Dave's sister baked $3$ dozen pies of which a third contained chocolate, a quarter contained marshmallows, a sixth contained cayenne, and one twelfth contained salted soy nuts. What is the smallest possible number of pies that had none of these ingredients?

Answer:

189

Step-by-step explanation:

Answer: The diver is 23 feet under sea level

Step-by-step explanation:

If we draw a vertical number line (image attached), where point 0 is sea level (the diver's initial position), the first point under sea level is -20, since we are told it dives a distance of 20 ft (the negative sign is only to indicate the direction, since a distance cannot be negative).

Then, the diver goes 10 ft deep. This means now it is 30 ft under sea level and the second point is -30.

After that the diver swims up 12 ft, hence we have to count 12 points up in our number line and the corresponding point is -18.

Finally, the diver swims 5 ft lower and keep that position. Hence, we have to count 5 points below point -18 in the number line, resulting in the last point: -23.

This means the diver's final position is 23 feet under sea level.

If we want to prove it with numbers, we can do it as follows:

20 ft (down)+10 ft (down)-12 ft (up)+5 ft (down)=23 ft

Answer: Doubling the radius.

Step-by-step explanation:

The volume of a cone can be found with the following formula:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height of the cone.

Let's find the volume of the conical tent with a radius of 10.4 feet and a height of 8.4 feet.

Identifiying that:

[tex]r=10.4\ ft\\\\h=8.4\ ft[/tex]

You get this volume:

[tex]V_1=\frac{1}{3}\pi (10.4\ ft)^2(8.4\ ft)\\\\V_1=951.43\ ft^3[/tex]

If you double the radius, the volume of the conical tent will be:

[tex]V_2=\frac{1}{3}\pi (2*10.4\ ft)^2(8.4\ ft)\\\\V_2=3,805.70\ ft^3[/tex]

When you divide both volumes, you get:

[tex]\frac{3,805.70\ ft^3}{951.43\ ft^3}=4[/tex]

Therefore, doubling the radius will quadruple the volume of the tent.

Answer: the answer would be B. ( 18y+35x over 15xy

Barney can make 3 costumes from the total fabric.

Step-by-step explanation:

Given,

Amount of fabric Barney has = [tex]16\frac{1}{5}=\frac{81}{5}\ yards[/tex]

Amount of fabric required for an elf costume = [tex]5\frac{2}{5}=\frac{27}{5}\ yards[/tex]

Let,

x represent the number of costumes that can be make from total fabric.

[tex]\frac{27}{5}x=\frac{81}{5}[/tex]

Multiplying both sides by 5/27

[tex]\frac{5}{27}*\frac{27}{5}x=\frac{81}{5}*\frac{5}{27}\\\\x=\frac{81}{27}\\\\x=3[/tex]

Barney can make 3 costumes from the total fabric.

Keywords: fraction, multiplication

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The shoot would last eight hours, and the cost would be $699 whether the photographer hires Craig or Kaya.

This question can be solved using algebra, particularly the concept of system of equations, where we set two linear cost equations equal to each other to find out when they cost the same. Given: Craig's cost is $195 + $63p, and Kaya's cost is $171 + $66p, we form an equation $195 + $63p = $171 + $66p. Subtracting $171 and $63p from both sides leaves us with $24 = $3p. So, dividing both sides by $3, we get p = 8.

This means the photo shoot would last 8 hours, and the cost would be either Craig's or Kaya's cost for 8 hours, which is $195 + $63*8 = $699 or  $171 + $66*8 = $699.

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The cost for the photo shoot would be $699, and the duration of the shoot would be 8 hours.

Let's denote:

- [tex]\( C_C \)[/tex]: Total cost if the photographer hires Craig.

- [tex]\( C_K \)[/tex]: Total cost if the photographer hires Kaya.

- [tex]\( h \)[/tex]: Number of hours of the photo shoot.

Given the charges:

- Craig charges $195 for showing up, plus $63 per hour.

- Kaya charges $171 for showing up, plus $66 per hour.

The equations for the total cost [tex]\( C_C \)[/tex] and [tex]\( C_K \)[/tex] are:

[tex]\[ C_C = 195 + 63h \][/tex]

[tex]\[ C_K = 171 + 66h \][/tex]

The photographer realizes that the costs are the same, so:

[tex]\[ C_C = C_K \][/tex]

Substitute the expressions:

[tex]\[ 195 + 63h = 171 + 66h \][/tex]

Now, solve for [tex]\( h \)[/tex]:

[tex]\[ 195 - 171 = 66h - 63h \][/tex]

[tex]\[ 24 = 3h \][/tex]

[tex]\[ h = \frac{24}{3} \][/tex]

[tex]\[ h = 8 \][/tex]

So, the duration of the photo shoot is 8 hours.

Now, substitute [tex]\( h = 8 \)[/tex] back into either equation to find the cost:

Using [tex]\( C_C \)[/tex]:

[tex]\[ C_C = 195 + 63 \cdot 8 \][/tex]

[tex]\[ C_C = 195 + 504 \][/tex]

[tex]\[ C_C = 699 \][/tex]

Using [tex]\( C_K \)[/tex]:

[tex]\[ C_K = 171 + 66 \cdot 8 \][/tex]

[tex]\[ C_K = 171 + 528 \][/tex]

[tex]\[ C_K = 699 \][/tex]

The coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

Next, we need to reflect ∆CDE across the line x = 0. This me The vertices of ∆CDE are C(–5, 3), D(–6, 1), and E(–1.5, 2). Which figure shows the image of ∆CDE for a glide reflection where the translation is (x, y) → (x, y – 3) and the line of reflection is x = 0?

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

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The statements which are true are:

(6, 6) is the midpoint of CD

(4, 3) is the intersection point of diagonals of parallelogram

Solution:

The mid point (x,y) = [tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

A(-2, -1) and B(6, 1)

[tex]\text{ midpoint of AB } = (\frac{-2+6}{2} , \frac{-1+1}{2})\\\\\text{ midpoint of AB } = (2, 0)[/tex]

Thus statement 1 is wrong

B(6, 1) and C(10, 7)

[tex]\text{ midpoint of BC } = (\frac{6+10}{2} , \frac{1+7}{2})\\\\\text{ midpoint of BC } = (8, 4)[/tex]

Thus statement 2 is wrong

Here ,

[tex]x_1[/tex] = 10

[tex]x_2[/tex]= 2

[tex]y_1[/tex]= 7

[tex]y_2[/tex]=5

now substituting these values,

mid point of CD  = [tex](\frac{10+2}{2},\frac{7+5}{2})[/tex]

mid point of CD  = [tex](\frac{12}{2},\frac{12}{2})[/tex]  

mid point of CD  = [tex](6, 6)[/tex]

Therefore (6, 6) is the midpoint of CD

Statement 3 is correct

A = (-2, -1) and D = (2, 5)

[tex]\text{ mid point of AD } = (\frac{-2+2}{2} , \frac{-1+5}{2})\\\\\text{ mid point of AD } = (0, 2)[/tex]

Thus statement 4 is wrong

Let AC and BD be the diagonals of parallelogram

The diagonals of a parallelogram bisect each other, therefore, the point of intersection is the midpoint of either.

Midpoint of AC:

A = (-2, -1) and C(10, 7)

[tex]\text{ Midpoint of AC } = (\frac{-2+10}{2} , \frac{-1+7}{2})\\\\\text{ Midpoint of AC } = (4,3)[/tex]

Thus statement 5 is correct

Max needs to run 15 laps around the track.

Step-by-step explanation:

Given,

Distance Max wants to run = 512 miles

Length around the track = 34 mile

34 miles = 1 lap

1 mile = [tex]\frac{1}{34}\ laps[/tex]

512 miles = [tex]\frac{1}{34}*512[/tex]

512 miles = 15.06 laps

Rounding off to nearest whole number;

512 miles = 15 laps

Max needs to run 15 laps around the track.

Keywords: unit rate, division

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Each friend should contribute $196.5 towards the party supplies.

To solve this problem, we need to follow these steps:

1. Calculate the total cost of all party supplies:

  - 100 balloons cost $720

  - 100 plates cost $475

  - 100 cups cost $5.45 each

  - 100 napkins cost $2.09 each

  - 10 invitations cost $1.60 each

  - We need to find the cost of the plastic punchbowl.

2. Find the cost of the plastic punchbowl:

  - To find the cost of the plastic punchbowl, we subtract the total cost of the known items from the total cost of all party supplies.

3. Calculate the total cost of all party supplies:

  - Calculate the cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]

  - Calculate the cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]

  - Sum up the costs of all known items.

4. Find the cost per friend:

  - Once we have the total cost of all party supplies, we divide this total by the number of friends (10) to find out how much each friend should contribute equally.

Let's calculate step by step:

1. Calculate the total cost of all party supplies:

  - Cost of 100 balloons: $720

  - Cost of 100 plates: $475

  - Cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]

  - Cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]

  - Cost of 10 invitations: [tex]\(10 \times \$1.60\)[/tex]

  - Total cost of known items [tex]= \(720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)\)[/tex]

2. Find the cost of the plastic punchbowl:

  - Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl

3. Calculate the total cost of all party supplies:

  - [tex]\(100 \times \$5.45 = \$545\)[/tex]

  - [tex]\(100 \times \$2.09 = \$209\)[/tex]

  - [tex]\(10 \times \$1.60 = \$16\[/tex]

  - Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16\)[/tex]

4. Find the cost per friend:

  - Total cost of all party supplies / Number of friends = Cost per friend

Let's compute these steps to find the solution.

Let's calculate step by step:

1. Calculate the total cost of all party supplies:

  - Cost of 100 balloons: $720

  - Cost of 100 plates: $475

  - Cost of 100 cups: [tex]\(100 \times \$5.45 = \$545\)[/tex]

  - Cost of 100 napkins: [tex]\(100 \times \$2.09 = \$209\)[/tex]

  - Cost of 10 invitations: [tex]\(10 \times \$1.60 = \$16\)[/tex]

  - Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16 = \$1965\)[/tex]

2. Find the cost of the plastic punchbowl:

  - Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl

  - Total cost of all party supplies  - $1965 = Cost of plastic punchbowl

3. Calculate the total cost of all party supplies:

  - Total cost of all party supplies = [tex]720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)[/tex] = 720 + 475 + 545 + 209 + 16 = $1965

4. Find the cost per friend:

  - Total cost of all party supplies / Number of friends = Cost per friend

  - [tex]\( \frac{\$1965}{10} = \$196.5 \)[/tex]

So, each friend should contribute $196.5 towards the party supplies.

the complete Question is given below:

For a party, 10 friends are buying 100 cups, 100 plates, a punchbowl, and 200 balloons. If the friends share the cost equally, how much should each friend contribute? Party Supplies 100 balloons $720 100 plates $475 100 cups $5.45 100 napkins $2.09 What steps do you need 10 invitations $1.60 to solve to find the plastic punchbowl

Answer:

D) Implement better procedures at the security gate.

Step-by-step explanation:

Answer:

The scale factor is 2.

Step-by-step explanation:

Take the vertical sides of the 2 triangles.

Their length is 3 and 6 so the scale factor is 6/3 = 2.

Also we see than the horizontal lines are in the same ratio 4 : 2  = 2:1.

Answer: 6x^2-5x+5

Step-by-step explanation:

Answer:

6x^2-5x+5

Step-by-step explanation:

Essentially, you just put the two in a column:

7x^2−6x+5

- y

=x^2-x

("y" represents answer)

Answer:

altitude

Step-by-step explanation:

Answer:

Circumcenter describes the point equidistant to the refrigerator, stove and the sink

Step-by-step explanation:

The basic construction of the circumcenter is to identify the midpoints of the original triangle. This circumcenter is the point where all the perpendicular bisector of the sides of the triangle intersects. For an triangle that is  acute-angled, its circumcenter will lie inside the triangle. For an obtuse-angled triangle, the circumcenter lies outside of the triangle

, In a right-angled triangle, Circumcenter lies at the midpoint of the hypotenuse side of triangle.

To Find the circumcenter of the triangle

Answer:

Circumcenter

Step-by-step explanation:

Answer: B. on e2020

Step-by-step explanation:

The transformation of parent function to h(x) = - ∛x + 3 is such that it is reflected over the horizontal axis, and then translated up 3 units.

The correct option is B.

Transformations are changes done in the shapes on a coordinate plane by rotation or reflection or translation.

Given function,

h(x) = - ∛x + 3

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis

Parent Function: f(x) = ∛x

Horizontal Shift: None

Vertical Shift: Up 3 Units

Reflection about the x-axis:

f(x) → -f(x)

∛x → - ∛x  

Reflection of the function is over x - axis.

Hence, the transformation from the parent equation to given function can be found  by reflecting over X- axis and translate up 3 units.

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Answer:

There are 7 chairs in each row.

Step-by-step explanation:

Hue is arranging some number of chairs. If she arranges them in 6 rows of equal lengths then there will be 3 chairs leftover, or she arranges them in 8 rows of that same length then she requires 11 more chairs.

Let us assume that there are P numbers of chairs and there are x chairs in each row.

Therefore, we can write that  

6x + 3 = P ....... (1) and  

8x = P + 11  

⇒ 8x - 11 = P ........ (2)

Now, from equations (1) and (2) we get,

6x + 3 = 8x - 11

⇒ 2x = 14

⇒ x = 7

Therefore, there are 7 chairs in each row. (Answer)

Answer:

R= {y|y>=1}

Step-by-step explanation:

D = all real numbers R= {y|y>=1}.

All polynomials have domain of all real numbers.

For the range, the vertex format is useful;

Y= (X-1)^2 + 1

Since (X-1) is never less than zero, Y>=1.

That is where the vertex is, at Y=1

Answer: 18

Step-by-step explanation:

1.We must total 14 and 22 (14+22) that brings the number of post which is 36.

2.The we must divide 36 by 2 (36÷2). It said two stacks that is why the division by 2 comes in place and it gives us our answer 18

Answer:

215

Step-by-step explanation:

215

3

647

6

04

 3

 17

 15

   2

hope this helped

Answer:

y=80x+50 for the one time service fee.

Anytime after that would be y=80x

Step-by-step explanation:

Y is how much the total is and 80 is how much it is an hour. X is the number of hours worked. With the first time fee of $50, your equation would be y=80x+50. Anytime after that, excluding the “one time fee,” the equation would be y=80x.

Answer: The nearest whole number to 6.58 would be 7.

Step-by-step explanation: The whole number 7 is closer to 6.58 than any other whole number. Hence, 6.58 rounded to the nearest whole number would be 7.

Answer:

[tex]\large \boxed{\math{8\frac{1}{4}}\text{ km}}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{lcll}2\frac{1}{5} \times 3\frac{3}{4} & = & \dfrac{11}{5} \times \dfrac{15}{4} & \text{Converted the mixed numbers to improper fractions}\\\\& = & 11 \times\dfrac{3}{4}& \text{Cancelled the 5s}\\\\& = & \dfrac{33}{4}& \text{Multiplied numerators and denominators}\\\\& = &\mathbf{8\frac{1}{4}} & \text{Converted the mixed number to a fraction}\\\end{array}\\\text{The length of the road is }\large \boxed{\mathbf{8\frac{1}{4}}\textbf{ km}}}[/tex]

There are triangles ΔABC, ΔFDE, and ΔGIH must be congruent. The correct answer is option A.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

In the given information, we can see that AB is congruent to both DF and GI, and BC is congruent to HI. Also, we know that ∠B is congruent to both ∠D and ∠G.

Using these properties, we can conclude that triangles ABC and FDE are congruent by the Side-Angle-Side (SAS) congruence theorem, since AB is congruent to DF, BC is congruent to DE, and ∠B is congruent to ∠D.

Similarly, we can conclude that triangles ABC and GIH are congruent by the Side-Side-Side (SSS) congruence theorem since AB is congruent to GI, BC is congruent to HI, and AC is congruent to GH.

Therefore,  ΔABC, ΔFDE, and ΔGIH must be congruent.

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Final answer:

Gary spends approximately 54.29% of his free time on video games and the internet.

Explanation:

To find the percentage of free time that Gary spends on video games and the internet, we need to calculate the total number of hours he spends on these activities and divide it by the total number of hours of free time he has.

First, calculate the total number of hours Gary spends on video games and the internet: 10 + 9 = 19 hours.

Next, calculate the total number of hours Gary has for free time in a week: 5 hours per day x 7 days = 35 hours.

To find the percentage, divide the total number of hours spent on video games and the internet by the total number of hours of free time and multiply by 100: (19 / 35) x 100 = 54.29%.

Therefore, Gary spends approximately 54.29% of his free time on video games and the internet.

To find the percentage of free time that Gary is using to play video games and use the internet, calculate the total free time and the proportion of time spent on video games and internet use.

To find the percentage of free time that Gary is using to play video games and use the internet, we need to calculate the total amount of free time Gary has and then determine the proportion of that time spent on video games and internet use.

Gary spends 10 hours per week on the internet and 9 hours per week on video games. This is a total of 10 + 9 = 19 hours per week.

Since Gary has 5 hours of free time per day, he has a total of 5 * 7 = 35 hours of free time per week.

To find the percentage, we divide the time spent on video games and internet use (19 hours) by the total free time (35 hours) and then multiply by 100. So, the percentage is (19/35) * 100 = 54.28% (rounded to two decimal places).

7.8 6.8 and 5.8

Is what they forgot to put

Answer is 7.8

Answer:

r=-2

Step-by-step explanation:

difference in y/difference in x =slope

-r-8/1-2=-9

-r-8=-9*-1

-r=10+8

r=-2

The GCF of given terms is: 2z

Step-by-step explanation:

A largest factor that is shared by all given terms is called greatest common factor.

So,

Given terms are:

4z , 6z^3

Factoring the terms

[tex]4z = 2.2.z\\6z^3 = 2.3.z.z.z[/tex]

The common factors in both terms are: 2 and z

So,

The GCF of given terms is: 2z

Keywords: GCF, factors

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Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

(x+4)/3=6

Multiply by 3 on both sides

x+4=18

Subtract 4 from both sides

x=14

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