you are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. you conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each meal, asking that they simply check off that the meal was either satisfactory or unsatisfactory. for simplicity in this problem, assume that the response was 1,000 returned questionnaires from the 1,200 meals each day. the results are as follows:

Answer:

x = 40 in

Step-by-step explanation:

the missing angle in the triangle on the left is

180° - (74 + 51)° = 180° - 125° = 55°

the missing angle in the triangle on the right is

180° - (74 + 55)° = 180° - 129° = 51°

the 2 triangles have 3 pairs of congruent angles and are therefore congruent.

Corresponding sides and angles are then congruent

consider the corresponding sides opposite 74° , that is x and 40 in , so

x = 40 in

Answer: c

Step-by-step explanation:

A is 190 divided by 125

B is 190 multiplied with 125 (product of the two numbers)

D is the sum of 190 and 125 (addition)

the difference will be found by subtracting the smaller number from the bigger number

The length of the diagonal AB of the cube is 8.7 cm.

Length of a face diagonal of cube = √2a, where a = Length of each side of a cube.

Length of body diagonal of a cube = √3a, where a = Length of each side of a cube.

Given:

Side length of the cube(a) = 5 cm

We have to find the length of the diagonal AB which is a body diagonal.

Length of Body diagonal(AB) = √3a

Substituting the given value in the formula,

Length of the body diagonal of cube = √3a

⇒ √3a ⇒√3 × 5 = 8.7 cm

Therefore, the length of AB i.e. the body diagonal of the cube is 8.7 cm.

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The equation of the line that has a slope of 7 and passes through the point (4, -2) is: y = 7x - 30.

If we are given a point on a line (x, y), and we know the slope (m) of the line, we can expressed the equation of the line in slope-intercept form as y = mx + b.

Given the following:

Slope of the line, m = 7

A point on the line = (4, -2).

Find the value of b by substituting x = 4, y = -2, and m = 7 into y = mx + b:

-2 = 7(4) + b

-2 = 28 + b

-2 - 28 = 28 + b - 28 [subtraction property of equality]

-30 = b

b = -30

To write the equation of the line, substitute m = 7 and b = -30 into y = mx + b:

y = 7x + (-30)

y = 7x - 30

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Answer:

x = 0, y = - 4

Step-by-step explanation:

7x + 3y = - 12 → (1)

2x - 5y = 20 → (2)

multiplying (1) by 5 and (2) by 3 and adding will eliminate y

35x + 15y = - 60 → (3)

6x - 15y = 60 → (4)

add (3) and (4) term by term to eliminate y

41x + 0 = 0

41x = 0 ⇒ x = 0

substitute x = 0 into either of the 2 equations and solve for y

substituting into (2)

2(0) - 5y = 20

0 - 5y = 20

- 5y = 20 ( divide both sides by - 5 )

y = - 4

∠GML ≅ ∠HMJ by the Vertical Angles Congruence Theorem.

∠GMH ≅ ∠LMJ by the Vertical Angles Congruence Theorem.

∠GMK ≅ ∠JMK by the Right Angles Congruence Theorem. They form a linear pair which means they are supplementary by the Linear pair Postulate and because one is a right angle so is the other by the Subtraction Property of Equality.

According to the congruence theorem of vertical angles or angles that are vertically opposing, two opposing vertical angles that are created when two lines intersect one other are always equal.

So from the figure, we can determine the vertically opposite angles,

∠GML ≅ ∠HMJ

Similarly, ∠GMH ≅ ∠LMJ

The angles ∠GMK and ∠JMK form a linear pair and are supplementary by the linear pair postulate which states that the two angles in the linear pair add up to 180°.

We know that all right angles are congruent from the Right Angle Congruence Theorem.

Hence,∠GMK ≅ ∠JMK

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Square root 12+Square root 6/Square root 3+1. After Rationalize the denominator we got 4.68.

Given that,

Square root 12+Square root 6/Square root 3+1

​We have to Rationalize the denominator.

If the denominator's radical is a square root, multiply by a square root that, when multiplied by the denominator, produces a perfect square beneath the radical.

The square root of a number is the element that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents.

[tex]\sqrt{12}+\sqrt{6} /\sqrt{3+1}[/tex]

Square root of [tex]\sqrt{12} is 2\sqrt{3}[/tex]

[tex]2\sqrt{3}+\sqrt{6}/\sqrt{4}[/tex]

Square root of [tex]\sqrt{4} is 2[/tex]

[tex]2\sqrt{3}+\sqrt{6}/2[/tex]

Calculating the terms

3.46+2.44/2

3.46+1.22

4.68

Therefore, After Rationalize the denominator we got 4.68.

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By using percentage, the deductible amount is $103.73 for each paycheck. So, option b is correct.

We are provided by some percentage here. A percentage is a part of a whole that is expressed in hundredths.

Sally paid 38% of her annual health insurance premium of $4,350.00 and left with the 62%.

62% of $4,350.00 is equal to $2697

      62/100 x 4,350.00 = 2697

So, the net amount that Sally has to pay is $2697 in equal distribution from her 26 paychecks throughout the calendar year.

Therefore, each paycheck will be deducted as = $2697/26

                                                                        = $103.73

Hence, $103.73 will be deducted from her paycheck.

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Answer:

Rotate AEFB 180 degrees counterclockwise around point G

Rotate AEFB 180 degrees clockwise around point G

Translate AEFB by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.    

Step-by-step explanation:

Answer: If you had a fraction, you would have to turn into a decimal, then a percent. You can turn a decimal into a percent by multiplying the decimal by 100 and adding the percent sign. Hopefully this helps!

Answer: Like so:

30 percent of 50...

30/100= 0.30 (percentage)

0.30*50= 15 (discount, deducted amount, etc...)

Subtract answer from original number:

50-15= 35

30% of 50= 15

New amount= 35

It will take 18 minutes to run 3 miles. For 7 miles, it will take him 42 minutes.

The unitary method is an approach for issue that involves first calculating the value of a single unit, then multiplying that value to find the required value. a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its linear algebra, mathematical study of a matrix or operator,

Given Data

Charlie can run 4 miles in 28 minutes.

To run 1 mile,

4 miles = 28 minutes

1 mile - 6 minutes

For 3 miles,

3 miles = 3(6)

3 miles = 18 minutes

It will take 18 minutes to run 3 miles.

For 7 miles,

7 miles = 7(6)

7 miles = 42

For 7 miles, it will take him 42 minutes.

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The population of the town in the year 1995 will be 61415.

From the information, the population of a town was 980 in 1970 and the population has been growing at a rate of 18% each year.

Therefore, it should be noted the difference in the number of years will be:

= 1995 - 1970

= 25 years

Therefore, the population of the town in the year 1995 is:

= 980 × (1 + 18%)^25

= 980 × (1.18)^25

= 980 × 66.6686

= 61415

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Answer:

126

Step-by-step explanation:

The area of the top triangle is (6)(6)/2 = 18 square meters.

The area of the bottom rectangle is (9)(12)=108 square meters.

Adding these, we get the total area to be 126 square meters.

Answer:

$21.40

Step-by-step explanation:

List price = $19.95

Sales Tax Rate = 7.25%

Total sales tax = 19.95 x 7.25/100 = $ 1.45

Total cost = 19.95 + 1.45 = $21.40

In ascending order the integers are arranged from the left to right of the integer line. The arrangements are shown below.

The arrangement of the set of integers in increasing order is as follows:

Every positive integer is greater than a negative integer. Zero is less than every positive integer. Zero is greater than every negative integer. The greater the number, the lesser its opposite,i.e., If a and b are two integers such that a>b, then -a<-b.

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For v = -4, 0, and 8 are not solutions of the equation 1 - 7v = - 69. The solution of the equation is v = 10.

Consider the equation,

1 - 7v = - 69

For the value of v = - 4,

1 - 7v = - 69

1 - 7 × - 4 = - 69

1 + 28 ≠ - 69

29 ≠ - 69

Hence, v = - 4 is not a solution.

For v = 10,

1 - 7v = - 69

1 - 7 × 10 = - 69

1 - 70 = - 69

- 69 = - 69

Therefore, v = 10 is a solution.

For the value of v = 0,

1 - 7v = - 69

1 - 7 × 0 = - 69

1 ≠ - 69

Hence, v = 0 is not a solution.

For the value of v = 8,

1 - 7v = - 69

1 - 7 × 8 = - 69

1 - 64 ≠ - 69

- 63 ≠ - 69

Hence, v = 8 is not a solution.

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A table of data for two different linear functions using the same values of x for both functions is shown below:

From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5.

Therefore, the graph of the two functions will intersect at (1, 5)

Step-by-step explanation:

-1/7 is exact form and Slash or / is division . -0.142857, Decimal form and horizontal line is division too . It is the simplest form .

A function in the mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as function's domain and codomain, respectively. Here f(x)= 60.

A function in the mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as function's domain and codomain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, the functions represented the idealized relationship between two changing quantities. A planet's position, for the instance, depends on time. In the past, idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

The most common letters used to represent functions are f, g, and h. A function's value at an element of its domain x is denoted by the symbol f(x), and the numerical value obtained by evaluating the function at a specific input value is denoted by replacing x with that value. For example, the value of f at x = 4 is denoted by the symbol f(x) (4). The value of the function at, say, x = 4 may be denoted by E|x=4 when the function has no name and is represented by the expression E.

if, f(x)= (-8),

f(-8)= (-9)*(-8)-12 = 60

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     In a point-to-point graph, also known as a line graph, particular values of a function are represented graphically by dots on a coordinate plane. Straight lines connect adjacent pairs of dots.

    Choose x and work out the equation for y, or, to locate points on the line y = mx + b. Decide on y, then find x.

         Depending on your preference, you can plot points one at a time, a few on a line, or all at once in a table. Start with the video on the right before continuing to the resources and challenges below to learn more.

          The point (-4, 482) is located on the y=6f[-(x-5)] graph. -4 What is the fundamental idea behind y=f(x).

  If x=-4 and y=482 are subtracted from y=6f[-(x-5)],

I obtain the result f=9 at -4.

When I adjust the slider to f=9 and enter y=6f[-(x-5)]-4 into Demos, the line goes through the point (-4,482)

Does this imply that y=9x is the solution.

None of this actually makes sense to me. I don't understand a single thing. Just rearranging the numbers is all. There were NO examples in the lessons of an equation with a "y". Additionally, the left side of the equation in each example contained "f(x)" or "g(x)".

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Answer: The answer should be 3 hours

Step-by-step explanation: 8+4=12, divide the sum by 36: 36÷12=3

She had worked 3 hours.

Starting with part a, question (i):

Find the average rate of change in both populations between 2002 and 2012.

Recall that the average rate of change of a function f(x) in the interval [ a, b] is given by the quotient:

rate of change = ( f(b) - f(a) ) / (b - a)

Therefore, for our population P1 case on the years 2002 and 2012 we have:

[ P1(2012) - P1(2002) ] / (2012 - 2002) = [62 - 42] / 10 = 20 / 10 = 2

for population P2 we have:

22 [72 - 82] /10 = -10/10 = -1

You can proceed doing the same process for the other cases (ii) and (iii).

Case (ii)Now part b of the problem:

Rate of change between 2002 and 2019:

99 [ 76 - 42] / ( 17) = 534 / 17 = 2

2(929 9[ 65 - 82] / 17 = -17 / 17 = -1

Case (iii)

Rate of change between 2007 and 2019:

9797 [76 - 52] / 12 = 24/12 = 2

22 [65 - 77] / 12 = -12 / 12 = -1

We see that the rates of change for each population remained constant over the years.

What we noticed in the table regarding both populations, is that while population P1 is increasing over the years, population P2 is going down in numbers year after year.

We can say therefore that P1 is INCREASING, while P2 is DECREASING. And that the rate of change they experienced was constant over the years.

The expression to represent the number of hours Erica babysits  each week is 7x .

In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number) .

Erica works x hours each day and there are 7 days in a week.

Hence Erica works 7x hours in a week

Therefore the expression to represent the number of hours Erica babysits  each week is 7x .

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Answer: 4 : 9

Step-by-step explanation:

Total number of blue shirts purchased by Alice = 4

Total number of yellow shirts purchased by Alice = 5

Hence, total number of shirts purchase by her = 4 + 5

= 9

Therefore, Ratio of number of blue shirts to the total number of shirts

[tex]=\frac{Total~number~of~blue~shirts}{Total~number~of~shirts}[/tex]

[tex]=\frac{4}{9}[/tex]

Hence, Ratio = 4 : 9

       The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.

         Except for when the points coincide, distances in geometry are always positive. The distance between points A and B is equal to their respective distances. We take two points A(a,b) and B into consideration in order to calculate the formula for the distance between two points in the plane (c,d).

     In coordinate geometry, the distance between two given points is calculated using the distance formula. D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2 is the formula for calculating the distance between two points (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2).

    Say, for instance, that you are asked to determine the distance between two points at ( -6,-2 ) and ( -1,10).

First step:  

Give x 1, y 1, x 2, and y 2 their respective assignments.

Consider the cases where (x 1, y 1 ) = ( -6,-2)) and (x 2, y 2 ) = ( -1,-10).

      x1 = -6

      y1 =- 2

      x2 =  -1

      y2  = 10

Second Step:

Replace in the Distance Formula

Now that we know the numbers for x1, y1, x2, and y2, we can enter them into the Distance Formula.

d = √(-6,-2)² + (-1-10)²

   = √(8)² + (11)²

   = √16+22

   = √38.

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The following are the solutions to the given problems by using binomial probability principle:

1.) P(X ≤ 3)

P(X ≤ 3) = p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)

Use a binomial probability calculator :

P(X ≤ 3) = 0.277 + 0.365 + 0.231 + 0.093

P(X ≤ 3) = 0.966

2.) P(X < 3)

P(X < 3) = p(x = 0) + p(x = 1) + p(x = 2)

Use a binomial probability calculator :

P(X < 3) = 0.277 + 0.365 + 0.231

P(X < 3) = 0.873

3.)P(X ≥ 4)

P(X ≥ 4) = p(x = 4) + p(x = 5) +...+ p(x = 50)

Use a binomial probability calculator :

P(X ≥ 4) = 0.034

4.) P(1 ≤ X ≤ 3)

P(1 ≤ X ≤ 3) = p(x =1) + p(x =2) + p(x =3)

Use a binomial probability calculator :

P(1 ≤ X ≤ 3) = 0.365 + 0.231 + 0.093

P(1 ≤ X ≤ 3)= 0.689

D.) σ(X)

E(X) = np = 25 × 0.05

E(X)  = 1.25

σ(X) = √(npq)

σ(X) = √(25 × 0.05 × 0.95)

σ(X) = √1.1875

σ(X) = 1.090

E. Probability for none do have food allergy :

P(X = 0) = ⁵⁰C₀ × 0.05^0 × 0.95^50

P(X = 0) = 0.0769

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Answer:

2318

Step-by-step explanation:

Answer:

Y = 60x

Step-by-step explanation:

Find the slope by finding Y2 - Y1/X2 - X1, 1 and 2 being two separate points on the graph. 120-0/2 = 6

The entered points belong to a vertical line. There is no slope.

Equation: x = -19.

Answer:

130 degrees

Step-by-step explanation:

When two lines intersect, the opposite angles are equal, therefore, in this example, 7c+36 = 5c+40. We can find c using this equation.
7c+36 = 5c+40
7c-5c = 40-36
2c = 4
c = 4/2 therefore c=2

now that we know c is equal to 2, we can find out both of those angles.
therefore 5c+40 = (5*2)+40 = 10+40= 50
and 7c+36 = (7*2)+36 = 14 +36 = 50

now we know that those two angles add up to 100.

to find the sum of x and the angle opposite to x, subtract 100 from 360
360-100 = 260

since the angle opposite of x is equal to x, x+x = 260
2x=260
x=260/2 = 130

x is 130 degrees

Answer:

x = 130

Step-by-step explanation:

7c + 36 and 5c + 40 are vertically opposite angles and are congruent , so

7c + 36 = 5c + 40  ( subtract 5c from both sides )

2c + 36 = 40 ( subtract 36 from both sides )

2c = 4 ( divide both sides by 2 )

c = 2

Then

7c + 36 = 7(2) + 36 = 14 + 36 = 50

5c + 36 and x are a linear pair and sum to 180° , that is

50 + x = 180 ( subtract 50 from both sides )

x = 130