance from directrix y = -5 i.e.

y + 5 = |y + 5|^2

Hence, equation of parabola:

(x - (-2))^2 + (y - (-3))^2 = |y + 5|^2

or, (x + 2)^2 + (y + 3)^2 = |y + 5|^2

x^2 + 4x + 4 + y^2 + 3y + 9 = y^2 + 10y + 25

or, x^2 + 4x + 13 + y^2 + 3y = y^2 + 10y + 25

x^2 + 4x - 12 = 7y

y = (x^2 + 4x - 12)/7

y = 1/7(x^2 + 4x +4 - 4) - 12/7

y = 1/7(x + 2)^2 - 12-4/7

y =  1/7(x + 2)^2 - 8/7

Hence, parabola's equation is y =  1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)

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Answer:

f(6)=42

Step-by-step explanation:

We know that the equaiton is f(x)=2x+3(x+4). So that means when it is f(6), we plug in 6 into all of the x. Therefore, the equation will be f(6)=2(6)+3(6+4). We combine like terms to get f(6)=12+3(10). We do 3x10 which is equal to 30. f(6)=30+12. 30+12=42. f(6)=42. Therefore, f(6)=42.

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Answer: 47

Step-by-step explanation:

That just means replace the x’s with 6 in the equation. So 2*6+3(6+4)+5. 6+4 is 10, 2*6 is 12. So the equation is now 12+3(10)+5. 3*10 is 30. 12+30+5=47.

Answer:

Each sandwich cost 8:50

Step-by-step explanation:

total 30$

total price of the waters 4:50

30-4:50=25:50

25:50÷3=8:50

Step-by-step explanation:

3 root 3 + 6 root 3 + 7/ root 3

= (27 +7)/ root 3

= 34 root 3 / 3

Answer:

A.

Step-by-step explanation:

D: there is no square root

for both C and B there is no decimal.

A should end up being y=-8x+5 which is in y=mx+b form

Answer:

A. -1008

Step-by-step explanation:

9x-4=-36

-36x-4=-144

-144x-7=-1008

Answer:

just go on playstore and search for photomath

Answer: m=-8

Step-by-step explanation:

Alright so take m over to the other side and the equation becomes:

-x^2 + 8x + 0 = -m

then use the quadratic formula to find out the 2 values for -m

those are: 8, 0

0 cant be it because it will give us 8 and 0, 0 cant be identified as a positive value so we are only left with 8 to choose.

8 = -m

m= -8

Answer:

\(m=-16\)

Step-by-step explanation:

\(-x^{2} +8x+m=0\)

Reverse the signs:

\(x^{2} -8x-m=0\)

if m = -16

\(x^{2} -8x-(-16)=0\\x^{2} -8x+16=0\)

Factoring:

\((x-4)(x-4)=0\)

When the factors are cleared, we are left with two positive roots (+4)

Hope this helps.

Answer:

Step-by-step explanation:

The answer is 7   1/3

The value of x are

1. x = 9

2. x = 16.64

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c² = a² +b²

Since the radius meet the tangent of the circle, the angle formed is 90°. Therefore ;

a. x² + 12² = (x+6)²

x²+144 = x²+12x +36

12x = 144-36

12x = 108

x = 9

b. x² = 14² + 9²

x² = 196 + 81

x² = 277

x = √ 277

x = 16.64

therefore the value of x is 16.64

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The amount of energy it takes to run a race is most likely to be a function of the; D: Length of the Race

We want to basically find the factor that influences the amount of energy expended by a sprinter.

Now, formula for potential energy is;

P = mgd

where;

m is mass

g is acceleration due to gravity

d is distance covered

Now, the only option that falls into the input that affects energy expended is the distance covered. This is true because the more the distance covered, the higher the energy expended.

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It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

if the bottle holds 3 cups pf water, and it was only one cup left, she drank

3-1=2 cups of water

Answer:

$108

Step-by-step explanation:

3X9= 27square foot. Then you multiply 27 by 4, which equals $108

Answer:

5

Step-by-step explanation:

The range is the highest value number minus the lowest value number. 9 minus 4 is 5.