SOLVING EQUATIONS Solve the equation. Check your solution.
50. y+4-1 = 18
52. v-7= 9+12
St 53.5+44=2+r
51. m+ 18+ 23 = 71
54. 22 +15=d-17

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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The percent table is:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

The initial price of the Loungy chair was $400.

So, the initial price(P₀) = $400

The price of the chair has gone up by 20%

So, increase in price(r) = 20%

The final price will be calculated by using the formula:

                          P = P₀(1 + r/100) (where P is the final price)

                          P = 400(1 + 20/100)

                          P = 400(1 + 0.2)

                          P = 400 × 1.2

                          P = $480

Hence, the final price of the Loungy chair is $480

Percent table:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

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If m + 1 is an even integer, then 2m + 1 is an odd integer.

Even number: An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number.

Odd number: Odd numbers are those numbers that are not completely divisible by 2.

let us understand by addition on different combinations of odd numbers and even numbers.

Odd number + Odd number = Even number

Even number + Even number = Even number

Even number + Odd number = Odd number

Odd number + Even number = Odd number

In subtraction

Even number - Even number = Even number

Even number - Odd number = Odd number

Odd number - Even number = Odd number

Odd number - Odd number = Even number

In multiplication

Even number × Even number = Even number

Even number × Odd number = Even number

Odd number × Odd number = Odd number

Given:

m + 1 is an even integer.

since alternate numbers are even.

Therefore, m must be an odd number.

If m is odd, then m - 1 is even.

2m is divisible by 2, so it is always an even number.

So,

2m - 2 is even.

2m + 1 is odd.

2m + 2 is even.

Since 2m + 1 is an odd number.

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The proof is as shown below

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If a² = b + c , b² = c + a and c² = a + b

We want to prove that 1/(a+1) + 1/(b+1) + 1/(c+1) = 1

Since a² = b + c

a²+a = a + b + c

a (a+1) = a + b + c

a+1 = (a + b + c)/a

Repeat the same process for b² = c + a and c² = a +b, we have:

1 + b= (a + b + c)/b

1 + c =(a + b + c)/c

Substitute the values 1+a, 1+b and 1+c into 1/(a+1) + 1/(b+1) + 1/(c+1):

1/(a+1) + 1/(b+1) + 1/(c+1) = a/(a+b+c) + b/(a+b+c) + c/(a+b+c)     (Taking LCM)

                                      = (a+b+c )/ (a+b+c ) = 1

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The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.

11.2 km = 11,200 meters (1 km = 1000 meters)

Stride length in meters = 70 cm / 100 cm/m = 0.7 m

Now, we can calculate the minimum number of strides as follows,

Minimum number of strides = (Distance covered in meters) / (Stride length in meters)

Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000

Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

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If Benjamin invests $400 in a savings account that earns 5% interest each year, the expression that shows the correct balance is  A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

The principal amount = $400

interest rate = 5%

The equation of the simple interest

A = P (1+ rt)

Where A is the final amount

P is the principal amount

r is the interest rate

t is the time period

The final amount after one year

= 400( 1 + 0.05×1)

= 400(1 + 0.05)

The final amount after two year

= 400(1 + 0.05)(1 + 0.05)

The final amount after three year

= 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

Therefore, the balance amount after three years is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

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Answer:

a) y - 4 =3(x - 1)

b)  y + 2 = 4(x+ 1)

c) y = -(x - 3)

d) y = -5x

Step-by-step explanation:

You did not say which form, so I put them in the point-slope form of a line that follows the pattern:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Answer:

see explanation

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 )

(a)

given m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (1, 4 ) into the partial equation

4 = 3(1) + c = 3 + c ( subtract 3 from both sides )

1 = c

y = 3x + 1 ← equation of line

(b)

given m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, - 2 ) into the partial equation

- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )

2 = c

y = 4x + 2 ← equation of line

(c)

given m = - 1 , then

y = - x + c ← is the partial equation

to find c substitute (3, 0 ) into the partial equation

0 = - 3 + c ( add 3 to both sides )

3 = c

y = - x + 3 ← equation of line

(d)

given m = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (0, 0 ) into the partial equation

0 = - 5(0) + c = 0 + c ⇒ c = 0

y = - 5x ← equation of line

answer:

if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio

5:8 = 10:16 multiplying by 2

5:8 = 15:24 multiplying by 3

5:8 = 20:32 multiplying by 4

5:8 = 25:40 multiplying by 5

5:8 = 30:48 multiplying by 6

5:8 = 35:56 multiplying by 7

and so on ...

Answer: The statement "The mean height of the students in Juan's math class is equal to the mean height of the students in his English class" means that the center or average of both groups is the same. However, the statement "the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches" implies that the heights of the students in the English class are more spread out than the heights of the students in the math class.

Therefore, the answer is:

D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.

Step-by-step explanation:

The amount of cubic feet that the storage shed can hold is 168 ft³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The volume of the storage shed is the product of the base area and the height. It is given by:

Volume = base area * height

From the diagram, the base is a triangle. Hence:

Area of base = (1/2) * base * height = (1/2) * 8 ft * 7 ft = 28 ft²

Volume = base area * height = 28 ft² * 6 ft. = 168 ft³

The volume of the storage shed is 168 ft³

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Answer:

[tex]10[/tex] four point questions and [tex]30[/tex] two point questions

Step-by-step explanation:

Let's say [tex]f =[/tex] [tex]\text{number of four point questions}[/tex] and[tex]t = \text{number of two point questions}[/tex]. The total number of questions is [tex]40[/tex], therefore [tex]t + f = 40[/tex]. We know the test is worth [tex]100[/tex] points so we can write [tex]2t + 4f = 100[/tex]. We have a system of equations: [tex]t + f = 40 \text{ and } 2t + 4f = 100[/tex]. We can rewrite [tex]t[/tex] as [tex]t = 40 - f[/tex]. We rewrite this in the equation [tex]2t + 4f = 100[/tex]. Since [tex]t = 40 - f[/tex], we have [tex]2 \cdot (40 - f) + 4f = 100[/tex]. Distributing & simplifying gives

[tex]2 \cdot (40 - f) + 4f = 100\\(80 - 2f) + 4f = 100,\\\text{Remove parentheses} 80 - 2f + 4f = 100,\\80 + (-2f) + 4f = 100\\80 + 2f = 100,\\\text{Subtract 80 from both sides} 2f = 20,\\\text{Divide 2 by both sides} f = 10.\\[/tex]

Since we determined [tex]t = 40 - f[/tex] and [tex]f = 10[/tex], subtracting [tex]10[/tex] from [tex]40[/tex] will give [tex]t = 30[/tex].

Therefore, there are [tex]10[/tex] four point questions and [tex]30[/tex] two point questions.

Hope that helps!

Answer: equation: 3/5 * 5/8 = 38 = 0.375

Spelled result in numbers/words is three eighths/ 3/8.

Step-by-step explanation:

the basketball field takes up 3/8 of the playground

3/5 * 5/8 = 38 = 0.375 = 3/8

then (simplify) 0.375 into a fraction.

3/5 * 5/8 = 38 = 3/8

Answer:

Equation: 3/8 * 5/8

Answer:3/8

Step-by-step explanation:

Equation: 3/5 * 5/8. Since it is 5/8 of 3/5, you can do 3/5 * 5/8.

Answer: 3/8. Since 3/5 * 5/8 = 3/8, the answer will be 3/8

The distance that a person with a height of 6 feet can see is given as follows:

10.5 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

d = 1.75h.

For the person with a height of 6 feet, the distance is obtained replacing the lone instance of h by 6, hence:

d = 1.75 x 6

d = 10.5 feet.

The problem asks for the distance that a person with a height of 6 feet can see.

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The corresponding p-value for this test statistic is 0.005, which is smaller than our significance level of α=0.05.

To begin, we define the population proportion of people who shop for groceries online in region A as p₁ and the population proportion of people who shop for groceries online in region B as p₂.

Our null hypothesis is that there is no difference in these proportions, which we can write as H0=> p₁ = p₂. Our alternative hypothesis is that there is a difference, which we can write as H1=> p₁ ≠ p₂.

Next, we need to calculate the sample proportions and standard errors for each region. We can do this using the formulas:

p₁ = x₁/n₁, p₂ = x₂/n₂

where x₁ and x₂ are the number of people in each sample who shop for groceries online, and n₁ and n₂ are the sample sizes. The standard errors are given by:

=> SE₁ = √(p₁(1-p₁)/n₁),

=> SE₂ = √(p₂(1-p₂)/n₂)

Using the given data, we find that p₁ = 0.16, p₂ = 0.24, SE₁ = 0.037 and SE₂ = 0.042.

We can now calculate the test statistic, which measures the difference between the sample proportions under the assumption that the null hypothesis is true. We use the formula:

z = (p₁ - p₂) / √(SE₁² + SE₂²)

Substituting the values we calculated, we get:

z = (0.16 - 0.24) / √(0.037² + 0.042²) = -2.83

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Complete Question:

A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.

Answer:

44

Step-by-step explanation:

Answer:

5.1

Step-by-step explanation:

11.5 + 5.6 + 8.8 = 29.5

31 - 29.5 = 5.1

Answer: nope

Step-by-step explanation:

No, the 200$ marked down 20% would be 200 - 0.2 * 200 = 160$. Then, if it is increased by 20%, it would be 160 + 0.2 * 160 = 192$. So, 200$ is not equal to 192$.

Answer:

20

Step-by-step explanation:

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Answer:

20

Step-by-step explanation:

70% is 70/100 = 0.70

20 x 0.70 = 14

Answer: 12: 6 and 24: 12 and 3: 1.5

Step-by-step explanation: A ratio can be equivalent through multiplication such as 6: 3 to 12: 6  

Answer:

2 : 1,

12/

Step-by-step explanation:

all you have to do is cross out the numbers, basically simplify the

the answer is 2:1 because in 3's multiplication table,

3×2=

and

3×1=

similarly , for 12/6, divide instead of multiplication, there area few other ratios equivalent to 6/

Percentage profit on a chocolate bar is 150%

Profit percentage is a top-level and the most common tool to measure the profitability of a business. It measures the ability of the firm to convert sales into profits. i.e., 20% means the firm has generated a net profit of $20 for every $100 sale.

%profit = (selling price - cost price)/cost price × 100

%profit =( 1.50-0.6)/0.6 × 100

%profit = 0.9/0.6 × 100

= 1.5 × 100

= 150 %

therefore the percentage profit on a chocolate bar is 150%

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Sara can read about 30 pages in 95 minutes.

To start, multiply the weekly hours by the number of weeks in a year to get the overall number of hours worked (52). Then subtract this amount from the annual pay. For instance, if a worker earns $50,000 annually and puts in 40 hours per week, their hourly rate would be $50,000/2,080 (40 x 52) = $24.04.

First, we need to convert 95 minutes to hours by dividing by 60:

95 min ÷ 60 min/hour = 1.5833 hours (rounded to 4 decimal places)

Next, we can use the conversion factor to find the number of pages Sara can read in 1.5833 hours:

19 pages/hour x 1.5833 hours = 30.1391 pages

Rounding to the nearest whole number, Sara can read about 30 pages in 95 minutes.

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The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The equation of function is,

⇒ f (x) = 3 log₂ (x + 1)

Now, By using tool we can draw the graph of the equation of function

f (x) = 3 log₂ (x + 1) as shown in figure.

Thus, The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.

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variety of statistics for 1057 inernet users are  = (0.9180, 0.8998)  solve by given question .

population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.

Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

where z* = Critical value p = Sample proportion,n = sample size.

As per given , we have

n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96

Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

=0.9+-1.96[tex]\sqrt{.9*(1-.9)/1057}[/tex]

=0.9180, .8998

Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)

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The second situation costs less by

The cost of the first situation is

Adult = 8 * 2 = 16

drink = 2 * 2 = 4

popcorn = 2 * 2 = 4

Total = $24

Second situation

rent a video = $3.50

buy a 2 liter of cola = $1.60

a bag of microwave popcorn = $1.98.

Total = $7.03

The second situation costs less by

$24 - $7.03

= $16.92

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The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:

k = zy/ab.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The figures for this problem are given as follows:

Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:

k = zy/ab.

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The width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm²

To calculate the area of a rectangle, we need to multiply its width by its height.

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover the surface in a single coat.

Area = width x height

Substituting the given values, we get:

Area = 7.6 cm x 3.3 cm

Area = 25.08 cm²

Since the width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm² (rounded to one decimal place).

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Answer: B: 15,080

Step-by-step explanation:

Alright, let's convert 20% into a decimal: 0.20

Then multiply 0.20 x 75,400  which gets you to 15080

So she needed to pay $15,080 in taxes

A

im going to guess that the top of the graph has a flat line.

its easy to visualize since the graph looks like a hill, and the story describes the graph the most accurately

Answer:

∠ CAB = 144°

Step-by-step explanation:

the central angle CAB is twice the measure of ∠ BDC , that is

∠ CAB = 2 × 72° = 144°

Answer: Distributive property and Commutative property (of multiplication)

Step-by-step explanation:

From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.

From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.

HOPE THIS HELPS _- MM