PLEASE HELP
Giada earns a salary of $42,670 a year and is paid every two weeks. What is her gross pay per pay period?

Answer:

56.84

Step-by-step explanation:

For rectangles and squares you multiply those two numbers and there is your answer. Then for triangles you multiply those two numbers but then you divide by 2 always. You got this! Keep going!

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:

5

Step-by-step explanation:

Artificial selection takes a comparatively longer time to occur while natural selection takes a comparatively shorter time to occur.

Thus, the given statement is False.

Artificial selection takes a very short time related to natural selection. The time taken to choose the individual having the required character and then making them produce the offspring is the only time needed for the entire process.

Artificial selection can be demonstrated as the series of steps for selecting the required character and making the individuals having those character to produce the offspring having the desired character.

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The area of the composite figure is 111 square units.

A composite figure is a 2D shape or figure that is made up of two or more simpler shapes or figures combined together. These simpler shapes can be any combination of polygons, circles, or other curves.

Composite figures are often formed when two or more basic shapes are put together to create a more complex shape. For example, a figure that consists of a rectangle and a triangle placed together is a composite figure.

To find the area of a composite figure like this, we can break it up into simpler shapes and then find the area of each shape and add them together.

First, we can see that the shape consists of three triangles and a rectangle:

Triangle 1: (0,3), (2,3), (2,7)

Triangle 2: (-7,7), (-7,6), (5,-6)

Triangle 3: (5,1), (-1,-2), (-5,2)

Rectangle: (-3,5), (0,3), (-7,7), (-7,6)

To find the area of each triangle, we can use the formula:

Area = 1/2 * base * height

For Triangle 1, the base is 2 - 0 = 2 and the height is 7 - 3 = 4. So the area is:

Area of Triangle 1 = 1/2 * 2 * 4 = 4

For Triangle 2, the base is 5 - (-7) = 12 and the height is 7 - (-6) = 13. So the area is:

Area of Triangle 2 = 1/2 * 12 * 13 = 78

For Triangle 3, we can see that it is a right triangle with sides of length 6, 6, and 8. So the area is:

Area of Triangle 3 = 1/2 * 6 * 8 = 24

To find the area of the rectangle, we can use the formula:

Area = length * width

The length is the distance between (-7,7) and (-7,6), which is 1. The width is the distance between (-7,7) and (-3,5), which is 5. So the area is:

Area of Rectangle = 1 * 5 = 5

Finally, we can add up the areas of all the shapes to get the total area:

Total Area = Area of Triangle 1 + Area of Triangle 2 + Area of Triangle 3 + Area of Rectangle

Total Area = 4 + 78 + 24 + 5

Total Area = 111 square units

Therefore, the area of the composite figure is 111 square units.

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The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10

To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.

Bus 47:

Median (Q2): 16

Q1: 10

Q3: 22

IQR = Q3 - Q1 = 22 - 10 = 12

Bus 18:

Median (Q2): 12

Q1: 8

Q3: 18

IQR = Q3 - Q1 = 18 - 8 = 10

Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.

Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.

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Answer:

x+2y=2 x-2y=-2. It has infinitely many solutions. It has no solution. It has one solution

Answer:

768

Step-by-step explanation:

16x48= 768

Answer:

768

Step-by-step explanation:

you multiply 16 times 48 to find the weekly wage

Let's do the first question which is 10 1/4. If converted to decimal, percent, and scientific notation, respectively, they are 10.25, 1025%, and 1.025 × 10².

Here are the steps to convert the rational number 10¼ to decimal, percent, and scientific notation:

Decimal representation: To convert a fraction to a decimal, divide the numerator by the denominator. In this case, 10¼ is equal to 10 + ¼, which is equal to 10.25 when expressed as a decimal.

Percent representation: To convert a decimal to a percent, multiply it by 100. In this case, 10.25 × 100 = 1025, so 10¼ can be expressed as 1025%.

Scientific notation: Scientific notation is a way of writing a number as a power of 10. To convert a number to scientific notation, we find a power of 10 that is close to the number and write the number as a product of the power of 10 and a number between 1 and 10. In this case, 10.25 can be written as 1.025 × 10², so 10¼ can be expressed as 1.025 × 10² in scientific notation.

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Answer:

The simplified expression is:

\(\dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr\)

Step-by-step explanation:

To find:

\(-\dfrac{1}{2}p^{2} q^{2} r+\dfrac{1}{3}p q^{2} r-\dfrac{1}{4}p q r^{2}-\dfrac{1}{5}rq^{2} p^{2} +\dfrac{1}{6}rq^{2} p-\dfrac{1}{7}r^{2}pq+\dfrac{1}{8}rp^{2}q\)

Solution:

We can see that pqr having power 1 is common throughout.

Let us take it common to make the expression simpler and then we will add by taking LCM:

\(\Rightarrow pqr(-\dfrac{1}{2}p q+\dfrac{1}{3}q-\dfrac{1}{4}r-\dfrac{1}{5}pq+\dfrac{1}{6}q-\dfrac{1}{7}r+\dfrac{1}{8}p)\\\Rightarrow pqr(-\dfrac{1}{2}p q-\dfrac{1}{5}pq+\dfrac{1}{3}q+\dfrac{1}{6}q-\dfrac{1}{4}r-\dfrac{1}{7}r+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-5pq-2pq}{2\times 5}+\dfrac{2q+q}{2 \times 3}+\dfrac{-7r-4r}{7 \times 4}+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-7pq}{10}+\dfrac{3q}{6}+\dfrac{-11r}{28}+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-7}{10}pq+\dfrac{1}{2}q+\dfrac{-11}{28}r+\dfrac{1}{8}p)\)

Now, multiplying pqr again to the expression:

\(\Rightarrow \dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr\)

So, the answer is:

\(\dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr\)

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:

Maria served 21 orders, Chau served 30 orders and Greg served 63 orders.

Explanation:

Total number of orders = 114

Let the number of orders served by Maria =x

Chau served 9 more orders than Maria.

Therefore:

Number of orders served by Chau = x+9

Greg served 3 times as many orders as Maria.

Therefore:

Number of orders served by Greg = 3x

Next, we take the sum of their orders. This is:

Therefore:

• Number of orders served by Maria =x=21

• Number of orders served by Chau = x+9 =21+9=30

• Number of orders served by Greg = 3x =3 X 21 =63

Maria served 21 orders, Chau served 30 orders and Greg served 63 orders.

Answer:

\(\large\boxed{\sf x = \frac{8y+1}{7} }\)

\(\large\boxed{\sf x = \frac{7x-1}{8} }\)

Group the Variable's:

2 x - 5 + 7 y - 3 = 9 x - 1 - y -8

2x -9x + 7y +y = -1 -8 +5 + 3

-7x + 8y = -1

From this find x and y

For X

-7x + 8y = -1

-7x = -1 -8y

7x = 8y + 1

x = (8y +1)/7

For Y

-7x + 8y = -1

8y = -1 +7x

y = (7x -1)/8

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

Answer:

(a) Accept the alternate hypothesis

(b) \(t = 104.86\)

Step-by-step explanation:

Given

\(\mu= 69\)

\(\sigma = 5.0\)

The sample data

Solving (a): Test whether the process increases the mean battery life

First, we state the null hypothesis

This states that the mean is 69

\(H_o :\mu = 69\)

Next, the alternate hypothesis is to test that the mean has changed.

i.e \(H_a: \mu \ne 69\)

Calculate the mean:

\(\mu = \frac{\sum x}{n}\)

\(\mu = \frac{82.5 +78.4 +80.2 +78.7 +67.8 +76 +74.8 +73.9 +68.8 +70.3 +70.7 +70.7......+69.6 +70.4}{40}\)

\(\mu = \frac{2923.5}{40}\)

\(\mu = 73.0875\)

Calculate the standard deviation

\(\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}\)

\(\sigma= \sqrt{\frac{(82.5-73.0875)^2 +(78.4 -73.0875)^2 +(80.2 -73.0875)^2 +(78.7 -73.0875)^2 +......+(70.4-73.0875)^2}{40}}\)\(\sigma= \sqrt{\frac{776.76375}{40}}\)

\(\sigma= \sqrt{19.41909375}\)

\(\sigma= 4.407\)

From the calculations above: The calculated mean 73.0875 is not the same as 69.

Hence, we accept the null hypothesis that: \(H_a: \mu \ne 69\)

Solving (b): The test statistic

This is calculated as:

\(t = \frac{\mu}{\sigma/\sqrt n}\)

This gives:

\(t = \frac{73.0875}{4.407/\sqrt {40}}\)

\(t = \frac{73.0875}{4.407/6.325}\)

\(t = \frac{73.0875}{0.697}\)

\(t = 104.86\)

The  measure of arc JM is 88 degrees, option D is correct.

Given that Chords JK and LM intersect at point O in a circle.

The measure of arc LK is 120° and the measure of angle JOM is 104.

We have to find  measure of arc JM

By angles of intersecting chord theorem

When two chords intersect inside a circle, the products of the segments of one chord are equal to the products of the segments of the other chord.

104=1/2(arc LK + arc JM)

Plug in the measure of arc LK which is 120 in above equation

=1/2(120+arc JM)

104×2 =120+arc JM

Subtract 120 from both sides

208-120=arc JM

arc JM =88 degrees

Hence, the  measure of arc JM is 88 degrees, option D is correct.

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Reason:

This graph passes the vertical line test, so it is a function.

The vertical line test is where we try to pass a single vertical line through more than one point on the curve. If such a thing is possible, then we say the curve fails the vertical line test and it's not a function.

Graph D for instance can have a vertical line through x = 1 and intersect the curve at (1,4) and (1,-4) simultaneously. The input x = 1 leads to multiple outputs (y = 4 and y = -4). Graph D fails the vertical line test for this very reason, and it is not a function. Graphs A and B are similar stories. Any vertical line itself is automatically not a function.

To have a function, any x input in the domain must lead to exactly one and only one y output in the range.

---------

Notice with graph C it is impossible to have a single vertical line intersect more than one point on the curve. So this is why graph C passes the vertical line test. Each input leads to exactly one output.

Answer:

.5

Step-by-step explanation:

brainlies please

Answer:

150

Step-by-step explanation:

Answer:

-74

Step-by-step explanation:

3(1-2) + (-71)

3(-1) - 71

-3 -71

-74

Answer:

509

Step-by-step explanation:

4581 ÷ 9 = 509

Quotient means to divide

I hope this helps you

(2/5) (-5/7)

To simplify the equation

Step 1:

\( \blue{= \dfrac{2}{5} \times \dfrac{ - 5}{7} }\)

\(\green{so \: after \: simplifying \: the \: equation \: it \: will \: look \: like \: this}\)

Step 2:

\( \blue{= \dfrac{2}{1} \times \dfrac{ - 1}{7} }\)

Step 3:

\( \blue{=\dfrac{ - 2}{7} }\)

Step 4:

\(\blue{=−0.28571✓}\)

With regards!

★Dull Star★

Answer: 2,-2

Step-by-step explanation: 9-7 is 2 and -9 minus -7 is minus 2.

Answer:

I hope I can help

Step-by-step explanation:

welcome po

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Step-by-step explanation:

\( {( ({3})^{4} })^{8} \\ = {3}^{32} \)

Based on a system of equaitons, the initial opening fee (one-time payment) is $5.00, the monthly maintenance fee is $11.00, while an equation that models Adam's fees over time in months, x is y = 11x + 5.

A system of equations or simultaneous equations are two or more equations solved concurrently or at the same time.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

While algebraic expressions combine variables with numbers and mathematical operands, equations use the equal symbol (=).

Total Fees after x months

x = # of months    y = total fees ($)

2                                      27

3                                      38 (11 x 3 + 5)

4                                      49 (11 x 4 + 5)

5                                     60

Let w = the monthly maintenance fee

Let z = the one-time opening fee

5w + z = 60 ... Equation 1

2w + z = 27 ... Equation 2

Subtract Equation 2 from Equation 1:

3w = 33

w = 11

b) The monthly maintenance fee is $11.00.

a) The initial (one-time) opening fee is $5.00.

z = 60 - 55

= 5

c) The total fees after x months is y = 11x + 5.

Thus, the one-time opening fee and the monthly maintenance fee can be computed using a system of equations.

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