. Ms. Johnson, a circus ringleader, made a cake in the shape of a circus tent to use as the centerpiece at a celebration. As shown in the illustration, the cake consists of a cylinder and a cone. The height of the cone is one-half the height of the cylinder. The volume of the cylinder is 3 1470 in . The diameter of the cylinder is 12 in. What is the volume of the circus tent cake? Use 3.14 for  . Round to the nearest hundredth.





Ms. Johnson wants all the circus employees to have miniature cakes in the shape of either a circus ball or a
clown hat. She wants the clown hat dessert and the circus ball dessert to have equal volumes. The radius of
both cake pieces will be 3 in. What must the height of the clown hat cake be for the two cakes to be equal in
volume? Round to the nearest hundredth if necessary. Explain or show your work.

Equivalent expressions are expressions with the same value.

The values of the variables are:

[tex]\mathbf{a = 1}[/tex]      [tex]\mathbf{b = 9}[/tex]      [tex]\mathbf{c = -2}[/tex]       [tex]\mathbf{d = 4}[/tex]

The expression is given as:

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49}}[/tex]

Expand

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x^2 + 9x - 7x - 21}{-2x^2 +4x -6x + 12} \cdot \frac{2x^2 + 14x + 9x + 63}{6x^2 + 21x - 14x - 49 } }[/tex]

Factorize

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x(x + 3) - 7(x + 3)}{-2x(x -2) -6(x - 2)} \cdot \frac{2x(x + 7) + 9(x + 7)}{3x(2x + 7) - 7(2x - 7) } }[/tex]

Factor out the terms

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(3x - 7) (x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{(3x - 7) (2x - 7) } }[/tex]

Cancel out 3x - 7

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]

Factor out -2

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{-2(x +3)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]

Cancel out x + 3

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{1}{-2(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) }}[/tex]

Rewrite as:

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x + 9)(x + 7)}{ -2(x - 2)(2x - 7) } }[/tex]

Expand

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{2x^2 + 25x + 63}{ -4x^2 + 22x - 28}}[/tex]

Factorize again

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x+ 7)(x + 9)}{(2x + 7)(-2x + 4)}}[/tex]

Cancel out common factors

[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{x + 9}{-2x + 4}}[/tex]

From the question, we have:

[tex]\mathbf{\frac{ax + b}{cx + d}}[/tex]

So, we have:

[tex]\mathbf{\frac{ax + b}{cx + d} = \frac{x + 9}{-2x + 4}}[/tex]

By comparison, we have:

[tex]\mathbf{a = 1}[/tex]

[tex]\mathbf{b = 9}[/tex]

[tex]\mathbf{c = -2}[/tex]

[tex]\mathbf{d = 4}[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/24242989

Mr. Simms used 1/4 of the 20 pencils he bought, which equals 5 pencils, and gave away an additional 4 pencils, totaling to 9 pencils used and given away.

To solve how many total pencils Mr. Simms uses and gives away, we first find out how many pencils he used by taking 1/4 of the 20 pencils he bought. To do this, we multiply 20 by 1/4:

20 times 1/4 = 5

Mr. Simms used 5 pencils. He also gave away 4 pencils to his students. To find the total number of pencils used and given away, we add the pencils used to the pencils given away:

5 (used) + 4 (given away) = 9

Therefore, Mr. Simms used and gave away a total of 9 pencils.

Use the theorem above to find the measure of angle formed by the intersection of the tangent that intersects chord AC.

By the theorem, the measure of angle is half of the intercepted arc which is 126.

Then, (1/2) · 126 = 63;

The correct answer is C. 63;

Answer:63

Step-by-step explanation:

Solution:

we are given that [tex]y=cos x[/tex]

Here we are going to plot two curves one for cosx and the othere also of cosx but after making a phase shift of [tex]\pi/2[/tex]

When we do a phase shift by an angle of theta , in that case actaully we add angle negative theta .

For example when we shift the phase of sinx by [tex]\pi/2[/tex] we get  [tex]sin(x-\pi/2).[/tex]

Hence we are going to plot the curve of

[tex]y=cosx\\ \\ y=cos(x-\pi/2)=sinx\\[/tex]

Hence the correct option is B.

Answer:

40B+30M≤300

200B+80M≤1200

Step-by-step explanation:

Answer:

The slope is [tex]-\frac{350}{month}\[/tex]

Step-by-step explanation:

This saving account is declining a fixed amount every month, this means that the function that represents this decline is linear.

The other thing we know is that originally (september 1), the account has a balance of $4900, and this is the intercept.

Therefore, for a linear function depending of the variable "x", we can write that

[tex]f(x)= (-\frac{350}{month}x+4900)\[/tex]

where the units were factored. Then the slope is

[tex]-\frac{350}{month}\[/tex]

Answer:

Option D is correct.

The fourth graph shows a system of equation with two solutions.

Step-by-step explanation:

From the given figure,

we can see that we have a parabola and a straight line.

Since, the line is touching the parabola at two points, one point and no point.

In the first graph, the line touches the parabola at one point.

In the second graph, the line does not touches the parabola at no point.

also,In the third graph,the line touches the parabola at one point and

In fourth graph, the lines touches the parabola at two points.

For the system of equations :

Therefore, the graph which is most likely shows a system of equation with two solutions is: In fourth graph

Answer:

Two solution to a system of equation means when we look at the graph of the function the graph of the two equations must intersect  at exactly two points.

The graph satisfying such condition is attached to the answer.

in this graph the curve that is downward parabola and a line intersect at exactly two points and hence result in two solutions.

Final answer:

To find the product of (2x + 9) and (x + 1), we use the distributive property and combine like terms, resulting in 2x² + 11x + 9.

Explanation:

The student is asking for the correct product when multiplying the binomials (2x + 9) and (x + 1). This is a math problem involving algebraic multiplication.

To find the product, we apply the distributive property (also known as FOIL method in binomials):

Combine the terms to get the final product: 2x² + 2x + 9x + 9, which simplifies to 2x² + 11x + 9.

The correct product of (2x + 9)(x + 1) is 2x² + 11x + 9.

Answer:

Step-by-step explanation:

I think its D.

The average time it takes to fill one bag of leaves is approximately 0.17 hours.

To find the average time to fill one bag of leaves, we use the formula

Average Time=Total Time÷Total Bags. In this scenario, the total time spent is the average workday hours, which is 9 hours, and the total number of bags filled is 36.

So,

Average Time=9hours÷36bags=0.25 hours/bag.

​Therefore, the average time it takes to fill one bag of leaves is 0.25 hours or 15 minutes. This means, on average, it takes 15 minutes to fill each bag of leaves.

In summary, the staff at Larry's Lawns spends 9 hours a day on lawn-related tasks, with mowing and raking taking 6 hours. Since they fill an average of 36 bags of leaves in that time, each bag takes approximately 0.25 hours or 15 minutes to fill, assuming a constant rate of filling.

To find the average time it takes to fill one bag of leaves at Larry's Lawns, divide the total time spent filling bags by the number of bags filled. Time per bag = 1/6 hours per bag.

To find the average time it takes to fill one bag of leaves, we need to divide the total amount of time spent filling bags by the number of bags filled. In this case, the staff at Larry's Lawns spend 6 hours mowing and raking and fill 36 bags of leaves. So to find the average time per bag, we divide 6 hours by 36 bags:

Time per bag = Total time / Number of bags = 6 hours / 36 bags

Since we want the average time per bag, we can simplify the fraction:

Time per bag = 1/6 hours per bag.

The value of x is 9.6.

To find the value of x to the nearest tenth, we can use the angle bisector theorem, which states that in a triangle, an angle bisector divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Given that:

[tex]\[\frac{6.3}{5.4} = \frac{11.2}{x}\][/tex]

We can solve for x by cross-multiplying:

[tex]\[6.3 \cdot x = 5.4 \cdot 11.2\][/tex]

[tex]\[6.3x = 60.48\][/tex]

Now, divide both sides by 6.3 to isolate x:

[tex]\[x = \frac{60.48}{6.3}\][/tex]

[tex]\[x \approx 9.6\][/tex]

So, the value of x to the nearest tenth is 9.6. Therefore, the correct option is x = 9.6.

The probability of a correct guess on the first​ try will be [tex]0.001[/tex] .

Probability is the ratio of number of favorable outcome to the

i.e. Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]

We have,

An ATM Card having three-digit code.

Repetition of digits is allowed.

So,

As Repetition is allowed, and we have [tex]10-[/tex]key keypad, and have to guess [tex]3[/tex] digit code,

Then

Total number of outcomes [tex]=10*10*10=1000[/tex]

And

Number of favorable outcome [tex]=1[/tex]

So,

Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]

[tex]P(E)=\frac{1}{1000}[/tex]

[tex]P(E)=0.001[/tex]

So, the Probability of correct guess is [tex]0.001[/tex] .

Hence, we can say that the probability of a correct guess on the first​ try is [tex]0.001[/tex] .

To know more about probability click here

brainly.com/question/11034287

#SPJ3

Answer:  The correct option is (C) 62500.

Step-by-step explanation:  We are given to find the 7-th term of the following geometric sequence :

4,   −20,   100,    .    .     .

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

For the given geometric sequence, we have

first term, a = 4

and common ratio r is given by

[tex]r=\dfrac{-20}{4}=\dfrac{100}{-20}=~~.~~.~~.~~=-5.[/tex]

Therefore, the 7-th term of the given geometric sequence is

[tex]a_7=ar^{7-1}=4\times(-5)^6=4\times 15625=62500.[/tex]

Thus, the required 7-th term is 62500.

Option (C) is CORRECT.