To make a homemade all-purpose household cleaner, you can mix the ingredients shown in the table.

All-Purpose Cleaner
1 cup vinegar
12 cup rubbing alcohol
1 gallon water (16 cups)
Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need?

Samuel will need
______ containers.

The total solution will include
cup(s)_____of vinegar,
cup(s)_____of rubbing alcohol, and
cup(s)_____ of water, which is a total of
cups of solution. Five containers will hold 5 × 6, or 30 cups of solution. So, he will need _____ total containers to hold all of the solution.

Answers

Answer 1

3 containers, 1 cup, 12 cup, 16 cups

Samuel will need

3 containers.

The total solution will include

cup(s) 1 of vinegar,

cup(s) 12 of rubbing alcohol, and

cup(s) 16 of water, which is a total of

cups of solution. Five containers will hold 5 × 6, or 30 cups of solution. So, he will need 3 total containers to hold all of the solution.

What are ingredients?

Ingredients refer to the materials or apparatuses combined together to have a single product. In other words, ingredients are the chemical makeups of a refined product which combine together to have new and entirely different product.

The ingredients for a homemade all-purpose household cleaner, in this case, are vinegar, rubbing alcohol, and water.

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Related Questions

How many turning points are in the graph of the polynomial function?
4 turning points
5 turning points
6 turning points
7 turning points

Answers

B 5 turning points. For example: The polynomial function y= ×^6 + 3x^5 +
4x^2 + 12 has six turning points. The degree of the polynomial is 6, which means that it has 6-1=5 turning points. These are the points where the function changes from increasing to decreasing or vice versa. In other words, these are the points where the derivative of the function equals 0. To find the exact locations of the turning points, you can set the derivative equal to 0 and solve for

Please help me answer this question ASAP!! It’s due tomorrow! Will mark as brainliest if explained very simply and correct.

Answers

Answer:

The answer is B:14

Step-by-step explanation:

When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.

From a point X, the bearing of a flag pole is 280⁰, from another point Y due south of X the bearing of the flag pole is 330⁰ . if the angle of elevation of the top of the flag pole from Y is 60⁰ and the distance (X,Y) is 92km . Calculate how far Y is from the flag pole​

Answers

Answer: 37km

Step-by-step explanation:

Simplify (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy).
O4xy³ - x²y - 3xy
O4xy³ - x²y + 3xy
O 10xy³ + x²y - 3xy
O 10xy³x²y + 3xy

Answers

Answer: 10xy³ - x²y + 3xy

Step-by-step explanation:

To simplify the expression (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy), we can combine like terms.

Adding the corresponding terms together, we have:

3xy³ + 7xy³ = 10xy³

8x²y - 9x²y = -x²y

-3xy + 6xy = 3xy

Combining these terms, the simplified expression becomes:

10xy³ - x²y + 3xy

Therefore, the correct option is:

O 10xy³ - x²y + 3xy

Brenda types 15 words per minute. How long will it take her to type 750 words?

Answers

It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.

To solve this problem, we can use the formula:

time = amount of work / rate

In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:

time = 750 / 15 = 50 minutes

This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.

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radius of 18 feet and a central angle of 52° is shown below. Which of the following is the closest to the length of the arc from point C to point D?

Answers

The closest length to the arc from point C to point D is 16.34 ft (option c).

To find the length of the arc from point C to point D, we need to calculate the circumference of the circle and then find the fraction of the circumference represented by the central angle.

The circumference of a circle can be calculated using the formula:

Circumference = 2 × π × radius

Given the radius of 18 feet, the circumference is:

Circumference = 2 × π × 18 = 36π feet

To find the length of the arc, we need to find the fraction of the circumference represented by the central angle of 52°. The fraction is calculated by dividing the central angle by 360° and then multiplying it by the circumference.

Length of the arc = (Central angle / 360°) * Circumference

Length of the arc = (52° / 360°) × 36π

Length of the arc = (13/90) × 36π

Length of the arc = 468π / 90

Length of the arc ≈ 16.41 ft

Among the given options, the closest length to the arc from point C to point D is 16.34 ft (option c).

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6 sin θ=5 to the nearest 0.1°

Answers

The value of the equation 6 sinθ=5 for θ is 56.4 degrees

How to evaluate the equation

From the question, we have the following parameters that can be used in our computation:

6 sinθ=5

Express the equation properly

So, we have the following representation

6 sin(θ) = 5

Divide both sides of the equation by 6

This gives

sin(θ) = 5/6

Evaluate the quotient

sin(θ) = 0.833

Take the arc sin of both sides

θ = sin⁻¹(0.833)

Evaluate

θ = 56.4

Hence, the value of the equation for θ is 56.4 degrees

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Complete question

Approximate θ in the equation, to the nearest 0.1 degrees

6 sin(θ) = 5

you
cou
Recommendations
Florida's B.E.S.T. Standards: Grade 8 > GG.5 Make predictions 38C
thro
Skill plans
pieces of vanilla cake
You have prizes to reveall Go to
Passersby have taken 4 pieces of vanilla cake and 6 pieces of coconut cake from a
sample tray. Based on past data, of the next 30 samples taken, how many should you expect
to be pieces of vanilla cake?
Vid

Answers

Out of the following 30 samples, you may expect that about 12 will be portions of vanilla cake.

How to determine probability?

To solve this problem, use the concept of probability and make a prediction based on the past data.

In this case, out of the 10 pieces of cake that have been taken, 4 are vanilla and 6 are coconut.

Therefore, the probability of selecting a piece of vanilla cake from the tray is 4/10, or 2/5.

To predict how many of the next 30 samples will be pieces of vanilla cake, multiply the probability of selecting a vanilla cake by the total number of samples:

(2/5) x 30 = 12

So expect that out of the next 30 samples taken, approximately 12 of them will be pieces of vanilla cake.

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The carrying capacity of a drain pipe is directly proportional to the area of its cross section.If cylindrical pipe drain can carry 36L/sec,determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second .

Answers

Step-by-step explanation:

x and y are directly proportional means that

y = kx

y grows with the same factor k applied to x.

the area of a circle (the cross section of a cylindrical pipe) is

pi × r²

r being the radius (which is half of the diameter).

so, the area in terms of the diameter is

pi × (d/2)² = pi × d²/4

so, we know

36 correlates to pi × (d small)²/4

60 correlates to pi × (d large)²/4

therefore (directly proportional),

d small² = 36×4/pi

d small = 12/sqrt(pi)

d large² = 60×4/pi

d large = sqrt(4×15×4/pi) = 4×sqrt(15/pi)

the difference between large and small diameter (increase from small to large) is then

4×sqrt(15/pi) - 12/sqrt(pi)

d small = 100%

1% = 100%/100 = 12/sqrt(pi) / 100 = 12/(100sqrt(pi))

the % of the diameter increase is then

increase/1% =

(4×sqrt(15/pi) - 12/sqrt(pi)) / 12/(100sqrt(pi)) =

= (400sqrt(pi)×sqrt(15/pi) - 1200sqrt(pi)/sqrt(pi)) / 12 =

= (400×sqrt(15) - 1200) / 12 = 100×sqrt(15)/3 - 100 =

= 100×(sqrt(15)/3 - 1) = 29.09944487...% ≈ 29.1%

the diameter has to increase by about 29.1%, so that the pipe can carry 60 liters per second.

please consider : only the area of the cross section and the carrying capacity are directly proportional.

the diameter of the cross section and the area of the cross section are NOT directly proportional.

they have the pi×(d/2)² relationship.

and so, while the capacity and the cycle area both increase by the same factor, the impact on the diameter (or radius) is different.

so, for capacity and area we have

60 = k×36

k = 60/36 = 5/3 = 1.66666666...

and therefore both increase by 66.66666...%.

but because of the square relation between diameter and cross section area, the diameter only increases by 29.1%.

Geometry problem (possible drop down answers are ellipse rectangle and circle) please help! Will give crown to first to give correct answer.

Answers

Answer:

ellipses

a pair of parallel straight

Step-by-step explanation:

Find the surface area of the prism. Round to the nearest tenth if necessary.

Regular pentagon base

B≈61.94 cm2

Base length=6cm
Lateral edge=5cm
A regular pentagonal prism is shown. The length of the side of the pentagon is six centimeters. The height of the prism is five centimeters.

Answers

The surface area of the prism is 248.88 cm²

What is surface area of prism?

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.

Base area = 61.94 cm²

height = 5cm

perimeter = 5 × 5 = 25cm

SA = 2 × 61.94 + 25 × 5

SA = 123.88+ 125

SA = 248.88 cm²

Therefore the surface area of the prism is 258.88 cm²

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you will get 10 points for each question and help

Answers

The probability is very high and the event is very likely to occur.

option B.

What is the explanation for the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

If the probability of a rolling a number greater than 1 on a six sided cube die  is 5/6, it implies that the chances of obtaining a number greater than 1 is very high.

We will convert 5/6 to percentage to see the actual value of 5/6.

5/6 x 100%

= 83.33 %

So the value of this probability is very high and the event is very likely to occur.

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Britney is a volunteer at the Westside Library. She collects the books that come down the
chute from the outside drop-off and puts them on the library shelves. Of the books that have
come down the chute so far today, 41 have been fiction and 23 have been nonfiction.
Based on the data, estimate how many of the next 100 books that come down the chute will
be nonfiction.

Answers

Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.

To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.

The total number of books that came down the chute so far is:

41 (fiction) + 23 (nonfiction) = 64

The ratio of nonfiction books to the total number of books in library is:

[tex]23/64[/tex]

To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:

[tex](23/64)*100=35.9375[/tex]

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Solution for
Y= x+3
Y= 3x+1

Answers

Starting with the two equations:

Y = x + 3    (1)

Y = 3x + 1     (2)

We can solve for x and y by equating equation (1) and (2) and solving for x.

x + 3 = 3x + 1

2x = 2

x = 1

Now we can substitute x = 1 into either equation (1) or (2) to solve for y.

Using equation (1):

Y = x + 3

Y = 1 + 3

Y = 4

Therefore, the solution for the system of equations is:

x = 1, y = 4

D. 17 °F 2. Franky earns $(100+ x) daily for five days, $(175 + 2x) for two days, and $(75 + 2x) for three days. If the average amount she earns is $80 per day, what is the median amount she earned?​

Answers

The median total of amount Franky earned is A = $81.67 per day.

Given data ,

For the first five days: $(100 + x) per day

For the next two days: $(175 + 2x) per day

For the final three days: $(75 + 2x) per day

Now , the average amount she earns is $80 per day

So , Average earnings = Total earnings / Total number of days

Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10

Simplifying the equation:

80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10

Multiplying both sides by 10:

800 = 1075 + 15x

Subtracting 1075 from both sides:

15x = -275

Dividing both sides by 15:

x = -18.33

For the first five days: $(100 - 18.33) = $81.67 per day

For the next two days: $(175 + 2*(-18.33)) = $138.34 per day

For the final three days: $(75 + 2*(-18.33)) = $38.34 per day

Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34

The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67

Hence , the median is $81.67

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?? geometry question

Answers

The measure of angle BGF from the given parallel lines is 108°.

Given that, measure of angle BGF=4x+28 and the measure of angle EHD = 2x+32.

1) From the given figure, angle BGF and angle EHC are interior alternate angles.

Angle FHC and angle EGA are corresponding angles.

Angle FHC and angle EGA are exterior alternate angles.

2) angle BGF+angle EHD=180°

3) 4x+28+2x+32=180°

6x+60=180

6x=120

x=20

Angle BGF=4x+28=108 °

Angle EHD = 2x+32

= 112°

Angle FHD=180-112=68°

Angle EGB=180-108=72°

Therefore, the measure of angle BGF from the given parallel lines is 108°.

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10. Kipp constructed a pentagonal pyramid for his social studies report. The base had an area of 12 cm². It took 48 cubic centimeters of clay to make his model. Find the height of the pyramid.

Answers

We can use the formula for the volume of a pentagonal pyramid to solve this problem:

Volume = (1/3) × Base Area × Height

We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:

48 = (1/3) × 12 × Height

Multiplying both sides by 3 gives:

144 = 12 × Height

Dividing both sides by 12 gives:

Height = 12

Therefore, the height of the pentagonal pyramid is 12 centimeters.

5. In AABC, ZA = 70°, ZB = 50°, and a = 15 cm. Solve ▲ABC. ​

Answers

In triangle ABC, side BC (a) is 15 cm, side AC (b) is 13.30 cm, and side AB (c) is 12.23 cm. Also angle A is 70°, B is 50°, and C is 60°

Understanding the Angles and Sides of Triangle

Using the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using this, we can find the lengths of the other sides of triangle ABC.

Let's denote side AB as c, BC as a, side AC as b, and angle C as ∠C.

Using the Law of Sines, we have:

sin(∠A) / a = sin(∠B) / b

Substitute in the known values, we get:

sin(70°) / 15 = sin(50°) / b

Make b the subject of the formula:

b = (15 * sin(50°)) / sin(70°)

Using a calculator, we can find the value of b:

b = (15 * 0.766) / 0.9397

  = 12.23 cm

Therefore side AC = b = 12.23 cm

Now, to find side AB (c), we can use the Law of Sines again:

sin(∠B) / b = sin(∠C) / c

But ∠C is unknown. To find ∠C, we apply the sum of angle in a triangle rule

∠A + ∠B + ∠C = 180

70 + 50 + ∠C = 180

∠C = 180 - 70 - 50

∠C = 60°

Substitute the values in the Sine rule equation

sin(50°) / 12.233 = sin(60) / c

Make c the subject of the formula

c = (12.233 * sin(60)) / sin(50°)

c = (12.233 * sin(60°)) / sin(50°)

  = 13.30 cm

Therefore, the lengths of the sides of triangle ABC are:

Side AB = c = 12.23 cm

Side BC = a = 15 cm

Side AC = b = 13.30 cm

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Question 2 (Multiple Choice Worth 1 points)
(06.02 MC)
Simplify (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab).
O-a³b-8ab2 + 10ab
O-a³b-8ab²
07a³b-8ab² + 10ab

Answers

The simplified expression of (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) is (b) -a³b - 8ab²

How to simplify the expression

From the question, we have the following parameters that can be used in our computation:

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab)

Open the bracket

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = 3a³b - 4ab² + 5ab -4a³b - 4ab² - 5ab

Evaluate the like terms

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = -a³b - 8ab²

Hence, the simplified expression is (b) -a³b - 8ab²

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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Find the volume of a rectangular prism with a length of 12 inches a width of 4.5 inches and a height of 3.6 inches

Answers

Answer:

194.4

Step-by-step explanation:

V=l*w*h

V=12*4.5*3.6

V=194.4

Which animal swims at a top speed of about 0.33 mile per minute? Explain how you found your answer

Answers

The animal that swims at a top speed of 0. 33 miles per minute would be the Dolphin .

How to find the animal ?

To find the animal that swims at a top speed of 0. 33 miles per minute, you need to convert their top speeds in miles per hour to miles per minute.

For every 1 mile per hour, the equivalent in minutes is 0.0166667 miles per minute.

Speed of Swordfish is:

= 60 mph x 0.0166667

= 1 mile per minute

Speed of Tuna :

= 45 mph x 0.0166667

= 0. 75 miles per minute

Dolphin :

= 20 mph x 0.0166667

= 0. 33 miles a minute

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Part A: Jan INCORRECTLY
finds the surface area of the
cone using the following
work. Explain Jan's error
and find the
correct volume AND
surface area of the cone.

Answers

The volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.

Given the height (h) of a cone as 22 m and the diameter (d) of its circular base as 22 m, we can find the radius (r) of the circular base using the formula:

r = d/2 = 22/2 = 11 m

Here, Jan made a mistake in the work of the surface area of the cone because she used the wrong value of slant height (l=22) in the calculation.

The volume (V) of a cone is given by the formula:

V = (1/3)πr²h

Substituting the values of r and h, we get:

V = (1/3)π(11)²(22)

V = 2786.2 cubic meters

The surface area (A) of a cone is given by the formula:

A = πr(r + l)

here l is the slant height of the cone, which can be found using the Pythagorean theorem:

l = √(r² + h²)

l = √(11² + 22²)

l = √(605)

l = 24.6

Substituting the values of r and l, we get:

A = π(11)(11 + 24.6)

A ≈ 1229.51 square meters

Therefore, the volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.

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Graph by completing the square x2-2x+y2+6y-6=0​

Answers

The equation in the standard form of a circle and find the centre and radius:

(x - 1)²/31 + (y + 3)²/31/3 = 1

To graph by completing the square, we need to rearrange the equation so that it has the form:

(x - h)² + (y - k)² = r²

Starting with x² - 2x + y² + 6y - 6 = 0:

First, we can factor out a 2 from the x terms and a 6 from the y terms:

2(x² - 2x) + 6(y² + 6y) - 6 = 0

Next, we need to complete the square for the x and y terms:

2(x² - 2x + 1) + 6(y² + 6y + 9) - 6 = 2(1) + 6(9)

Simplifying, we get:

2(x - 1)² + 6(y + 3)² = 62

Now we can rewrite the equation in the standard form of a circle and find the centre and radius:

(x - 1)²/31 + (y + 3)²/31/3 = 1

The centre of the circle is (1, -3), and the radius is √(31/3).

The graph is attached with the answer below.

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Given f(x) = x³ - 6x + k, and the remainder when f(x) is divided by x - 1 is 14, then what is the value of k?

Answers

Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!

Can someone answer this question

Answers

The options 2nd and 3rd are the monomials with degree 2.

Given are the expressions we need to find the monomials with degree 2.

So,

The general form of a monomial with degree 2 is:

ax²

The highest exponent of a polynomial's variable(s) in any of its terms is referred to as the polynomial's degree in mathematics.

It controls the polynomial's behavior and complexity.

A non-negative integer is used to represent the degree.

And,

A monomial is a mathematical expression consisting of a single term. It is composed of a coefficient multiplied by one or more variables raised to non-negative integer exponents.

Here, the monomials can be 2x² and x²

Hence the options 2nd and 3rd are the monomials with degree 2.

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Identify the unit rate in each graph. Then, order the graphs by unit rate, from least to greatest.

Answers

The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

How did we determine their unit rates?

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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Please help me with this statistics question. Photo attached

Answers

a) The data in the above table about the statistics class asked the city where they live are b) Quantitative and Discrete.

b) The completion of the frequency distribution for the data is as follows:

Class            Frequency

Fort Pierce          7

Port St. Lucie      6

Vero Beach        7

Sebastian           4

Okeechobee     6

Total                 30

c) The completion of relative frequency and percentage distribution for the data is as follows:

Class            Frequency    Relative Frequency    Percentage

Fort Pierce          7                       0.233                     23.3%

Port St. Lucie      6                      0.200                     20.0%

Vero Beach        7                       0.233                     23.3%

Sebastian           4                        0.133                      13.3%

Okeechobee     6                       0.200                    20.0%

Total                 30

How the relative frequencies and percentages are computed:

Class            Frequency    Relative Frequency        Percentage

Fort Pierce          7                 0.233 (7/30)           23.33% (7/30 x100)  

Port St. Lucie      6                0.200 (6/30)           20.00% (6/30 x100)  

Vero Beach        7                 0.233 (7/30)           23.33% (7/30 x100)  

Sebastian           4                  0.133 (4/30)            13.33% (4/30 x100)  

Okeechobee     6                 0.200 (6/30)           20.00% (6/30 x100)  

Total                 30

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Answer Options for a):

a) Time-Series

b) Quantitative and Discrete

c) Cross-Sectional Qualitative

d) Quantitative and Continuous

A shirt manufacturer pays a worker $0.47 for each acceptable shirt inspected under the prescribed job description. If the worker had the following work record, find the gross earnings for the week: Monday, 250 shirts; Tuesday, 300 shirts; Wednesday, 178 shirts; Thursday, 326 shirts; Friday, 296 shirts

Answers




(250 shirts * 0.47) + (300 shirts * 0.47) + (178 shirts * 0.47) +
(326 shirts * 0.47) + (296 shirts * 0.47) =


$85.07


(0.47*670) = $85.07

The perimeter of a right triangle is equal to 4x + 3. If two sides of the triangle measure: x + 7 and x – 7, what is the measurement of the hypotenuse?

Answers

If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.

In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:

a² + b² = c²

where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:

a + b + c = 4x + 3

Substituting the given side lengths, we get:

(x + 7) + (x - 7) + c = 4x + 3

Simplifying, we get:

2x + c = 4x + 3 - 7 + 7

2x + c = 4x + 3

Solving for c, we get:

c = 2x + 3

We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.

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