Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.2 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.

96.93 cubic inches
553.90 cubic inches
581.59 cubic inches
2,326.36 cubic inches

We obtain a straight line when we plot the slope-intercept form equation graph. The ideal form is the slope-intercept. It is simple to graph and solve word problems based on it as it has the form "y=". When we enter the x values, the equation is already solved for y.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Using the slope and y-intercept, draw an equation as follows.

1. To solve for the y-intercept in the equation y = mx + b.

2. Draw the y-intercept on a graph. The purpose will be (0, b).

3. Ascertain what the slope=m of the equation y = mx + b is.

4. Take one step, utilizing the elevation, and sprint away from the slope. If it's good, move up to the right; if it's negative, move down to the right.

5. Join these two spots together with your line.

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The height of the antenna on the roof of the local building is approximately 2 meters.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

The situation forms a right angle triangle.

Properties of a right angle triangle:

One of its angles is equals to 90 degrees

The sides of the triangles can be calculated using Pythagoras theorem.

Therefore, let's find the height of the building and the radio antenna from the eye point.

Using trigonometric ratios,

tan 35° = opposite / adjacent

tan 35° = x / 28

where

x = the height of the building and the radio antenna from the eye point.

x = 28 tan 35

x = 28 × 0.700207

x = 19.60581 meters

Let's find the height of the building from his eye point.

tan 32° = y / 28

where

y = height of the building from his eye point

y = 28× tan 32°

y = 28 × 0.6248693

y = 17.496341 meters

Height of the antenna

=  19.60581 -17.496341

=2.109469

hence, Height of the antenna ≈ 2 meters

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Answer:

just put your mind to it fam

Step-by-step explanation:

Answer:

this is nonsense

Step-by-step explanation:

(4x³ + 23x² + 22x - 10) [tex](x + 2)^{-1}[/tex]

(4x³ + 23x² + 22x - 10) (1 / (x + 2))

(4x³ + 23x² + 22x - 10) / (x + 2)

4x² + 2x³ + 23x + 11.5x² + 22 + 11x - 10/x - 5

2x³ + 15.5x² + 44x - 10/x + 17 ??????

y = 2x + 2

Think about the equation Ax + By = C for a straight line. You may also use y = 0 and solve for x to determine the x-intercept. Substituting x = 0 and y-solving will reveal the y-intercept.

Step 1: y =

Step 2: y = x

Step 3: y = x + 2

Answer: y = 2x + 2

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The table that shows a proportional relationship is Table D.

Please find attached the graph of Table D created with MS Excel

The variables x and y in a set of ordered pair (x, y), are proportionally related, when the ratios of the x and y values for of all data points in the set are equivalent, such that a proportional relationship can be expressed in the form; y = k·x

Where;

k = The constant of proportionality

Therefore; k = y/x

The ratio of the y-values to the corresponding x-values in the table that shows a proportional relationship is therefore a constant.

Analyzing the Table C, we get;

The points are; (2, 1), (4, 3), (6, 5), (8, 7)
x/y for each data point is therefore;

1/2 ≠ 3/4 ≠ 5/6 ≠ 7/8

Table C does not show a proportional relationship

The coordinate points in Table D are; (2, 1), (6, 3), (8, 4), (10, 5)

The ratio, x/y at each point in the table are therefore;

1/2 = 3/6 = 4/8 = 5/10 = 1/2

The ratio, x/y at each point in the table is constant, therefore, Table D ahows a proportional relationship.

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Answer:

The answer is 48.6667 or 48 2/3

Step-by-step explanation:

From the ratio test, r=1/3. The series converges.

We must calculate the ratio between two successive phrases in order to perform the ratio test:

The nth term is n / 3n.

The (n + 1)th term is (n + 1) / 3n + 1.

The ratio test:  lim |   [ (n + 1) / 3n + 1 ]  /  [  n / 3n ]   |

                =    lim |    [ (n + 1) / n ]  ·  [ 3n  / 3n + 1 ]   |

                =    lim |    [ (n + 1) / n ]  ·  [  1/3  ]   |

                =   (1/3) · lim |  (n + 1) / n  |

                =   (1/3) · lim |  ( n/n ) + (1/n)  |

                =   (1/3) · lim |  1 + (1/n)  |

                =   (1/3) · [ lim | 1 | + lim | 1/n |

                =   (1/3) · [ 1 + 0 |

According to the ratio test, the series converges if this ratio is between -1 and 1 (excluded). This sequence thus comes together.

                =   (1/3)   <---  converges

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The full question:

A series is given by 1/3^1+2/3^2+3/3^3+4/3^4+5/3^5+...

Francine correctly applies the ratio test to determine whether the series converges or diverges.

Which statement reflects Francine's conclusion?

From the ratio test, r = 3. The series converges.

From the ratio test, r=1/3. The series diverges.

From the ratio test, r = 3. The series diverges.

From the ratio test, r=1/3. The series converges.

Answer:

From the ratio test, r=13. The series converges.

Step-by-step explanation:

I took the Test

The missing value in the ratio table will be calculated is 4.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

The missing values in the ratio table will be calculated this:

1/2 = x / 8

The next thing to do after the above is to cross multiply in order to get the value of x. This will be:

2 × x = 1 × 8

2x = 8

Then, we have to divide through by 2.

x = 8 / 2

x = 4

Therefore, the value of x is 4.

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Complete question

Find the missing values in the ratio table.

1/2 : x/8

Answer:

No

Step-by-step explanation:

They did not get everyones imput

The probability that at least one psychologist is chosen is 5/9 and the probability that exactly three psychologists are chosen is 16.3.

Total number of Attendants in a certain conference are 54

There are 24 psychiatrists and 30 psychologists

Total number of attendants = 24 + 30= 54.

Therefore total number of cases is 54

1 ) Since there are 30 psychologists, the number of favorable outcomes is 30.

So P ( 30 psychologists) =Number of favorable cases/ Total number of cases

= 30/54

= 5/9.

So probability of at least one psychologist is 5/9.

2 ) If we have to choose 3  psychologist favorable outcomes are

= 30/54 x 29/53 x 28/52

= 1015/6201

= 16.3

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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Answer:

x=-3

Step-by-step explanation: 5x+6=2x-3

Answer:

x = -3

Step-by-step explanation:

5x + 6 = 2x - 3

Subtract 2x + 6 on both sides,

5x + 6 - (2x+6) = (2x-3) - (2x + 6)

3x = -9

x = -3

Answer:

X=30

Step-by-step explanation:

The angle of a straight line is 180

You were given 150 and the angle across is X

180-150= X

X = 30

Proof:

4x + 2x must equal 180

Plug in 30

4(30)+2(30) = 120 + 60 = 180

The result of this calculation is -20xyz. This answer can be verified by taking 5x, which is 5 times x, and -4xyz, which is -4 times xyz, and multiplying them together. This gives -20 times x times y times z, which is -20xyz.

The product of 5x and -4xyz is -20xyz.

-20xyz

5x * (-4xyz) = 5x * (-4) * xyz = -20xyz

Multiplying 5x and -4xyz together yields -20xyz. To calculate this, first take the 5x and multiply it by -4. Then take the answer and multiply it by xyz. The result of this calculation is -20xyz. This answer can be verified by taking 5x, which is 5 times x, and -4xyz, which is -4 times xyz, and multiplying them together. This gives -20 times x times y times z, which is -20xyz.

The product of 5x and -4xyz is -20xyz.

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Answer:

Step-by-step explanation:

200

Answer:

3x - 5=-3

3x - 5+5=-3+5

3x=2

3x/3=2/3

x=2/3

Positive :D Hope this helped!!

Step-by-step explanation:

Answer:

x is positive.

Step-by-step explanation:

3x - 5= -3   ==> isolate x

3x = 2  ==> add 5 on both sides

x = 2/3  ==> divide 3 on both sides

Hence, x is positive.

Answer:

The expression. 7 plus the sum of a number x and 5 will be written as 7 + (x + 5).

Step-by-step explanation:

From the information given, the phrase is written as 7 plus the sum of a number x and 5. Therefore, the expression will be:= 7 + (x + 5).

Let's say x is 2. The the value will be:= 7 + (2 + 5)

= 7 + 7 = 14 

In conclusion, the correct option is 7 + (x + 5).

Penelope would have to pay 11.80 for a mug with her own name on it. the fixed cost would be 5.40 and cost per letter would be 0.80.

Total cost = Fixed cost + (no. of letters*cost per letter)

let us take the fixed cost as x and cost per letter as y

so for alexander,

12.60 = x + 9y (eq 1)

for lucia,

9.40 = x + 5y (eq 2)

equating eq1 and eq 2

12.60 - 9y = 9.40 - 5y

12.60 - 9.40 = - 5y + 9y

4y = 3.20

y = 0.80

x = 9.40 - 5y

= 9.40 - 4 = 5.40

therefore, the cost for penelopes mug will be,

= 5.40 + (8*0.80)

= 5.40 + 6.40 = 11.80

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The factors of the given polynomial as calculated from the given data is found as , (x−1) and (x 2 +x+1) .

The equation given in the question is , x³ - 1 .

On solving this equation we will get the result as ,

x³  −1

=(x−1)(x 2 +x+1)

Therefore, the factors of the given equation is both (x−1) and (x 2 +x+1) .

A quadratic equation factored form is used to find the roots or solutions of the given equation.  Example , the factored form of x2 +5x+6 = 0, is  x^2 +5 x + 6 = 0 is= 0 (x-2)(x-3) = 0.

When the product of two terms is zero, it signifies that any of them might be zero.

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So, the midpoint is at a ratio of 1/2 of the way from the first point to the second point on both x and y axis.

The ratio used to find the midpoint of a line segment is 1:1 or 1/2:1/2.

To find the midpoint of a line segment, we need to average the x-coordinates and the y-coordinates of the two given points.

The x-coordinate of the midpoint = (x1 + x2)/2

The y-coordinate of the midpoint = (y1 + y2)/2

So we can say that the midpoint is at a ratio of 1/2 of the way from the first point to the second point on both x and y axis.

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The volume of the picnic basket is 1920in^3.

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross section is same as its base, then its volume is:

[tex]V = B \times h[/tex]

where h is the height of that prism and B is the area of the base of that prism.

Given;

The height of the basket is 8 inches

The bottom of the basket has an area of 240 square inches.

Now,

V=B x h

V= 8 x 240

V= 1920

Therefore, the volume will be 1920in^3

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The quotient when (x³ + 8) is divided by   (x+2) is (x² - 2x + 4)

A polynomial is an equation that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. Using Descartes' Rule of Signs, the degree is used to calculate the greatest number of polynomial problem solutions.

The polynomials are (x³ + 8) and (x+2)

                         dividing  (x³ + 8) by  (x+2) we get,

                                     x + 2 ) x³ + 8 ( x² - 2x + 4

                                              - x³ - 2x²

                                                    -2x² + 8

                                                     2x² +4x

                                                              4x + 8

                                                             -4x - 8

                                                                  0

The quotient when (x³ + 8) is divided by   (x+2) is (x² - 2x + 4)

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Answer:

Step-by-step explanation:

           OK, first what I did was keep 0.70 the same and then I make 4/5 into a decimal and I get 0.8 so now that both are decimals we can compare them and 0.8 is greater so that means Louis walks a greater distance than Kell does

Answer:

We know that the total age of both kids is 36

we also know that Ahmed is 4 years older than Tamir.

To find the answer we will first divide 36 by 2

36/2 = 18

Now we will subtract 4 from 18 and we get 14

lastly, subtract 14 from 36

36 - 14 is 22

Hence, Ahmed is 22 while Tamir is 14

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There are 10 ways to put 5 balls in 2 boxes

A Combination formula C(n , r) = [tex]\frac{n!}{r! (n -r)!}[/tex]  is used when

Given that, the total balls are 5:

n=5

We have wished to distribute them in 2 boxes:

r=2

Since the objects are indistinguishable, we can be used the combinations formula:

C(n , r) = [tex]\frac{5!}{2! 3!} = 10[/tex]

Hence, there are 10 ways to put 5 balls in 2 boxes.

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We can solve a quadratic equation by factoring only if always the equation is in the form "(quadratic expression) equals (zero)".

We need to use the following steps to solve the quadratic equation by factoring:

Step 1. Place the quadratic expression on one side of the "equals" sign, with zero on the other side.

Step 2. Factor the given quadratic expression into its two linear factors.

Step 3. Put each of these linear factors equal to zero, forming two linear equations.

Step 4. Solve the two linear equations.

For example, Solve (x − 2)(x − 4) = 0 by factoring.

x − 2 = 0   or   x − 4 = 0

x = 2   or   x = 4

x = 2, 4

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Answer:

x= -18.6666666667

Step-by-step explanation:

[tex]3/4x+5=-9\\ \\3/4x=-9-5\\ \\3/4x=-14\\ \\x= -14 X \frac{4}{3}\\ \\x= \frac{-14 X4}{3}\\ \\x= \frac{-56}{3}\\\\x= -\frac{56}{3}\\\\x= -\frac{56}{3} = -18.6666666667[/tex]

The value of w is 100

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

Example of linear equations are 5x +2 = 7. This is an example of linear equation with one variable. Example of linear equation with two variables is :

5x+2y = 3 and 7x+6y = 5.

Where x and y are the variables.

Similarly , 35 = 0.35w is an example of linear equation with one variable , here the variable is w. And to find the value if the variable we divide both sides by the coefficient of w.

Therefore, divide both sides by 0.35

35/0.35 = w

w = 100

therefore the value of w = 100

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Answer: The measure of an angle is the same as the measure of its reference angle in the first or fourth quadrant. Since, m∠884° is in the 8th quadrant, we can use the reference angle in the first quadrant, which is m∠4°.

So, m∠1 = m∠4°

To find the measure of the angle m∠3, we can use the fact that angles in different quadrants that share a terminal side have measures that add up to 180°.

m∠3 = 180° - m∠1

m∠3 = 180° - m∠4°

m∠3 = 180° - 4° = 176°

Therefore, m∠1 = m∠4° and m∠3 = 176°.

Step-by-step explanation:

Answer: The opposite of a number is the number that, when added to it, equals zero. In this case, the opposite of -2/5 is 2/5. When you add -2/5 and 2/5, the result is 0.

Step-by-step explanation:

Answer: 2/5

Step-by-step explanation: If it’s negative you change it, if it’s positive you keep the number the same so in this question the fraction 2/5 is negative so the opposite of -2/5 is 2/5.