Derek shopping for hot dogs and buns. He is surprised to find that the hot dogs come in
packs of 8, while the buns come in packs of 12. How many hot dogs and buns will Derek
have to buy if he wants to have the same number of each?

Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

=====================================

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

6.0x74=444

4.5x80=360

5.1 x 78 = 397.8

1.9 x 70=133

\(y=-6x+12\\\\\text{When}~ x = -1\\\\y=-6(-1)+12 = 6+12 = 18\)

Answer:

3

Step-by-step explanation:

Plug in 6 for the y value. Solve for x.

Answer:

x=3 (3,6)

Step-by-step explanation:

Y = 15 - 3x

Y = 6

6= 15-3x

-15 from each side

-9 = -3x

devide each side

ny -3

x=3

(check)

15-3(3) = 6

The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.

To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

Scale factor = Length of corresponding side in D' / Length of corresponding side in D

For the corresponding sides, we have:

Scale factor = 6/18 = 1/3

Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.

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A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

The area of AEDC is 25 cm². Therefore,

AEDC = AC²

25 cm² = AC²

AC = 5 cm

In ΔABC,

AB² + BC² = AC²

Since AB=BC,

2(AB²) = AC²

AB² = 25/2

AB = 5/√2 cm

Hence, the length of side AB is 5/(√2) cm.

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9514 1404 393

Answer:

  {x ∈ ℕ : 15 ≤ x ≤ 23}

  {15, 16, 17, 18, 19, 20, 21, 22, 23}

Step-by-step explanation:

This "set-builder notation" tells you the set consists of natural numbers between 15 and 23, inclusive. In this notation, the colon (:) and vertical bar (|) are interchangeable.

  {x ∈ ℕ : 15 ≤ x ≤ 23}

__

This "roster form" lists all of the elements of the set, the integers between 15 and 23, inclusive.

  {15, 16, 17, 18, 19, 20, 21, 22, 23}

Answer:

Option C

Step-by-step explanation:

Zeros of a function are also called as x-intercepts of a function, which means where the graph/function intersects the x-axis.

In the image we see the graph intersects the x-axis at three points

x=0 , x=2 , x=4 so our answer is option C

The roots or zeros of the graphed function f(x) are 0, 2 and 4.

The x - intercepts of the graph of the function gives the zeros of the function. It is at this value that the dependent variable [y] is zero.

Given is a graph of a function f(x).

The graph of the function f(x) is shown. The total number number of x - intercepts will tell us about the degree of the function which is equal to three. The degree of a function also represents the total number of possible solutions or zeros of the function and the values of the x - intercepts will be the zeros of the function. The graph of the function cuts the x - axis at x = 0, x = 2 and x = 4.

So, we can conclude that the graph has a degree of 3 and the possible roots or zeros of this function f(x) are x = 0, x = 2 and x = 4 repsectively.

Therefore, the roots or zeros of the graphed function are 0, 2 and 4.

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Answer:

the number of possible reading schedules is 1.064301638 × 10¹²

Step-by-step explanation:

Given that :

The English teacher needs to pick 10 books to put on her reading list for the next school year.

If the English teacher picks at most  3 poetry books i.e no  more than 3 poetry books from 8 books. and other books are picked from (6+4+4 ) = 14 books

Thus; the number of ways to pick the books are :

\(\left[\begin{array}{c}8\\0\\ \end{array}\right] \ \left[\begin{array}{c}14\\10\\ \end{array}\right]+ \left[\begin{array}{c}8\\1\\ \end{array}\right] \left[\begin{array}{c}14\\9\\ \end{array}\right] + \left[\begin{array}{c}8\\2\\ \end{array}\right] \left[\begin{array}{c}14\\8\\ \end{array}\right] + \left[\begin{array}{c}8\\3\\ \end{array}\right] \left[\begin{array}{c}14\\7 \\ \end{array}\right]\)

\(= [ \dfrac{8!}{0!(8-0)!}* \dfrac{14!}{10!(14-10!)} ] + [ \dfrac{8!}{1!(8-1)!}* \dfrac{14!}{9!(14-9)!}]+ [ \dfrac{8!}{2!(8-2)!}* \dfrac{14!}{8!(14-8)!}] + [ \dfrac{8!}{3!(8-3)!}* \dfrac{14!}{7!(14-7)!}]\)

\(= [ 1*1001]+[8*2002]+[28*3003]+[56*3432]\)

\(\mathbf{= 293293}\)

However, to determine how many reading schedules that are possible we use the relation:

Number of ways to pick a book × \(^{10}P_{10}\)

\(= 293293* \dfrac{10!}{(10-10)!}\)

= 293293 ×  10!

= 1.064301638 × 10¹²

Thus , the number of possible reading schedules is 1.064301638 × 10¹²

Answer:

19 topings

t=(13.5-4)/.5

Step-by-step explanation:

13.5-4

=9.5

9.5/.5

=19

Step-by-step explanation:

7/2

=3.5

10/8

=1.25

Hence, 3.5>1.25

Therefore, 7/2>10/8

Answer:

Ok, So....

Step-by-step explanation:

Since m3=74 that must mean that m4 and m1 are 74 because they are vertical angles. and since m2 is a vertical angle of m1 it is also 74. Then you have m8 m6 m7 m5 which are suplementary to them meaning they sum to 180 and since m3+m8=180, 74+m8=180. m8=180-74.

m8=m7=m6=m5= 106

I hope this helped!

The point where two lines meet is known as an angle.

From the diagram shown, we can see that l is parallel to m

Given

Based on geometry:

m<3 = m<4 = 74 degrees (vertically opposite)

m<3 = m<1 = 74 degrees (corresponding angles)

m<1 = m<2 = 74degrees (vertically opposite angles)

m<1 and <6 are supplementary, that is:

m<1 + m<6 = 180

74 + m<6 = 180

m<6 = 180 - 74

m<6 = 106degrees

Similarly:

m<2 and <5 are supplementary, that is:

m<2 + m<5 = 180

74 + m<5 = 180

m<5 = 180 - 74

m<5 = 106degrees

Also, m<4 and <7 are supplementary, that is:

m<4 + m<7 = 180

74 + m<7 = 180

m<7 = 180 - 74

m<7 = 106degrees

m<7 = m<8 = 108 degrees (vertically opposite angles)

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The number which is not the part of the solution set to the inequality below is 27.

Given inequality is,

w - 10 ≤ 16

WE have to find the solution for the inequality.

Adding both side of the inequality with 10,

w - 10 + 10 ≤ 16 + 10

w ≤ 26

So the solution of the inequality consists of all the points which are less than or equal to 26.

So it contains 11, 15 and 26.

It does not contain 27.

Hence the solution does not contain 27.

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Answer:

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

Step-by-step explanation:

Area of square x^2

area of rectangle is given by length * width

Length of rectangular strip = x

width of rectangular strip = 2

area of rectangular strip =  length * width = 2*x = 2x

Area of square piece of paper when  rectangular strip is taken away from it

= Area of square - area of rectangular strip

= \(x^2 -2x\)

It is given that Area of square piece of paper when  rectangular strip is taken away from it is 120 square units.

Thus,

\(x^2 -2x = 120\\=> x^2 -2x -120 = 0\\=> x^2 -12x +10x-120\\=> x(x-12) +10(x-12)\\=> (x+10)(x-12) = 0\\\\\)

Thus,

either x+10 = 0 or x -12= 0

x = -10 or x = 12

but length cannot  be negative hence neglecting x = -10

hence value of x is 12.

Hence,

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

The probability that 200 or fewer homes were purchased as investment properties is 0.937. This is calculated using the binomial distribution formula, where n = 600, p = 0.31, and x = 200.

1. The binomial distribution formula for calculating the probability of an event occurring is:

P(x) = nCx * p^x * q^(n-x)

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1 - p).

2. In this problem, n = 600, p = 0.31, x = 200, and q = 1 - 0.31 = 0.69.

3. Plugging these values into the formula, we get:

P(x) = 600C200 * 0.31^200 * 0.69^400

4. Solving this equation, we get P(x) = 0.937.

5. Therefore, the probability that 200 or fewer homes were purchased as investment properties is 0.937.

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Answer:

To convert a ratio into the form of a percentage

Answer:

Answer:

What do we have to do in this? Find x? Let me know I'll explain it in the comment section

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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Answer:

86493225

Step-by-step explanation:

Hope it helps

\(_____________________________________\)

\(\sf\huge\underline\red{SOLUTION:}\)

Use formula:

\(\sf{V = \pi(\frac{d}{2})^2h}\)

Solving for diameter:

\(\sf d = 2 \times \sqrt{ \frac{V}{\pi h} } \\ \sf = 2 \times \sqrt{ \frac{40}{\pi \times 1800} } \approx0.16821 \\ = \sf \large\boxed{\sf{\green{d = 0.17}}}\)

\(\sf\huge\underline\red{FINAL \: ANSWER}\)

\(\large\boxed{\sf{\green{d=0.17}}}\)

\(_____________________________________\)

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢ

Answer:

C; Basketball

Step-by-step explanation:

Although Greg Ridley wants to play for the Scorpions when he grows up, he learns along the way that there are things that are more important, hence the use of the term "treasure."

He learns from this that memories, friendships, and family are all that matters and if having to let go of basketball to sustain the aforementioned elements (which may or may not be an easy thing to do), then it is much more of a necessity than a choice.

Hope this helped! :D

Answer:

330 cm^3

Step-by-step explanation:

Volume of figure=Volume of the cuboid+Volume of the other cuboid

Volume of figure=240+90=330

Answer:

Refer the photos above and have a good day

Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

The percentage population increase from 2001 to 2011 is 50%.

To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.

The formula to calculate the percentage increase is:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

Plugging in the values:

Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%

Therefore, the percentage population increase from 2001 to 2011 is 50%.

Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.

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The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

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