solve the following problems using 5-D process part 2
(Describe/Draw, Define, Do, Decide, and Declare)

a. The number of girls in the Spanish Club is four more than twice the number of boys. There are 61 students in the Spanish Club. Find the number of boys and the number of girls in the Spanish Club.

b. Carrie and John went bowling together. They each bowled one game. Carrie knocked down 12 more pins than John did. The sum of their bowling games was 230. What was Carrie's and John's bowling scores?​

Answer:

150 people took the test.

Step-by-step explanation:

Given:

Number of people liked the new flavor = 69

Percentage of people liked the new flavor = 46%

We need to find the number of people who took the test.

Solution:

Let the number of people who took the test be 'x'.

So we can say that;

Percentage of people liked the new flavor multiplied by the number of people who took the test is equal to Number of people liked the new flavor.

framing in equation form we get;

[tex]46\%\times x =69\\\\\frac{46}{100}x=69\\\\0.46x =69[/tex]

Dividing both side by 0.46 we get;

[tex]\frac{0.46x}{0.46}=\frac{69}{0.46}\\\\x= 150[/tex]

Hence 150 people took the test.

Answer:

The sampling method used is Convenience sampling.

Step-by-step explanation:

Convenience sampling is a non-probability sampling method that involves the selection of sample from the easiest source available. In this sampling method the samples are selected from the most convenient possible way.

Foe instance, samples taken from social media, nearest shopping mall, and so on.

In this case the students selected 10 friends to answer the survey.

This is an example of convenience sampling method because sampling your friend is the easiest sample anyone could collect.

Thus, the sampling method used is Convenience sampling.

The length of AB is 31 yd.

Solution:

Given data:

The side opposite to angle A is "a" = 22 yd

The side opposite to angle B is "b" = 26 yd

The side opposite to angle C is "c" = AB

Angle C = 80°

To find the length of AB:

Using cosine formula,

[tex]c^2=a^2+b^2-2ab \cdot \cos C[/tex]

Substitute the given values in the formula, we get

[tex]c^2=22^2+26^2-2(22)(26)\cdot \cos 80^\circ[/tex]

[tex]c^2=484+676-1144\cdot \cos 80^\circ[/tex]

[tex]c^2=1160-1144\cdot (0.1736)[/tex]

[tex]c^2=1160-198.5984[/tex]

[tex]c^2=961.4016[/tex]

Taking square root on both sides, we get

c = 31

AB = 31 yd

The length of AB is 31 yd.

Carl has [tex]\( \frac{163}{36} \)[/tex] inches of string left out of the 20 inches he started with after tying the parcel and the box.

To find out how much string Carl has left after tying the parcel and the box, we'll subtract the lengths of string used from the total length he started with.

1. Convert the mixed numbers to improper fractions:

  -[tex]\(10 \frac{2}{9}\) inches = \(10 + \frac{2}{9} = \frac{90}{9} + \frac{2}{9} = \frac{92}{9}\)[/tex] inches

  - [tex]\(5 \frac{1}{4}\) inches = \(5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}\)[/tex] inches

2. Add the lengths of string used:

  [tex]\[\text{Total length used} = \frac{92}{9} + \frac{21}{4}\][/tex]

3. Find a common denominator to add the fractions:

  The common denominator for 9 and 4 is 36.

  [tex]\[\frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36}\] \[\frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36}\][/tex]

4. Add the fractions:

  [tex]\[\frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36}\][/tex] inches

5. Subtract the total length used from the total length Carl started with:

  [tex]\[20 - \frac{557}{36}\][/tex]

6. Convert the mixed number result to an improper fraction:

  \[20 = \frac{720}{36}\]

7. Subtract the fractions:

  [tex]\[\frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36}\][/tex] inches

Now, Carl has [tex]\(\frac{163}{36}\)[/tex] inches of string left.

We can convert this to a mixed number if necessary.

The correct question is:

Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?

Ans:          

Carl has [tex]\( {4 \frac{19}{36}} \)[/tex] inches of string left after tying both the parcel and the box.

1. Convert the mixed numbers to improper fractions:

  - 10 2/9 inches = [tex]\( \frac{92}{9} \) inches[/tex]

  - 5 1/4 inches = [tex]\( \frac{21}{4} \) inches[/tex]

2. Add the lengths of string used:

[tex]\( \frac{92}{9} \) inches (parcel) + \( \frac{21}{4} \) inches (box)[/tex]

  To add these fractions, find a common denominator:

  The least common multiple of 9 and 4 is 36.

[tex]\( \frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36} \)\\ \( \frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36} \)\\ \( \frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36} \) inches[/tex]

3. Subtract the total used from the initial length of string:

  Initial length of string = 20 inches

  Total used = [tex]\( \frac{557}{36} \) inches[/tex]

  To subtract, convert 20 inches to a fraction with the common denominator of 36:

[tex]\( 20 = \frac{720}{36} \)[/tex]

  Now, subtract:

[tex]\( \frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36} \) inches[/tex]

4. Convert the fraction to a mixed number (if necessary):

[tex]\( \frac{163}{36} \)[/tex] inches is already in its simplest form. To convert to a mixed number:

 [tex]\( 163 \div 36 = 4 \) remainder \( 19 \)[/tex]

  So, [tex]\( \frac{163}{36} = 4 \frac{19}{36} \) inches[/tex]

The correct question is:

Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?

Ans:_______

Answer:

radius = 6

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² - 12x + y² + 4y = - 4

Using the method of completing the square on the x and y terms

add (half the coefficient of the x/y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is

(x - 6)² + (y + 2)² = 36 ← in standard form

with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6

Answer:

6

Step-by-step explanation:

h = -12/-2 = 6

k = 4/-2 = -2

h² + k² - r² = 4

6² + (-2)² - 4 = r²

r² = 36

r = sqrt(36) = 6

Answer:

The minimum of cows he needs are: 2

Step-by-step explanation:

There's a relation between each animal:

5 chickens equals 1 pig

3 pigs equals 2 sheep

5 sheep equals 2 cows

You can understand it as the following three abstractions:

5c = 1p              (1)

3p = 2s             (2)

5s = 2o             (3)

Where:

c is for chickens

p is for pigs

s is for sheep

o is for cows

So now you have three equations with 4 variables. The next step is to obtain an equation that relates directly the variable c (chickens) with the variable o (cows). In order to do that from the equation 2 we obtain s in terms of p, as follow:

[tex]3p =2s\\s=\frac{3p}{2} \\[/tex]

Then we replace s in the equation 3 and we obtain v in terms of p:

[tex]5(\frac{3p}{2} )=2v\\\\2v=\frac{15}{2} p\\\\[/tex]

[tex]v=\frac{15}{2*2} p \\\\v=\frac{15}{4} p[/tex]

Now we replace v in the equation 1:

[tex]4c = \frac{4}{15} v[/tex]

[tex]c=\frac{1}{15} v[/tex]                    (4)

The equation 4 means that  1 chicken equals the fifteenth part of a cow. For this case the farmer needs 20 chikens, so we multiply per 20 each part of the equation 4:

[tex]20c = 20 * \frac{1}{15} v\\ \\\ 20c = \frac{20}{15}v = \frac{4}{3}v \\\\20c = 1.3333v[/tex]

As it is impossible to have 1.3333 cows, the answer  is 2 cows approximately.

Answer:

2

Step-by-step explanation:

To determine the amount of candy per sack, divide the total one fourth pound of rock candy by four, resulting in 1/16 pound of candy in each sack.

Demont has made one fourth pound of rock candy and needs to divide this equally into four sacks. To find the amount of candy in each sack, we divide the total amount of rock candy by the number of sacks.

Here's the calculation:

Total rock candy = 1/4 pound

Number of sacks = 4

Amount of candy per sack = 1/4 pound ÷ 4 = 1/16 pound per sack

Therefore, each sack will contain 1/16 pound of rock candy.

Answer:

-√(3/10)

Step-by-step explanation:

cos(x) = 2[cos(x/2)]² - 1

-2/5 = 2[cos(x/2)]² - 1

3/5 = 2[cos(x/2)]²

3/10 = [cos(x/2)]²

cos(x/2) = +/- sqrt(3/10)

Since x is in the 3rd quadrant, x/2 would be in the second quadrant.. so cos(x/2) is negative

[tex]x[/tex] is in quadrant III, so [tex]\pi<x<\frac{3\pi}2[/tex].

This makes [tex]\frac\pi2<\frac x2<\frac{3\pi}4[/tex], which means [tex]\frac x2[/tex] lies in quadrant II, for which we expect [tex]\cos\frac x2<0[/tex].

Recall the double-angle identity:

[tex]\cos^2\dfrac x2=\dfrac{1+\cos x}2[/tex]

[tex]\implies\cos\dfrac x2=-\sqrt{\dfrac{1-\frac25}2}=-\sqrt{\dfrac3{10}}[/tex]

Answer:

I) There are [tex]8.760\times 10^3[/tex] hours in 1 year.

II) The exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.

Step-by-step explanation:

Given : 1 hour=3600 seconds

1 year = 31556952 seconds.

To find :

I)  Use scientific notation to estimate the number of hours in one year.

1 day = 24 hours

1 year = 365 days

So, number of hours in one year is given by,

[tex]n=24\times 365[/tex]

[tex]n=8760[/tex]

In scientific notation,

[tex]8760=8.760\times 10^3[/tex]

So, there are [tex]8.760\times 10^3[/tex] hours in 1 year.

II) 1 year = 31556952 seconds.

1 hour = 3600 seconds

In one year the number of hour is given by,

[tex]n=\frac{31556952}{3600}[/tex]

[tex]n=8765.82[/tex]

In scientific notation,

[tex]8765.82=8.76582\times 10^3[/tex]

So, the exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.

III) In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.

Answer: the area of the original rectangle is 300 square meters.

Step-by-step explanation:

Let L represent the original length of the rectangle.

Let W represent the original width of the rectangle.

The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. This means that the length of the new rectangle is 2L and the width of the new rectangle is 3W

If the area of the new rectangle is equal to 1800 square meters, it means that

2L × 3W = 1800

6LW = 1800

LW = 1800/6

LW = 300 square meters

Answer:

Option B) 31.348  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 49

Sample standard deviation, s = 2.6 minutes

Population  standard deviation, [tex]\sigma[/tex] =  2.9 minutes

Significance level, [tex]\alpha[/tex] = 0.05

We have o find the test statistic.

Formula:

[tex]\chi^2 = \dfrac{(n-1)s^2}{\sigma^2}\\\\\chi^2 =\displaystyle\frac{(40-1)(2.6)^2}{(2.9)^2}\\\\\chi^2=31.348[/tex]

Thus, the test statistic is

Option B) 31.348

Answer:

Step-by-step explanation:

We are to find 62×1000

We can write in standard form

62×10³

6.2×10×10³

Using indices

a^m × a^n = a^(m+n)

Therefore,

6.2×10¹+³

6.2×10⁴

Using the normal multiplication

................1000

...............×. .62

...…......-------------

....., ... ..2 0 0 0

.......+.6 0 0 0

-------------------

..........6 2 0 0 0

----------------------

Answer:

  50% of market value

Step-by-step explanation:

The actual tax rate on the Combs home is ...

  $8719.38/$361800 = 0.0241 = 24.1 mils

The rate of assessment is ...

  (24.1 mils)/(48.2 mils) = 0.50 = 50%

The Combs pay tax on 50% of their home's market value.

Answer:

Boi

Step-by-step ex:

Answer:

Option 4

Step-by-step explanation:

x - 4 is negative for x < 4

Mod makes it positive,

-(x - 4) = 4 - x

4 - x for x < 4,

x - 4 for other x values (which are greater than/equal to 4)

Answer:

2884.8 millimeters squared

Step-by-step explanation:

Given:

The radius of the disc is 35 millimeters, so the area of it is:

π[tex]r^{2}[/tex] = 3.14*[tex]35^{2}[/tex] = 3846.5

Then, we find out the area of the circular hold cut out of the bigger one, its radius is a haft of the radius of the bigger circle = 35/2 = 17.5

π[tex]r^{2}[/tex] = 3.14*[tex]17.5^{2}[/tex] =961.6

=>  the area of the pendant = 3846.5  - 961.6  =2884.8 millimeters squared

The final result is the area of the pendant is 2887.1 mm².

To find the area of the pendant:

Therefore, the area of the pendant is 2887.1 mm².

Answer:

c= 1/26

Step-by-step explanation:

The joint probability mass function for X and Y must comply that:

[tex]\[\sum\]\sum\] c(x +y) = 1[/tex]   for  x∈{1,2,4} and  y∈{1,3}

thus, all the possible values for the pairs (x,y) are:

(1,1)  (1,3) (2,1) (2,3) (4,1) (4,3)

and then

c [(1+1)+(1+3)+(2+1)+(2+3)+(4+1)+(4+3)] = 1

c[26] = 1

c= 1/26

Answer:

Total amount of books in the bookcase =  225 books

Step-by-step explanation:

Each shelf is to have 15 books

Therefore total amount of books in the bookcase = {9×15} + {6×15} = 225 books

Answer:

y = 4/5x -3

Step-by-step explanation:

in order to do this :

use the formula :

[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]

= [tex]\frac{-5 + 5}{2} , \frac{-7 + 1}{2}[/tex]

midpoint =(0 , -3)

use the formula :

[tex]\frac{y2-y1}{x2-x1}[/tex]

= [tex]\frac{1-(-7)}{5-(-5)}[/tex]

=[tex]\frac{8}{10}[/tex]

simplified to 4/5

gradient = 4/5

formula for the equation of a line

(Y-y1) = m( X-x1)

now use the values of the midpoint and the gradient(m)

y +7 = 4/5 (x + 5)

y = 4/5x + 4-7

Answer:

y = 0.8x - 3

Step-by-step explanation:

Slope = (-7-1)/(-5-5) = -8/-10 = 0.8

When x = 5, y = 1

1 = 0.8(5) + c

1 = 4 + c

c = -3

y = 0.8x - 3

Answer:

Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.

Answer:

b m d j and k z y a

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) The retail price (r) is the wholesale price (w) plus 20% of that price plus $2.50:

  r = w + 0.20w + 2.50

  r = 1.20w + 2.50

__

b) Substituting w=8.40, we have ...

  r = 1.20·8.40 +2.50 = 12.58

The retail price of the chair is $12.58.

__

c) Substituting r=13.30, we have ...

  13.30 = 1.20w +2.50

  10.80 = 1.20w . . . . . . . subtract 2.50

  9.00 = w . . . . . . . . . . . . divide by 1.20

The wholesale price of the chair is $9.00.

Step-by-step explanation:

Below is an attachment containing the solution.

Final answer:

The dimensions are 24cm x 15cm x 20cm.

Explanation:

To find two possible sets of lengths and widths for the rectangular prism with a height of 20cm and a surface area of 2400cm2, we need to understand the formula for the surface area of a rectangular prism: SA = 2(lw + lh + wh). Here, l = length, w = width, and h = height.

Since we know the height (h = 20cm) and the surface area (SA = 2400cm2), we can set up the equation:

2(lw + 20l + 20w) = 2400

We will consider two cases: one where the length and width are equal (since that is a specific request), and another where they are not.

Case 1: Length and width are equal (l = w). We simplify the equation to:

2(l2 + 40l) = 2400

Solving for l gives us l = w = 20cm. Therefore, the dimensions are 20cm x 20cm x 20cm.

Case 2: Length and width are not equal. To find a possible set, we can assume a width and solve for the length:

Let's assume w = 15cm. Plugging this into the equation gives us:

2(l15 + 20l + 20 x 15) = 2400

Solving for l gives us l = 24cm.

Therefore, the dimensions are 24cm x 15cm x 20cm.

Answer:

This is true

Step-by-step explanation:

10x1 is 10. 10x10 is 100. but if u did 100x10 you would add the amount of zeros total. which would be 1000. so 400x10 is 4000

Answer:

Yes, the approximate length of one side is a prime number less than 25.

The approximate dimensions of the room are 19 ft by 18 ft.

Step-by-step explanation:

Assuming the dining room is rectangular in shape

Approximate area of the dining room = 342 ft^2

The area of a rectangle is calculated by multiplying the length of the rectangle by the width.

Assuming the approximate length is a prime number less than 25

The closest prime number to 25 is 19

Approximate length = 19 ft

Approximate width = approximate area ÷ approximate length = 342 ft^2 ÷ 19 ft = 18 ft

Approximate dimensions of the room = 19 ft by 18 ft

Answer:

Therefore, Jane can create 80 different dinners.

Step-by-step explanation:

We know that Jane must select three different items for each dinner she will serve. If at least one of the selections must be vegetarian.

The items are to be chosen from among five different vegetarian and four different meat selections.

First we count the number of combinations for one vegetarian dinner and 2 meat dinners.

[tex]C_1^5\cdot C_2^4=5\cdot \frac{4!}{2!(4-2)!}=5\cdot 6=30[/tex]

Now we count the number of combinations for 2 vegetarian dinner and 1 meat dinners.

[tex]C_2^5\cdot C_1^4=10\cdot 4=40\\[/tex]

Now we count the number of combinations for 3 vegetarian dinner.

[tex]C_3^5=\frac{5!}{3!(5-3)!}=10\\[/tex]

We get 30+40+10=80.

Therefore, Jane can create 80 different dinners.

Answer:

3840 cubic inches

Step-by-step explanation:

The volume of a rectangular prism is 960 cubic inches

Let the dimensions be lXwXh,

l=length of the base

w=width of the base

h=height of the base

The volume, lwh=960 cubic inches

If the dimensions of the base are doubled and the height remains the same

Volume of the new rectangular prism=2l X 2w X h =4lwh

=4 X 960 =3840 cubic inches

Answer:

1.19 revolutions per second.

Step-by-step explanation:

Given:

A rotating object makes 5/6 of a revolution in 7/10 second.

To find:

Find the approximate speed in revolutions per second ?

Solution:

As here given that a rotating object makes 5/6 of a revolution in 7/10 second,

we will have to find that in one second how many revolution does this object make:

By unitary method:

In [tex]\frac{7}{10}[/tex] second, a rotating object makes = [tex]\frac{5}{6}[/tex]  revolution

In 1 second, a rotating object makes = [tex]\frac{5}{6}\div\frac{7}{10}[/tex]

                                                            [tex]=\frac{5}{6}\times\frac{10}{7} = \frac{50}{42}=1.190\ revolution[/tex]

Therefore, the approximate speed of object is 1.19 revolution per second.

We can also find by, [tex]speed = \frac{distance}{time}[/tex]

                                            [tex]=\frac{5}{6} \div\frac{7}{10} \\=\frac{5}{6} \times\frac{10}{7} =\frac{50}{42} = 1.19[/tex]

We can use any one to solve this type of question:

Finally, the approximate speed is 1.19 revolutions per second.

Answer:

Step-by-step explanation:

I think the photo below is your full question and my answer is presented in that too.

We create a table of values:

p      c

0      5

1       6

2       7

Then draw on the graph.

Hope it will find you well

The domain is the X value ( input).

The line starts at (0,2) so 0 is the first part of the domain. The horizontal line has an arrow on it pointing to the right which means the line can continue to infinity.

The answer is the second choice, 0 to infinity

Answer:

This system have 9000 different numbers.

Step-by-step explanation:

We know that the internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0.

We have total 10 digits.

In the first place we have 9 possibilities, because from the conditions of the task in the first place there cannot be 0.

In second, third and fourth place we have 10 possibilities.

Therefore, we get

[tex]N=9\cdot 10\cdot10 \cdot 10=9000[/tex]

This system have 9000 different numbers.

In this phone system, there are 9,000 different internal telephone numbers that can be assigned.

The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. To find the number of different numbers that can be assigned in this system, we need to consider the possibilities for each digit position. Since the first digit cannot be 0, there are 9 choices (1 through 9) for the first digit. For the remaining three digits, each digit can be any number from 0 to 9, resulting in 10 choices for each of the three remaining digits. Therefore, the total number of different numbers that can be assigned in this system is

9 * 10 * 10 * 10 = 9,000.

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