A circus is composed of acrobats, ballerinas, clowns, and dogs. The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Twice the combined number of acrobats and ballerinas is five more than three times the number of clowns. If the number of dogs is one more than the number of clowns, how many people and animals belong to the circus

Answer:

[tex]\boxed{192~cupcakes}[/tex]

Step-by-step explanation:

dozen = 12

3 × 12 = 36 cupcakes

I.

36 cupcakes ----------------  90 minutes

                x    ----------------  60 minutes

[tex]x=\dfrac{36\cdot 60}{90 } ~ cupcakes\\\\x=24~cupcakes[/tex]

II.

24 cupcakes ---------------------- 60 minutes = 1 hour

          y         ----------------------    8 hours

[tex]y=\dfrac{8\cdot 24 }{1} ~cupcakes\\\\\boxed{y=192~cupcakes}[/tex]

They will produce 192 cupcakes in 8 hours.

Answer:

Step-by-step explanation:

Answer:

9% only a guess.May not be correct..

Answer:

a. 6x^5- 3x^3+ 21

b. (6x^5+ 4x^4+21) -  (4x^5+ 3x^4+11)=  2x^5+ x^4+10 

Step-by-step explanation:

The degree of the polynomial is the highest power of the terms of the polynomial .e.g

x³+ 2ax+ b² is a polynomial of 3rd degree because the highest power of the terms given is 3.

As we need a polynomial of 5th degree the highest power will be

5.6x^5+ 4x^4+ 3x^3+ 5x^2+ x+21

But this polynomial has 5 terms. We need a 5th degree polynomial with three terms so it can be any one of the following

6x^5- 3x^3+ 21

6x^5+ 4x^4+21

6x^5+  5x^2+21

6x^5 + x+21

All of the above polynomials are in the standard form because the powers of the terms are given in decreasing order. The first term has the highest power and so on.

Part B:

Suppose we have 2 polynomials 

6x^5+ 4x^4+21 and 4x^5+ 3x^4+11

When the closure property of subtraction is applied 

(6x^5+ 4x^4+21) -  (4x^5+ 3x^4+11)

= 6x^5+ 4x^4+21 -  4x^5- 3x^4-11  → coefficients are changed b/e of subtraction

= 2x^5+ x^4+10 

the coefficients are changed because of subtraction.

In Polynomials the sign is changed due to subtraction and  same degree terms ( like terms) are subtracted to get the answer.

ΔFGH is congruent to ΔFJH They are not congruent because only one pair of corresponding sides is congruent.

The correct option is (C)

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Given:

ΔFGH and ΔFJH share common side FH. Sides FG and GH are congruent.

As, per the information, it can be seen that the triangles are not congruent as one pair of corresponding side is not congruent.

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Answer: C

Step-by-step explanation: edge

The true options include the following:

This is defined as a pictorial representation of data or variables in an organized manner.

Function f(x) = (x + 4)(x – 6)

Graph intersects the x-axis at points (-4,0) and (6,0).

x-coordinate of vertex = -4+6/2 = 1

y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25

The vertex is at the point (1,-25).

The graph is positive for all x< -4 or x>6.

The graph is negative for –4 < x < 6.

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Answer:

5

Step-by-step explanation:

........................

Answer:

If Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.

Then she needs to cook 5 pounds of pasta if she has 2.5 quarts of sauce.

Step-by-step explanation:

Step 1 of 2

Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.

If one quart of sauce calls for two pounds of pasta,

Then to find how much pasta is needed for 2.5  quarts of sauce we need to form a proportion.

Let the pounds of pasta needed be x .

[tex]$$\begin{aligned}\frac{\text { pasta }(\text { inPounds })}{\text { Sauce }(\text { inQuarts })} &=\frac{\text { pasta }(\text { inPounds })}{\text { Sauce(inQuarts })} \\\frac{2}{1} &=\frac{x}{2.5}\end{aligned}$$[/tex]

Multiplying both sides by 2.5 we get,

[tex]$$\begin{aligned}\frac{2}{1} \times 2.5 &=\frac{x}{2.5} \times 2.5 \\x &=2 \times 2.5 \\x &=5\end{aligned}$$[/tex]

Step 2 of 2

To check if the answer is reasonable, we substitute it back in the formed proportion

[tex]$\frac{2}{1}=\frac{x}{2.5}$$[/tex]

We found x=5 hence,

[tex]$$\begin{aligned}\frac{2}{1} &=\frac{5}{2.5} \\2 &=2\end{aligned}$$[/tex]

Here, LHS =RHS

Hence, our answer is correct.

Answer:

12

Step-by-step explanation:

This is a special triangle with angle measure 45-45-90

The side lengths for this special right triangle is as follows:

The side length that sees angle measure 90 is represented by a[tex]\sqrt{2}[/tex]

The side lengths that see angle measures 45 is represented by a

We can see from the image hypotenuse (the side that sees angle 90)

is given as 12[tex]\sqrt{2}[/tex] that means a = 12

So the missing side lengths (both see angle measure 45) = 12

Serena should focus on a certain amount and track her spending. Option B

From the information given, Serena wants to reduce debt and to do this she needs to pay attention on how she borrows and the possible way to pay her debts.

Some possible ways to reduce debts include;

Thus, Serena should focus on a certain amount and track her spending. Option B

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Answer:

Angle CAE is congruent to angle    CBE  

Angle CBF is congruent to angle    CAF  

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

Explanation:

Angle CAE is an inscribed angle that subtends the minor arc CE

Minor arc CE is the distance around the circle from C to E following the shorter path. All minor arcs are smaller than 180 degrees.

What other inscribed angle also subtends minor arc CE? That would be inscribed angle CBE

Notice that CAE and CBE both have "C" and "E" as the first and last items. The only change is the middle letter. This is a quick nonvisual way to determine inscribed angles.

Recall that if two inscribed angles subtend the same arc, then they are congruent. Therefore, angle CAE is congruent to angle CBE

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

For similar reasoning, angles CBF and CAF are congruent inscribed angles that subtend minor arc CF.

For more information, check out the inscribed angle theorem. Also I recommend using GeoGebra as a handy tool.

Answer:

b = 4.5

Step-by-step explanation:

a = 4

c = 6

c² = a² + b²

6² = 4² + b²

36 = 16 + b²

b² = 36 - 16

b² = 20

[tex]b = \sqrt{20} [/tex]

b = 4.5

Answer: one

Step-by-step explanation:

     When a system of equations is graphed the solutions are the point of intersections. Here, we only have one point of intersection since these are both linear equations. That means there is only one solution.

The perimeter of the inside of the track is 444.44m

Based on the information given, the length will be 150m and the width is 46m.

The circumference will be:

=2πr

= (2 × 3.14 × 46/2)

= 144.44

The length will be:

= 2 × 150

= 300

The perimeter of the oval will be:

= 300 + 144.44

= 444.44m

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The graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x

From the table of values, we can see that:

As the time increases, the distance increases

However, the increment in the distance is not a linear increment.

This means that:

The graph (b) represents an exponential model.

When the points on the table are entered in a graphing calculator, we have the regression equation to be

y = 1.030 * 3.709^x

Hence, the graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x

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1. x = a

2. y = b

3. It has an undefined slope.

4. You can either use, rise/run or change in y / change in x.

5. Rewrite the given equation in slope-intercept form, then determine the y-intercept, b, of the line.

Equation of a line with m as slope and b as y-intercept is given as: y = mx + b.

1. Vertical lines have undefined slope. This implies that, for a given point, (a, b), the equation that models the line would be expressed as x = a, where a is the x-intercept.

Vertical line equation is: x = a.

2. Horizontal lines have 0 as a slope value, therefore, given (a, b), the equation that models the line is: y = b.

3. Equation for a vertical line cannot be written in slope-intercept form because the slope for a vertical line is undefined.

4. Using the following, rise/run or change in y / change in x, the slope (m), can be calculated given the coordinates of two points on a line.

5. To find an equation in point-slope form, e.g. y - 3 = 6(x - 4), rewrite the equation in slope-intercept form:

y - 3 = 6x - 24

y = 6x - 24 + 3

y = 6x - 21

The y-intercept, b, is: -21.

Therefore, the coordinate of the y-intercept would be: (0, -21).

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Based on the vertices of quadrilateral PQRS, we can infer that quadrilateral PQRS is NOT a parallelogram.

Quadrilateral PQRS would be a parallelogram if the sides have the same slope as this would prove that they are parallel.

The slope of PQ is:

= (6 - 5) / (6 - 4)

= 1/2

The slope of RS is:

= (2 - 4) / (7 - 9)

= -2 / -2

= 1

The slopes are not the same so quadrilateral PQRS is NOT a parallelogram.

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Answer: The quadrilateral is not a parallelogram.

Step-by-step explanation:

I am given that the vertices of quadrilateral  PQRS are P(4,5), Q(6,6), R(9,4) and S(7,2). The slope formula applied to each pair of adjacent vertices gives the slopes of the sides:

slope of PQ= 1/2

slope of QR= -2/3

slope of RS= 1

slope of SP= -1

Since each side has a different slope, none of the sides are parallel. So quadrilateral  PQRS is not a parallelogram.

Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]

Answer:

1/4

Step-by-step explanation:

The ratio of the areas is the square of the ratio of the lengths of sides.

(1/2)² = 1/4

Answer: 1/4

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:

y - k = C · (x - h)²

Where:

Please notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:

7 - 1 = C · (0 - 3)²

6 = 9 · C

C = 2/3

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

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Answer:

OB

Step-by-step explanation:

it's not a beacuasenhes not doing everyone

and we have no info on whether anyone serveylayed a sport so the only possible option is 2

Answer: 12

Step-by-step explanation:

For this counting question, we need to figure out the possible choices for each selection.

For main protein, there are four options, so we can make four slots

_ _ _ _

For beans, there's three options, so we can make three slots
_ _ _

Doing some casework, we know that 4*3 = 12, which is the answer.

The 97% confidence interval for the proportion of adults is 0.801<P<0.851.

Given that 867 adults are randomly selected from 1050 who always wear seat belts.

A confidence interval refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Let's assume n=1050 and x=867

Find the sample proportion by dividing the given proportion with sample size as,

[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\\hat{p}&=\frac{867}{1050}\\ \hat{p}&=0.826 \end[/tex]

Find the α by subtracting the given confidence interval that is 97% from 1 as

α=1-(97÷100)

α=1-0.97

α=0.03

To find the critical value that is [tex]Z_{\frac{\alpha}{2}}[/tex] by dividing alpha with 2,

[tex]\begin{aligned}Z_{\frac{\alpha}{2}}&=Z_{\frac{0.03}{2}}\\ Z_{\frac{\alpha}{2}}&=Z_{0.015}\end[/tex]

From this table which is shown in the figure it says that the critical value is

[tex]Z_{crit}=\pm 2.17[/tex]

Use this formula to find the confidence interval [tex]P=\hat{p}\pm Z_{Crit}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Substitute the values in the formula,

[tex]\begin{aligned}P&=0.826\pm 2.17\times \sqrt{\frac{0.826(1-0.826)}{1050}}\\ P&=0.826\pm 2.17\times \sqrt{\frac{0.826\times 0.174}{1050}}\\ P&=0.826\pm 2.17\times 0.0116995\\ P&=0.826\pm 0.025\end{aligned}[/tex]

Hence, a 97% confidence interval for the proportion of adults who always wear seat belts is 0.801<P<0.851.

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Answer:

Raheem

Step-by-step explanation:

Answer:

The Three options are

1.  m∠5 + m∠6 = 180°  ...........Linear Pair

2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle

3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Step-by-step explanation:

Consider Δ ABC with Exterior angles as

∠ 1 , ∠ 4 ,and ∠ 6

Exterior angle Property of Triangle:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠ 1 we have

∠ 1 = ∠ 5 + ∠ 3 .................Exterior angle Property of Triangle

Similarly,

For Exterior ∠ 4 we have

∠ 4 = ∠ 5 + ∠ 2.................Exterior angle Property of Triangle

Similarly,

For Exterior ∠ 6 we have

∠ 6 = ∠ 2 + ∠ 3.................Exterior angle Property of Triangle

Triangle Sum Property:

Ina triangle sum of the measures of angles is equal to 180°

∴ m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Linear Pair:

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

∴ m∠5 + m∠6 = 180°  ...........Linear Pair

Answer:

m∠5 + m∠6 =180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

got it correct on my test

Answer:

90 degrees

Step-by-step explanation:

the clock is a circle so the entire # of degrees is 360.

there are 12 sections on the clock so 360 /12 =30

so each section is 30 degrees.

if you go from 3:00 to 3:15, that is 3 sections.

so 3 times 30 is 90

Answer:

117 bags

Step-by-step explanation:

Day 1: 3 bags

Day 2: 3 × 3 = 9 bags

Day 3: 9 × 3 = 27 bags

Day 4: 27 × 3 = 81 bags

Total: 9 + 27 + 81 = 117 bags

Answer:

81 bags of cement in the last 3 days.

Step-by-step explanation:

On the first day he used 3 bags.

The second day he used twice that amount so that would be 3²=9

The third day he used twice the amount he used the second day. So that would be 9²=81.

He used 81 bags of cement in the last 3 days.

Hope this helps!

If not, I am sorry.

What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.

The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.

In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.

Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.

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Answer:

AngleA ≅ AngleQ because of the third angle theorem

Step-by-step explanation:

right on edge

Answer:

1 4/5

Step-by-step explanation:

On the number line, for every whole integer, the line is divided into fifths. The dot is one fifth away from the number two. Therefore, it is 4/5 in from 1 and the answer is 1 [tex]\frac{4}{5}[/tex].

[<Answer>] (3):

Hello! I'm Avery. And I would love to help you :)

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

[<The Explanation>}:

Step one: Distribute

[tex]144 = -12(x + 5)[/tex]
[tex]144 = -12x - 60[/tex]

Step two: Add 60 to both sides

[tex]144 = -12x - 60\\144 + 60 = -12 - 60 + 60[/tex]

Step three: Simplify

Adding..Adding..(Done!): [tex]204 = -12x[/tex]


Step four: Divide both sides by the same factor

[tex]204 = -12x\\\frac{204}{-12} = \frac{-12x}{-12}[/tex]

Last and not least..Step five:

Divide then, Cancel the terms, Move the Variable to the left...

And.. x = -17 is the answer :D

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

[<Ending>] <3

Hope this helps and if it's wrong, you can't sue me! >:D

Bye! Hope this works for you :)

Have a nice day! - Avery <3

There are 10 line segments on a line with five different points on it.

Line:

A line is formed with infinite points and it is extended infinitely along a straight path in both directions.

Line segment:

The part of the line that lies between two distinct points on the line. This is also called the shortest distance between two points on the line.

Consider a line with five points on it as A, B, C, D, and E.

So, the possible line segments are

AB, AC, AD, AE, BC, BD, BE, CD, CE, DE

So, there are 10 line segments are formed on line with five different points.

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