A cake recipe requires 4 and one-half cups of flour to make 1 cake. How many cakes can be made by a baker who has 16 cups of flour?

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts.  For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

Parts of a circle

Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).

Let's call the diameters of each of our curves "[tex]d_{big}[/tex]"  "[tex]d_1[/tex]"  "[tex]d_2[/tex]"  "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle.  So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]

Substituting back into the main equation above:

[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]

Note that all terms have common factors of "one-half" and "pi" in them.  These can be factored out:

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]

The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]

Substituting and simplifying (in terms of pi):

[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]

Additional Understanding

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]

[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]

[tex]P_{overall}=\pi d_{big}[/tex]

Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.  

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.

Answer:

A 2kg block is moved a long a level floor by a horizontal force of 20N if the coefficient of sliding friction is 0.4

what is the acceleration of the blove

Answer:

  3

Step-by-step explanation:

The fundamental theorem of algebra tells you the number of zeros is equal to the degree of the polynomial.

__

The given degree-3 polynomial has 3 zeros.

__

Additional comment

Descarte's rule of signs tells you the absence of sign changes among the coefficients means that there are no positive real roots. Changing the sign of the one odd-degree term gives one sign change, so there is one negative real root. The other two zeros are complex.

  one negative real zero, and two complex zeros

A graph confirms that the only real zero is negative and irrational, about -7.04.

Answer:

152cm²

Step-by-step explanation:

math and stuff and things

Answer:

96

Step-by-step explanation:

The formula for average = [tex]\frac{Sum \hspace{0.15cm} of\hspace{0.15cm} Items}{No.\hspace{0.15cm} of \hspace{0.15cm} Items}[/tex]

After taking 3 tests, the average is 88.

∴ 88 = Sum of Items / 3

Sum of Items = 88 x 3

                      = 264

This means Lenny's total score after 3 tests is 264.

We now have to calculate how many marks needs to be added to 264 so that after four tests, the average is 90.

Now the number of items (tests) = 4, and average = 90.

Let the marks required in 4th test = [tex]x[/tex]

∴ [tex]\frac{264 + x}{4} = 90[/tex]

264 + [tex]x[/tex] = 360

[tex]x[/tex] = 360 - 264

  = 96

Answer:

  (d)  see attached

Step-by-step explanation:

There are a couple of quick checks you can do to identify the correct graph.

__

Find a variable with a positive coefficient, and write that in the given relation to the inequality symbol:

  x >

This tells you ...

The x-coefficient is a factor of the constant, so the x-intercept of the boundary line is easily found. Set y=0, and you have ...

  2x = 6

  x = 3

The boundary line you're looking for has an x-intercept at x=3.

__

The correct graph is shown in the attachment.

Answer:

7s²7p⁴

Step-by-step explanation:

Livermorium is located in the seventh period and sixteenth column of the periodic table. The noble gas configuration for livermorium is [Rn]7s²5f¹⁴6d¹⁰7p⁴. The valence electrons are the ones in the orbitals with the highest quantum number (coefficient). Remember, there can be up to 8 valence electrons at one time. Therefore, the valence electron configuration is 7s²7p⁴.

Let's check

Electronic configuration

Valence electrons

Answer:

54.6 ÷ 8.4 = 6.5 hours

6 hours, 30 minutes:)

Answer: 2xy

Step-by-step explanation: 2xy is the answer bra

The missing value in the table is 12 , Option A is the correct answer.

A graph is a mathematical representation of the data available , It makes the study of the data over a wide period easier.

It is given in the question that there are 40 students and the frequency they select for each pattern is mentioned as number , which can be seen in the image attached with the answer.

It has been asked to determine the missing value in the frequency table corresponding to the pink Polka dots

The other number in the frequency table is 4, 6 ,8 ,7, 3

Total students are 40

Therefore the value corresponding to the pink polka dot is given by

40 - ( 4+6+7+8 +3)

= 12

Therefore The missing value in the table is 12 , Option A is the correct answer.

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Answer:

B

Step-by-step explanation:We know Volume = (a*b*c)

Answer:

B) 54 cubic feet

Step-by-step explanation:

Answer:

88 cm

Step-by-step explanation:

body to tail = length of body + length of tail

body to tail = 54 cm + 34 cm

body to tail = 88 cm

Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:

n = 4, p = 1/5 = 0.2.

The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096[/tex]

0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

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Square perimeter =4x cm.

The complete length that a square's edge encompasses is referred to as its perimeter. Any enclosed geometric shape's perimeter may be computed by measuring the space around it.

By calculating the total of all the sides of a square, the perimeter may be determined. The perimeter of a square will be stated as,

The perimeter of square = s + s + s + s

⇒Perimeter of square = 4s, where "s" is the side length of the square.

This is because all edges of a square are equal and each edge measures "s" units.

Mathematically, the formula for calculating a square's perimeter is: Square perimeter, (P) = 4 Side

⇒P= 4x cm

It is concluded that the solution is 4x cm.

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Answer:

09

Step-by-step explanation:

07

The value of x in the given expression x² = 50 is 5√2

x² = 50

Thake the square root of both sides

x = √50

Recall

√50 = √(25 × 2) = 5√2

Thus,

x = √50

x = 5√2

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The solution to the given linear equation is x=1

Linear equations are equations that has a leading degree of 1.

Given the linear equation as shown below;

8x - 5= 2x + 1

Subtract 2x from both sides

8x - 2x - 5 = 2x + 1-2x

6x - 5  = 1

Add 5 to both sides

6x - 5 + 5 = 5 + 1

6x  = 6

Divide both sides by 6

6x/6 = 6/6

x = 1

Hence the solution to the given linear equation is x=1

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The value of x in the segment is 3

Using the secant and segment theorem, we have:

x * (x + 21) = (x + 1) * (x + 1 + 14)

Evaluate the sum

x * (x + 21) = (x + 1) * (x + 15)

Expand

x^2 + 21x = x^2 + 15x + x + 15

Subtract x^2 from both sides

21x = 15x + x + 15

Evaluate the like terms

5x = 15

Divide both sides by 5

x = 3

Hence, the value of x is 3

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The area of wafer required to make the ice cream cone 68.75 cm²

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

Given:

r= 2cm, l=9 cm

Surface area,

=πr(l +r)

=3.14*2(9 + 2)

= 6.25*11

=68.75 cm²

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Answer:

$980

Step-by-step explanation:

Given the cost of gasoline = $2.80/mile

Total Distance = 175miles x 2 (Back and forth)

= 350 miles

Total Cost = Cost of gasoline x Total Distance =

= $2.80 x 350

= $980

The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The driving distance from Seattle to Portland is 175 miles.

Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Now,

Since, The driving distance from Seattle to Portland is 175 miles.

Hence, The total distance from Seattle to Portland and back = 175 + 175

                                                                                            = 350 miles

And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Hence, The cost of gallon = 350/25 x $2.50

                                        = 100 x $2.50

                                        = $250

Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

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Answer:

See Pictures

Step-by-step explanation:

The line that represents the graph satisfying all condition is  f(x) = |x − 7| − 3.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

As, the points are given.

We have to find which equation  satisfies all the points.

f(x) = |x − 7| − 3

put x= -6

y=  13-3 = 10

Similarly by putting all the values the only condition that satisfies is

f(x) = |x − 7| − 3

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Answer + Step-by-step explanation:

y= e^x + 1

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Answer:

0.76

Step-by-step explanation:

-8+3=-6x^(2/3)

-5=-6 x^(2/3)

-5/-6=x^(2/3)

(2/3)√{5/6}=x

0.76=x

x=0.76

The length of C from A is 3.5 miles if AB=3.5 miles and BC is 6 miles .

Given The length of triangle ABC AB=3.5 miles , BC=6miles and AC=d

We have to find the value of d

First of all we have to draw a perpendicular from point A on side BC .

It forms two triangles ABE and AEC if E is the point where perpendicular stands on BC.

In triangle BEA

AE=[tex]\sqrt{3.5^{2} -3^{2} }[/tex]

=[tex]\sqrt{12.25-9}[/tex]

=[tex]\sqrt{3.25}[/tex]

=1.8

Now in triangle AEC

AC=[tex]\sqrt{1.8^{2} +3^{2} }[/tex]

=[tex]\sqrt{3.24+9}[/tex]

=[tex]\sqrt{12.24}[/tex]

=[tex]\sqrt{12.24}[/tex]

=3.49 MILES

By rounding off to the nearest tenth we will get 3.4 miles

Hence the value of d is 3.4 miles.

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Answer:its 7.7

Step-by-step explanation: i did it on edge

We found a counterexample, so the statement is false.

Let's use the matrix:

[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]

This is a 4x4 matrix with determinant equal to -2.

The inverse matrix is:

[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]

If we multiply it by 2, we get:

[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]

The adjoint of that is the original matrix, actually:

[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]

Which we already know, has a determinant of -2.

So the statement is false, as we found a counterexample.

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Answer:

Step-by-step explanation:

step-by-step explanation:

#1: simplify both sides of the equation.

2(x+3)−4x=x

(2)(x)+(2)(3)+−4x=x

2x+6+−4x=x

(2x+−4x)+(6)=x

−2x+6=x

−2x+6=x

***

#2: subtract x from both sides.

−2x+6−x=x−x

−3x+6=0

***

#3: subtract 6 from both sides.

−3x+6−6=0−6

−3x=−6

***

step 4: divide both sides by -3.

−3x/-3 = -6/-3

solution x = 2

Answer:

m∠GLI = 2m∠GLH

Step-by-step explanation:

Angle GLI (red) is made of angles GLH (purple) and HLI (green).

m∠GLI = m∠GLH + m∠HLI

First option: ∠GLH ≅ ∠ILM (Angle GLH is congruent to angle ILM.)

This doesn't tell us anything about the relationship between angles GLI, GLH and HLI. So it can't be used.

Second option: m∠KLM = 5m∠ILM (Measure of angle KLM is 5 times the measure of angle ILM.)

This also cannot be used, because it doesn't include angles GLI, GLH or HLI.

Third option: m∠GLI = 2m∠GLH (Measure of angle GLI is two times the measure of angle GLH.)

Now this option is more interesting. It includes two angles of three that we are interested in.

If angle GLI is two times angle GLH, then that means that angle GLH is congruent to angle HLI!

Let's prove this with equations.

1) m∠GLI = m∠GLH + m∠HLI (from picture)

2) m∠GLI = 2m∠GLH (from third option)

Substitute m∠GLI in first equation with m∠GLI in second.

m∠GLI = m∠GLH + m∠HLI

2m∠GLH = m∠GLH + m∠HLI

m∠GLH = m∠HLI

So this proves that the angles GLH and HLI have the same measure, therefore ray LH is bisector of GLI.

Fourth option: m∠GLI = 1/2m∠GLH + 1/2m∠HLI​

There are all angles we are interested in, but there is a mistake. We can see in the picture that angle GLI is made of angle GLH and HLI and not of half of them. This just is not true. The correct equation would be m∠GLI = m∠GLH + m∠HLI.