6 bowls of cereal to 20 pancakes simplest ratios

Answer:

135°

Step-by-step explanation:

Answer:

[tex]\frac{92}{100\\}[/tex], 77%, 58%,  [tex]\frac{36}{100}[/tex], [tex]\frac{11}{100}[/tex], 3%

Step-by-step explanation:

I changed them all to percents

3 %

[tex]\frac{11}{100}[/tex]  Percent means what out of 100? 11%

77%

92/100  = 92%

36/100 = 36%

58%

The Surface area are shown below.

The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.

1. The measure of sides are

A = 3

B = 15

C= 17

D= 8

So, the Lateral Surface Area

= ( 15+17+8) x 3

= 117 mm²

and, the total surface Area

= Area of two triangles + Area of rectangle

= 2 x 1/2 x 8 x 15 + 117

= 120 + 117

= 237 mm²

2. The measure of sides are

A = 5

B = 2

C= 9

D= 2

So, the Lateral Surface Area

= 2 x (5 x 9) + 2 (2 x 5)

= 110 m²

and, the total surface Area

= 110 + 2 (2 x 9)

= 146 m²

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The polynomials is divided using synthetic division and the remainder theorem to 3x³ -6x² - 20x - 77/x + 4

Synthetic division is described as one of the methods that is used to manually perform the Euclidean division of polynomials.

The steps taken in a synthetic division include;

Given the polynomial;

f(x) = 3x³ + 6x² + 4x +3 by x + 4

We have;

        3          6        4         3

-4     _____-12__24___80__

        3          -6       -20      -77

Then, we have;

3x³ -6x² - 20x - 77/x + 4

Hence, the expression is 3x³ -6x² - 20x - 77/x + 4

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The confidence interval has a lower bound of 6.04 and an upper bound of 9.96.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally employed. The confidence interval is the range of values within which you expect your estimate to fall a given proportion of the time if you repeat your experiment or re-sample the population in the same manner. A 95% confidence interval is a range of values above and below the point estimate where the real value in the population is 95% likely to reside.

Here,

For a two-tailed 95% confidence interval, the alpha value is 0.025, and the corresponding critical value is 1.96. This means that to calculate the upper and lower bounds of the confidence interval, we can take the mean ±1.96 standard deviations from the mean.

sample mean=8

upper and lower bounds of the confidence interval,

=mean ±1.96

=[8-1.96,8+1.96]

=[6.04,9.96]

The lower bound of the confidence interval is 6.04 and the upper bound is 9.96.

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Check the picture below.

0.947 g/ml is the cube density the volume was 9.01.

The term "density" refers to the ratio between the volume (the amount of space taken up by an item or substance) and the amount of matter contained inside (its mass). The quantity of mass per unit of volume is another method to define density.

We are know that items float in liquids when their density is less than that of the liquid.

Objects floating in a liquid are those whose density is equal to that of the liquid.

So, in this case, the cube is solely suspended in the first liquid combination. Therefore, the first liquid mixture's density is the same as a cube. The other mixes have densities that are higher than that of the cube.

Density of methanol = 0.7913 g/ml

Density of water = 1 g/ml

Density of the 6th liquid mixture:

= {(2 × 0.7913 ) + (1 × 6)}/8 g/ml

= 0.947 g/ml

Therefore density of cube = 0.947 g/ml

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The complete question is as follows:

What Is The Cube Density The Volume Was 9.01? The Cube Floated Up To 8.1 Ml

If the Circle has Center: (6, 1); and solution point: (5, 9) , then the standard form of Equation is (x - 6)² + (y - 1)² = 65 .

The standard form of a circle is given by ⇒ (x - h)² + (y - k)² = r²,

where (h, k) is the center of the circle and r is the radius.

To find the standard form of the circle that has center (6, 1) and a solution point (5, 9), we need to find the radius "r" first.

The distance(r)  between the center and the solution point is given by the Pythagorean theorem:

⇒ r = √((5 - 6)² + (9 - 1)²)

⇒ r = √((-1)² + (8)²)

⇒ r = √65

Now substituting  radius(r = √65) in  the standard form of the circle:

we get ;

⇒ (x - 6)² + (y - 1)² = √65²

⇒ (x - 6)² + (y - 1)² = 65

Therefore , the standard form of circle is (x - 6)² + (y - 1)² = 65  .

The given question is incomplete , the complete question is

Write the standard form of the circle that has Center: (6, 1); and solution point: (5, 9) .

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The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

Joint variation describes a situation in which, while the other variables are held constant, the value of one variable relies on the values of two or more additional variables.

Joint variation is used to describe when more than two variables are directly correlated or when one variable changes as a result of the change product of more than two variables. X can be symbolically expressed as X YZ if it is in joint variation with Y and Z. If Y is also constant, then X and Z directly depend on one another.

Joint variation is a type of variation where a quantity changes when two or more other numbers are multiplied together. For instance, when a rectangle's length or breadth changes, so does its area. Where A is the area, l is the length, and w is the width, we say that A = lw.

Joint Variation of x,y and z

z = kxy

k is the cofficient

for x = 7, y = 3 and z = -14

-14 = k*3*7

⇒k = -2/3

for x= 3 and z = -8

-8 = (-2/3)*3*y

y = 4

The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

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Answer:

3 Degrees each hour

Step-by-step explanation:

27 divided by 9 = 3

Answer:

y = (9/2)x + 26.5

Step-by-step explanation:

Lets rewrote the equation in standard format of y = mx + b, where m is the slope and b is the y-intercept.

-2x-9y = 1

-9y = 2x + 1

y = -(2/9)x - (1/9)

The slope of this line is -(2/9)

A line that is perpendicular to this line will have a slope that is the negative inverse of -(2/9).  That would be (9/2).  So a perpendicular line will have the form of y = (9/2)x + b.  Any value of b can be chosen and the lines will still be perpendicular to each other.  However, we want to find a value of b that will force the line through point (-7,-5).  This is done by using the point in the above equation and solving for b:

y = (9/2)x + b

-5 = (9/2)(-7) + b  for point (-7,-5)

-5 = -(63/2) + b

b = -5 + (63/2)

b = -5 + 31.5

b = 26.5

The equation is y = (9/2)x + 26.5

See the attached graph.

The value of x for the expression is 168 = 18x + 12.2x.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

168 = 18x + 12.2x

Add like terms.

168 = 30.2x

Divide both sides by 30.2

168/30.2 = x

x = 5.56

Thus,

The value of x is 5.56.

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The scatter plot shows [negative linear] association.

From the question, we have the following parameters that can be used in our computation:

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values decreases

This represents a negative linear] association.

Hence, the association is a negative linear] association.

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Answer:

Step-by-step explanation:

q x q + r² and 2q + (r + r)

q × q + r² = q² + r²

----------

2q + (r + r) = 2q + 2r

(a) The tree diagram by filling in the missing path probabilities by subtracting the given value by 1 is given below.

(b) The probability that the car is repaired under budget, on time, and with company D is 0.00652.

(c) The probability that the cost of the repair exceeds the estimate is 0.3909.

(d) The probability that the car is repaired under budget, given that it is ready on time is 0.5804.

D = driver takes his car to shop D.

L = driver takes his car to shop L.

T= the work is complete on time.

B= the cost is less than or equal to the estimate (under budget).

(a) We have to complete the tree diagram by filling in the missing path probabilities.

The complete tree diagram is given below:

We used to complete the tree

1 - 0.634 = 0.366

1 - 0.226 = 0.774

1 - 0.844 = 0.156

(b) We have to determine the probability that the car is repaired under budget, on time, and with company D.

P(DTB) = 0.634 × 0.226 × 0.455

P(DTB) = 0.00652

(c) We have to determine the probability that the cost of the repair exceeds the estimate.

P(B') = P(DTB') + P(DT'B') + P(LTB') + P(LT'B')

P(B') = 0.634 × 0.226 × 0.545 + 0.634 × 0.774 × 0.622 + 0.366 × 0.156 × 0.105 + 0.366 × 0.844 × 0.005

P(B') = 0.390855

P(B') = 0.3909

(d) We have to determine the probability that the car is repaired under budget, given that it is ready on time.

P(B|T) = P(BT)/P(T)

P(B|T) = (0.634 × 0.226 × 0.455 + 0.366 × 0.156 × 0.895)/(0.634 × 0.226 + 0.366 × 0.156)

P(B|T) = 0.580373

P(B|T) = 0.5804

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Cost of goods manufactured= $905,000 Overhead cost applied to Work in Process and hence option c is correct

To calculate the cost of goods manufactured, we need to use the following formula:

cost of goods manufactured= beginning WIP + direct materials + direct labor + allocated manufacturing overhead - Ending WIP

Schedule cost of goods manufactured:

Beginning WIP= 40,000

Direct materials used= 20,000 + 400,000 - 30,000= 390,000

Direct labor= 60,000

Allocated manufacturing overhead= 485,000

Ending WIP= (70,000)

Cost of goods manufactured= $905,000

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The slope of the equation c=450+28g represents the increase in cost per additional guest.

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is frequently used to signify slope.

We can see that the preceding equation is in the slope-intercept format, where m denotes the line's slope and b is its y-intercept or starting point.

In this case, the slope is 28 dollars per additional guest. This means that for every additional guest, the cost of the banquet increases by $28.

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Answer: 12

Step-by-step explanation:

you would first add up all of the numbers togeather, and it would give you 60. You then need to divide 60 by the amount of numbers which is 5. So you would do 60 divided by 5 to get 12.

The cost of a 32-ounce container is 2.92 and the cost of 6 8-ounce containers is $4.18.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let's call the unit price of 8-ounce yogurt x.

32-ounce unit price = x + 0.002

32-ounce container cost = 32 * (x + 0.002) =0.064 + 32x

6 * 8-ounce container cost = 6 * 8 * x = 48x

Given, 32-ounce container cost = 6 * 8-ounce container cost - $1.33

Substituting the costs,

0.064 + 32x = 48x - 1.33

Solving for x,

48x - 32x = 0.064 + 1.33

16x = 1.394

x = $0.087125

So, the unit price of 8-ounce container is $0.087125

Cost of 32-ounce container = $0.064 + 32 * (0.087125 + 0.002) = $2.92

Cost of 6 8-ounce containers = 6 * 8 * 0.087125 = $4.18.

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The equation of the plane that passes through (1, 3, 6) and is parallel to x = 11 is x = 1.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division). It represents a value that can be determined if the values of the variables are known. An algebraic expression does not contain an equal sign and cannot be solved like an equation, but it can be simplified or manipulated using algebraic rules. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

A plane can be represented by a normal vector (a,b,c) and a point (x⁰,y⁰,z⁰) that lies on the plane. If a plane is parallel to the plane x = 11, the normal vector must be in the direction of the x-axis, meaning (a,b,c) = (1,0,0).

The equation of the plane can then be found using the point-normal form, which is given by:

ax + by + cz = d, where d = ax⁰ + by⁰ + cz⁰

Plugging in the values for (1,3,6) and (a,b,c) = (1,0,0), we get:

a(1) + b(3) + c(6) = d

1 + 0 + 0 = d

d = 1

So the equation of the plane that passes through (1,3,6) and is parallel to x = 11 is: x = 1

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The equation for the volume of a cylindrical shell is:

V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.

The volume of the solid can be found using the method of cylindrical shells. The volume of each cylindrical shell is equal to the product of the area of the base (a semicircle), the height of the shell, and the width of the shell (which is equal to the difference in the x-coordinates of the two vertices that define the height).

To find the total volume, we would sum up the volumes of all the cylindrical shells, from the top to the bottom of the solid.

The equation for the volume of a cylindrical shell is:

V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.

The height of the shell is given by the difference in the y-coordinates of the two points that define the height, and the width of the shell is given by the difference in the x-coordinates of these two points.

To find the total volume, we would integrate the volume of the cylindrical shell over the height of the solid. The limits of integration would be the y-coordinates of the bottom and top of the solid.

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Answer:

12. m = 1/3

14. m = 5/6

16. m = -5/2

Step-by-step explanation:

m = y2-y1/x2-x1

The length of AL, BK and CH are 12, 9 and 6 respectively.

Similar triangles are those triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

Given a figure of a big triangle.

We can clearly see that angles made by each of the triangles ALE, BKE, CHE and DGE are equal and thus they are similar triangles.

The sides of similar triangles are proportional.

DG / GE = CH / HE = BK / KE = AL / LE

We have DG = 3, GE = 5,HG = 5, KH = 5, LK = 5

HE = 5 + 5 = 10

KE = 5 + 5 + 5 = 15

LE = 5 + 5 + 5 + 5 = 20

Substituting,

Consider DG / GE = CH / HE

3 / 5 = CH / 10

CH = (3/5) × 10 = 6

Consider DG / GE = BK / KE

3 / 5 = BK / 15

BK = (3/5) × 15 = 9

Consider DG / GE = AL / LE

3 / 5 = AL / 20

AL = (3/5) × 20 =  12

Hence the length of AL is 12, length of BK is 9 and length of CH is 6.

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The segment drawn from the apex to the edge of the circular base is 24.2 units.

A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.

The volume of the cone can be found using the formula:

V = (π/3)r²h

Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:

72π = (π/3)r²h

72π = (π/3)3²h

72π = (π/3)9h

72π = 3πh

24 = h

Using the Pythagorean Theorem, we can find the slant height as follows:

c² = a² + b²

Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:

c² = 24² + 3²

c² = 576 + 9

c² = 585

c = 24.2

Hence, the segment drawn from the apex to the edge of the circular base is 24.2 units.

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The postulate theorem used to prove the congruence of triangles MNQ and PXN is given as follows:

B. SAS.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

The congruent sides are given as follows:

The angle between these two sides is a vertical angle, having the same measure in each of the triangles, hence the SAS theorem can be applied and the correct option is given by option B.

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The formula of standard deviation method is

[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]

[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

population mean:

[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]

X- the value in the data distribution

[tex]\mu[/tex]  - the population mean

N- total number of observations

[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]

[tex]\bar{x}[/tex]  - the sample mean

n- total number of observations

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The standard form of the equation of the circle with the given characteristics is  (x - 6)² + (y - 1)² = 65.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Given, center:  (6, 1) and solution Point: (5,9)

By solution point, it means that the circle passes through that point. Hence, the radius of the circle is the distance between  (6, 1) and  (5,9)

Distance formula is given by

D = √[(x2 - x1)² + (y2 - y1)²]

D=  √[(5 - 6)² + (9 - 1)²] = 8.062

r= 8.062  or r²=65

We have, equation of the circle centered ant (h, k) and radius ‘r’ as

(x - h)² + (y - k)² = r².

=>  (x - 6)² + (y - 1)² = 65.

The standard form of the equation of the circle with the given characteristics is  (x - 6)² + (y - 1)² = 65.

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Answer:

Step-by-step explanation:

this is a case of linear pair...

52° + 90° (of the right angled triangle) + x° = 180°

52° + x° = 180° - 90°

x° = 90° - 52°

x° = 38°

Answer:

The percent error of Jack's measurement was 3.6%, to the nearest tenth of a percent. This is calculated by subtracting the actual length (16.6 inches) from the measured length (17.2 inches) and dividing by the actual length, then multiplying by 100.

Step-by-step explanation:

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