Two employees Maggie and Rachel earn $18 per hour. Maggie receives 1.00 raise each 6 months and Rachel receives a 6% raise each year. Write an equation to represent Maggie pay over x years

Answer:

3 faces

A cylinder has 3 faces - 2 circle ones and a rectangle (if you take the top and bottom off a tin can then cut the cylinder part on the seam and flatten it out you would get a rectangle). It has 2 edges and no vertices (no corners).

Step-by-step explanation:

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A cylinder has 3 faces - 2 circle ones and a rectangle

The percentage increase in the cost of the airline tickets is 38%.

Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency. In order to convert a value to a percentage, multiply the value by 100.

in order to determine the percentage increase, multiply the fraction of the change in price and the initial price by 100.

Percentage increase = (change in price / initial price)  100

Change in price = new price - initial price = $310 - $225 = $85

Initial price = $225

($85 / $225) x 100 = 38%

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$1470 more money  does Michael have  than Steven after 1 year.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.

Rate of interest is simple interest for Steven in a savings account. He can withdraw his money any time he wishes to.

Steven will receive after 1 yr an interest payment of

=35000×1.8/100

=35000×0.018

=630

Michael invests his inheritance in a CD (Certificate of Deposit) account. He gave up access to his money for a specified period of time. Assuming that given rate of interest is annual.

=35000×6/100

=35000×0.06

=2100

Therefore, Micheal has more money than Steven.

=2100-630

=1470.

Hence $1470 more money  does Michael have  than Steven after 1 year.

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Subtract what they already have from what they needed:

895 - 351 = 544

They need$544 more.

Divide how much more they need by the number of teams:

544/34 = 16

They need to charge each team $16

The sketch of the sine curve with amplitude 2 and period π/3 consists of one complete wave oscillating between y = 2 and y = -2.

To sketch the sine curve with the given amplitude and period, we need to understand the characteristics of the sine function. The general equation for a sine function is y = A * sin(Bx), where A represents the amplitude and B represents the frequency.

In this case, the amplitude is given as 2, which means the curve will oscillate between y = 2 and y = -2. The period is given as π/3, which represents the length of one complete cycle of the sine curve. Since the period is the distance it takes for the curve to repeat itself, we can divide it into smaller intervals to create the sketch.

Starting at the origin, we can mark points on the curve at intervals of π/3. The curve will reach its maximum value (amplitude) at π/6 and its minimum value at 5π/6. These points represent the peaks and troughs of the wave. We can then connect these points smoothly to form the curve.

The resulting sketch will show one complete cycle of the sine curve, oscillating between y = 2 and y = -2, with a period of π/3.

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Answer:

The solution of the system of equations be:

\(x=8,\:y=4\)

Hence, option C is true.

Step-by-step explanation:

Given the system of equations

\(\begin{bmatrix}4x+7y=60\\ -4x+7y=-4\end{bmatrix}\)

adding both the equations

\(-4x+7y=-4\)

\(+\)

\(\underline{4x+7y=60}\)

\(14y=56\)

so the system of equations becomes

\(\begin{bmatrix}4x+7y=60\\ 14y=56\end{bmatrix}\)

solve 14y for y

\(14y=56\)

Divide both sides by 14

\(\frac{14y}{14}=\frac{56}{14}\)

Simplify

\(y=4\)

\(\mathrm{For\:}4x+7y=60\mathrm{\:plug\:in\:}y=4\)

\(4x+7\cdot \:4=60\)

\(4x+28=60\)

Subtract 28 from both sides

\(4x+28-28=60-28\)

Simplify

\(4x=32\)

Divide both sides by 4

\(\frac{4x}{4}=\frac{32}{4}\)

\(x=8\)

Therefore, the solution of the system of equations be:

\(x=8,\:y=4\)

Hence, option C is true.

Answer:

4(9 + 4)

Step-by-step explanation:

36 + 16 ← factor out HCF of 4 from each term

= (4 × 9) + (4 × 4)

= 4(9 + 4)

another way to write 36 + 16 is 4(9) + 4(4).

To rewrite the expression 36 + 16 using the distributive property, we need to find a common factor that can be factored out. In this case, both 36 and 16 are divisible by 4. So, we can rewrite the expression as:

36 + 16 = 4(9) + 4(4)

Using the distributive property, we can further simplify this expression:

4(9) + 4(4) = 4 * 9 + 4 * 4

Now, we can calculate the values:

4 * 9 = 36

4 * 4 = 16

Therefore, another way to write 36 + 16 is 4(9) + 4(4).

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Answer: 12.50= 2x + 3y,

5.50= 2x+y,

5=x+Y

Step-by-step explanation: Use a graphing calculator bro

Answer:

Cross Sectional

Step-by-step explanation:

A cross sectional is one in which an association is developed between a risk factor or an outcome.

In the given question the device is used to record the viewing habits of about 2500 ​households, and the data collected today will be used to determine  the proportion of households tuned to a particular news program. There will be risk factor in today's research with the future developed program which will the outcome.

For example there are 20 students in my class who cannot write. So I develop a program to help them write. But the next year there may not be any student who would require such help.So there's a risk factor associated with the outcome.

Cross sectional results are recorded in a two ways table showing do's and don'ts.

Answer:

C.

Step-by-step explanation:

5/7=.714285714 and so on

7/9=.777777778 and so on

Answer:

y = 1/4x + 4

Step-by-step explanation:

y = mx + b

Since the lines are parallel, the slope is the same. m = 1/4

y = 1/4x + b

Substitute (4,5)

5 = 1/4(4) + b

5 = 1 + b

4 = b

The y-intercept is (0, 4).

y = 1/4x + 4

Answer:

226.8 grams

Step-by-step explanation:

After applying the method of Lagrange multipliers and considering the cases separately, we find that there are no critical points that satisfy the given constraint equation x^2 + y^2 = 62.

To apply the method of Lagrange multipliers, we first define the Lagrangian function L(x, y, λ) as follows:

L(x, y, λ) = f(x, y) - λ(g(x, y))

where f(x, y) = (x^2 + 1)y is the objective function and g(x, y) = x^2 + y^2 - 62 is the constraint equation. λ is the Lagrange multiplier.

To find the critical points, we need to solve the following system of equations:

∂L/∂x = 2xy - 2λx = 0 ...(1)

∂L/∂y = x^2 + 1 - 2λy = 0 ...(2)

∂L/∂λ = -(x^2 + y^2 - 62) = 0 ...(3)

Now let's consider the cases separately:

Case 1: y = 0

From equation (2), when y = 0, we have x^2 + 1 - 2λ(0) = 0, which simplifies to x^2 + 1 = 0. However, there are no real solutions for this equation. Hence, there are no critical points in this case.

Case 2: x = 0

From equations (1) and (2), when x = 0, we have -2λy = 0 and 1 - 2λy = 0, respectively. Since -2λy = 0, it implies that λ = 0 or y = 0. If λ = 0, then from equation (3), we have y^2 = 62, which has no real solutions. If y = 0, then equation (2) becomes x^2 + 1 = 0, which again has no real solutions. Thus, there are no critical points in this case either.

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The probability of randomly selecting a tree or an insect is 3/10

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

10 insects, 8 trees, 8 flowers, and 4 birds.

To find the probability of randomly selecting a tree or an insect,

We need to find the number of tree and insect cards and divide by the total number of cards.

There are 8 tree cards and 10 insect cards, for a total of 8 + 10 = 18 cards.

So the probability of randomly selecting a tree or an insect

P = 18/30

P = 3/5.

hence, the probability is 3/5.

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a. Sketch of the whole network:

   A(5)     B(Z+1)

    |         |

    Y+1       |

    |         |

   ---       ---

  |   |     |   |

  D(А) X+6 E(1) |

    |   |   |   |

   ---  |   |   |

         |   |   |

         F(4)  |

          |   ---

          |     |

          G(10) |

          |     |

         ---    |

        |   |   |

        H(B,C)  |

            8   |

            |   |

           ---  |

          |   | |

          1 GH 2

b. Calculation of critical path by analyzing and showing ES, EF, LS, LF and float in a table:

Activity Immediate Predecessors Activity Time (days) ES EF LS LF Float

A - 5 0 5 0 5 0

B - Z+1 0 Z+1 0 Z+1 0

C B 0 Z+1 Z+1 Y+1 Y+1 Z-Y-1

D A X+6 5 X+11 5 X+11 0

E A 1 5 6 5 6 0

F E 4 6 10 6 10 0

G D,F 10 X+11 X+21 X+11 X+21 0

H B,C 8 Y+1 Y+9 Y-7 1 8

GH H 2 Y+9 Y+11 1 3 0

The critical path is A-D-G-H-GH, with a total duration of X+21 days.

c. Project completion time: X + 21 days.

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\(\frac{119}{780}\) fraction of the whole piece you play middle C.

To find  for what fraction of the whole piece do you play middle C:

Since 7 out of every 13 beats in the finale are played at middle C, \(\frac{7}{13}\) the finale is played at middle C.

The finale is 17 measures out of a 60-measure piece or \(\frac{17}{60}\) of the whole piece.

\(\frac{7}{13}\) of \(\frac{17}{60}\) is \(\frac{7}{13}\) x \(\frac{17}{60} = \frac{119}{780}\)

Therefore,  \(\frac{119}{780}\) for a fraction of the whole piece you play middle C.

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The magnitude of the force on the test charge will be the magnitude of the net force acting on the test charge due to its interaction with the other 2 charges.

The magnitude of the force on a test charge is the measurement of the strength of the interaction between the test charge and other charges.

In this scenario, a test charge of 1 µc is placed halfway between two charges of 3.2 µc and 8.2 µc separated by 10 cm. To find the magnitude of the force on the test charge, we can use Coulomb's law.

The magnitude of the force is given by the formula

=> F = k * q1 * q2 / r²,

where k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

The magnitude of the force between the test charge and the 3.2 µc charge is given by the formula

=> F = k * 1 * 3.2 / (0.05²).

The magnitude of the force between the test charge and the 8.2 µc charge is given by the formula

=> F = k * 1 * 8.2 / (0.05²).

The magnitude of the force on the test charge is the sum of these two forces, which can be calculated using the formula

=> F = k * q1 * q2 / r².

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a. The product of numbers by using distributive property is -605/7.

b. The product of numbers by multiplying fractions is -605/7.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

To find the product of number -11 (7 6/7).

Now, The product of numbers by using distributive property is calculated as;

⇒ -11 (7 6/7) = -11 * (7 + 6/7)

                  = -11 * 7 - 11 * 6/7

                  = -77 - 66/7

                  = (-539 - 66)/7

                  = -605/7

Hence, The product of numbers by using distributive property is -605/7.

And, The product of numbers by multiplying fractions is;

⇒ -11 (7 6/7) = -11 * 55/7

                  = -605 /7

Hence,  The product of numbers by multiplying fractions is -605/7.

So, a. The product of numbers by using distributive property is -605/7.

b. The product of numbers by multiplying fractions is -605/7.

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Answer:

Step-by-step explanation:

The relation is not a function!

Answer:

p²q³ + pq and pq(pq² + 1)

Step-by-step explanation:

Given

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Required

Collect like terms

We start by rewriting the expression

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Collect like terms

3p²q² -3p²q² - 3p²q³ +4p²q³ + pq

Group like terms

(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq

Perform arithmetic operations on like terms

(0) - (-p²q³) + pq

- (-p²q³) + pq

Open bracket

p²q³ + pq

The answer can be further simplified

Factorize p²q³ + pq

pq(pq² + 1)

Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)

An example of an even function is f(x) = x² and odd function if f(x) = x³

An even function is a function that is symmetric about the y-axis, meaning that f(-x) = f(x) for all x in the domain of the function. An odd function is a function that is antisymmetric about the origin, meaning that f(-x) = -f(x)

for all x in the domain of the function. This function is symmetric about the y-axis, and f(-x) = (-x)^2 =  x² = f(x) for all x. An example of an odd function is f(x) = x³. This function is antisymmetric about the origin, and f(-x) = (-x)^3 = -x³ = -f(x) for all x.

It's important to note that not all functions are even or odd. Some functions can be neither even nor odd. Even and odd functions have specific properties that make them useful in solving problems in various fields such as physics and engineering.

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Answer:

Jack has a toy poodle names Lucy. He is supposed to feed Lucy 11 ounces of dog food a day. He has s ounces of food in the bag he bought for the month. The amount of dog food left in the bag after feeding Lucy today is represented by s-11.

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Answer:

Step-by-step explanation:

Given points:

Slope is:

Use formula y = mx + b, substitute x = -2, y = 1, m = -3/5, find y-intercept b:

Correct option is B.

Step-by-step explanation:

\( m \: = \: -3/5 \: and \: b \: = \: -1/5\)

The equation of the circle with centre C and passing through points N and W is x² + y² = 400.

From the question, we know the following:

- point C is the midpoint of WN,

- CN = CW = 20  

- radius of the circle = 20.

To write the equation of this circle, we need to use the standard form equation of a circle:

(x - h)² + (y - k)² = r²

where

(h,k) = centre of the circle,

r is its radius.

Since the centre of the circle is at the origin (0, 0), we can simplify the equation to:

x² + y² = r²

Now we just need to find the value of r. Since we know that the radius is 20 units, we can substitute r = 20 into the equation to get:

x² + y² = 20²

Simplifying further, we get:

x² + y² = 400

Therefore, the equation of the circle with center C and passing through points N and W is:

x² + y² = 400

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To prove that two triangles △ABC and △DEF are similar, we can use the following theorem:

The Angle-Angle (AA) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Or else, if ∠A ≅ ∠D and ∠B ≅ ∠E, then △ABC ~ △DEF. This theorem relies on the fact that when two angles of one triangle are congruent to two angles of another triangle, the third angle must also be congruent due to the fact that the sum of the angles in a triangle is always 180 degrees. Thus, the triangles must have the same shape and are therefore similar.

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The volume of the square-based pyramid is 3888 units³. Your answer is option B. 3888 units³.

The formula to calculate the volume of a pyramid is V = (1/3)Bh,

Where B is the area of the base and h is the height.

In this case, the base is a square with edge length 9 units, so the area is B = 9² = 81 units².

The height is given as 48 units.
Plugging these values into the formula, we get:
To find the volume of a square-based pyramid, you can use the following formula:

V = (1/3) * base area * height.

In this case, the base edge is 9 units and the height is 48 units.

First, find the base area:

A = side * side = 9 * 9

= 81 square units.

Next, calculate the volume:

V = (1/3) * 81 * 48 = 3888 cubic units.
V = (1/3)(81)(48)
V = 1296 units³
Therefore, the volume of the pyramid is 1296 units³, which is option b.

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