If Calvin gets paid on the 15th and last day of the month, how many paychecks will he receive in
one year?
Will he receive the same number of paychecks if gets a paycheck
very two weeks? Y/N explain.

Answer:

- x² + 7x + 13

Step-by-step explanation:

a parabola in standard form id expressed as

ax² + bx + c ( a≠ 0 )

given

(x + 1)² - (2x + 3)(x - 4) ← expand factors using FOIL

= x² + 2x + 1 - (2x² - 5x - 12) ← distribute parenthesis by - 1

= x² + 2x + 1 - 2x² + 5x + 12 ← collect like terms

= - x² + 7x + 13 ← in standard form

7 1/5 divided by 8 in fraction form is 36 / 40 = 9/ 10 and in decimal form = 0.9

A fraction is a numerical expression expressing a portion of the whole. There are two parts: a numerator and a denominator. The denominator is the total number of pieces that make up the whole, while the numerator is the number of equally sized portions of the whole. For instance, in the percentage of 3/8 has a denominator of 8 and a numerator of 3.

We have been given that -

7 1/5 divided by 8

Rewrite as

(36/5) / 8

36 / 5×8

Multiplying 5 with 8 and we get

36 / 40

Follow these steps to convert an incorrect fraction to a mixed number: Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.

36/ 40 in decimal form = 0.9

0.9 = 0.9 × 10 /1 × 10

= 9 / 10

Hence, When 7 1/5 is divided by 8, the result is 36/40 (9/10) and 0.9 (in decimal notation).

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The percentage change of the given exponential function f(x) = 400(0.85)^(x) is; 15%

How to Interpret Exponential decay function?

The general form of an exponential decay function is:  

y = a(1 – b)^(x)

where:

y is the final amount that remains after a period of time decayed

a is the initial amount

x is the time

Decay factor = (1 – b).

where;

b is the percent change written in decimal form.

We are given the exponential function as;

f(x) = 400(0.85)^(x)

Now, from the general form of an exponential decay function, we can say that;

1 - b = 0.85

b = 1 - 0.85

b = 0.15 or 15%

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Answer:

b. 18/51

Step-by-step explanation:

There is a total of 18 blue and yellow candies, so in a total of 51, there would be a chance of 18/51 that you draw a yellow or blue piece.

Answer:

18/51

Step-by-step explanation:

Translation of negative 6 units x, 1 units y composition reflection across the x-axis

The composition transformation that maps ABCD to A''B''C''D'' comprises

of two or more transformations that maps the image

The rule that describes the composition transformation that maps ABCD to

A''B''C''D'' is the option;

Translation of negative 6 units x, 1 units y composition reflection across the x-axis.

The given coordinates of parallelogram ABCD are (3, 5), (6, 5), (4, 1), (1, 1)

The coordinates of the parallelogram A'B'C'D' are; A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)

The coordinates of the parallelogram A''B''C''D'' are;

D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)

The image of the point (x, y), following a reflection about the x-axis is the point (x, -y)

The difference in the coordinates of the parallelogram ABCD and A'B'C'D'

is the change in the sign of the y-coordinates

Therefore, the transformation that gives the parallelogram A'B'C'D' from

the parallelogram ABCD is a reflection about the x-axis

The difference between the coordinates of the vertices of the

parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the

x-value by (-6), and a change in the y-value by (+1)

Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram

A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation

of 1 unit, x in the y-direction

Which gives;

The composition transformation that maps the pre-image ABCD to the

final image A''B''C''D'', (given that in a composition transformation, the

transformation to the right is done first) are;

[tex]$\mathrm{T}_{-6,1} \cdot \mathrm{r}_{\mathrm{x}-\{axis}}(\mathrm{x}, \mathbf{y})$[/tex]which is the option;

Translation of negative 6 units x, 1 units y composition reflection across the x-axis

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Answer:

175 x 20

Step-by-step explanation:

You said that bacteria doubles every day, so it's x2. Since it's the course over 10 days, it's 10 x 2 = 20. So the expression is 175 x 20.

Answer:

t=-20/3

Step-by-step explanation:

Let's solve your equation step-by-step.

8=−6/5t

Step 1: Flip the equation.

−6/5t=8

Step 2: Multiply both sides by 5/(-6).

(5/−6)*(−6/5t)=(5/−6)*(8)

t=−20/3

Answer:

t=−20/3

The value of x that makes line l, m and n parallel is 12.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The value of x that makes the line l, m and n parallel can be calculated as follows:

124 + 5x - 4 = 180 (supplementary angles)

124 - 4 + 5x = 180

120 + 5x = 180

subtract 120 from both sides of the equation

120 - 120 + 5x = 180 - 120

5x = 60

divide both sides by 5

x = 60 / 5

x = 12

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The more likely event is (B) Enzo passes the test , the correct option is (B).

In the question ,

it is given that

the probability that Felipe will pass the test is 0.19

Converting 0.19 to percent , we get

0.19 = 0.19/100 = 19%

the probability that Enzo will pass the test is 1/4 ,

Converting 1/4 to percent , we get

1/4 = 1/4 * 100 = 100/4 =25%

hence , the probability of Felipe passing the test is 19% and the probability that Enzo passes the test is 25% ,

On comparing we see that 25% > 19% , which means Enzo has higher chance of passing the test than Felipe .

Therefore , the more likely event is (B) Enzo passes the test , the correct option is (B).

The given question is incomplete , the complete question is

Both Felipe and Enzo forgot to study for their science test. The probability of Felipe passing the test is .19 , the probability of Enzo passing the test is 1/4.

Which of these events is more likely?

(A) Felipe passes the test.

(B) Enzo passes the test.

(C) Neither. Both event are equally likely.

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Answer:

$36.40

Step-by-step explanation:

.04x35

Answer:

it is ten 10

Step-by-step explanation:

By using linear equation, When the swimsuit was twice as much as the goggles and the swim cap was half the price of the goggles. If the total cost of the items was $59.50, then the price of the swimsuit is $34

The total cost of the items = $59.50

Consider the cost of goggles = 2x

The swimsuit was twice as much as the goggles

The cost of the swimsuit = 4x

Swim cap was half the price of the goggles

The cost of the swim cap = x

Then the price of the items = The cost of goggles + The cost of the swimsuit + The cost of the swim cap

Substitute the values in the equation

2x + 4x + x = 59.50

7x = 59.50

x = $8.5

The cost of the swimsuit = 4x

= 4×8.5

= $34

Hence, by using linear equation, when the swimsuit was twice as much as the goggles and the swim cap was half the price of the goggles. If the total cost of the items was $59.50, then the price of the swimsuit is $34

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The graph of each function in the piecewise function is added as an attachment

The equation of the piecewise function is given as

f(n) = n/2 if n is even

        3n + 1 if n is odd

In the above definition of the piecewise function, we have the following functions and the domains

Note that:

The domain of the function is the set of input values of the graph

This in other words mean the domain of a function is the set of x values of the graph.

Next, we plot the graph of each function in the piecewise function in their respective domain

See attachment for the graph of each function in the piecewise function,

On the graph, the blue line represents f(n) = n/2 while the other line represents f(n) = 3n + 1

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Pythagoras theorem - The length of the third side is 6.71unit

What is Pythagoras theorem ?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The triangle's third side will be the following length:

Let x represent the triangle's third side's length.

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

x = 6.71 units

Hence, the third side of the triangle is 6.71unit

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The amount that Reshma spent on comic books is Rs. 165.

The amount that is left with her is Rs. 495.

A fraction is a quantity that is not a whole number. A fraction consists of a numerator and a denominator. An example of a fraction is 1/4. 1 is the numerator and 4 is the denominator.

In order to determine the amount she spent on comics, multiply the fraction spent by the amount of her pocket money. Multiplication is the process used to determine the product of two or more numbers. The sign that represents multiplication is ×.

Money spent on comics = fraction of the money spent x pocket money

1/4 x 660 = Rs. 165

The amount left can be determined by subtracting the amount spent on comics by the value of her pocket money.

Amount left = pocket money - amount left

Rs 660 - Rs 165 = Rs 495

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Answer:

-1

Step-by-step explanation:

-10+11+x = 0

1+x = 0

x = -1

Answer:

draw the diagram out

Step-by-step explanation:

BC=17-11

= 6

Table of ordered pair for the equation y =-13x +4 is given by (0,4) and (1,-9).

As given in the question,

Given equation is equal to :

y = -13x + 4

Substitute x =0 in the given equation

y = -13 (0) + 4

⇒ y = 0 +4

⇒ y = 4

Ordered pair is (0,4)

Substitute x=1 in the given equation

y = -13(1) +4

⇒ y = -9

Ordered pair is (1,-9)

Table of the ordered pair is

x  :   0        1

y  :   4       -9

Graph of the two plot points A(0,4) and B(1,-9) attached.

Therefore, table of ordered pair for the equation y =-13x +4 is given by (0,4) and (1,-9).

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About Nevada state, it is true that "The rural air pollution level for this state is much higher or much lower than the rest of the states in the data set."

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The graph intersects the x-axis at ( 1/2 , 0) .

A cartesian coordinate system, which uses signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.

We know that at the x-axis the value of y is 0 .

Now substituting the value of y in the equation of the graph we get :

y = - 2x + 1

at y = 0 ,

0 = -2x + 1

or, -1 = -2 x

or, x =  1 / 2

Hence the co-ordinate of the point where the graph passes through x-axis is ( 1/2 , 0 ) .

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For the given quadratic function, we have that:

The x-intercepts of the function are the same as the zeros, that is, the values of x for which f(x) = 0.

For this problem, the function is defined as follows:

f(x) = -2x² - 4x.

Hence the x-intercepts are given as follows:

-2x² - 4x = 0

2x² + 4x = 0

2x(x + 2) = 0.

Hence:

The numeric value at x = -4 is calculated replacing each instance of x by -4, hence:

f(-4) = -2(-4)² - 4(-4) = -16.

We have to solve for x as follows:

-2x² - 4x = 2

2x² + 4x + 2 = 0

x² + 2x + 1 = 0

(x + 1)² = 0.

x = -1.

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Answer:

a) ¹⁰√4

Step-by-step explanation:

(4 ⅖)¼ = 4 ^ 2/5 × 1/4 = 4^ 2/20 on simplifying further we get answer as a

Using the rules of complementary angles we calculate that the value of x is  12° .

Pairs of complementary angles have measures which are one right angle.

The two given angles are 29° and ( 5x + 1 )°.

There are a pair of complementary angles.

Therefore 29° + ( 5x + 1 )° = 90 °

or, 5x + 30° = 90 °

or, 5x = 60

or, x = 12°

Therefore using the rules of complementary angles we calculate the value of x is 12°.

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Based on the sample of students and the family income, the point estimate of the mean score of the group is 511.

The Point Estimate refers to a figure in a population that is meant to describe a value for the entire population. For instance, a point estimate can be the mean of scores for a sample of students.

Going by that logic, the point estimate for the sample of 400 students who had family income between $70,000 and $80,000 is 511. This Verbal SAT Score refers to the mean score that the group got in their Verbal SAT.

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The solution to the linear-quadratic system of equations are: [tex]\begin{pmatrix}x=1,\:&y=3\\ x=-5,\:&y=-3\end{pmatrix}[/tex].

The Standard form for a quadratic equation is  ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b\±\sqrt{\Delta} }{2a}[/tex].

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=4x+3. Where:

m= the slope. It can be calculated for Δy/Δx .

b= the constant term that represents the y-intercept.

The question asks the solution of the system the following equations

y=x²+5x-3 (1)

y=2+x      (2)

Firstly, you should subtract equation 1 and 2, as result, you have

y-y= x²+5x-3 -(2+x)

y-y= x²+5x-3 -2 -x

0= x² +4x -5

After that for finding x, you should  solve the equation  x² +4x -5=0. Then,

D=b²-4ac

D= 4²-4*1*(-5)

D=16+20

d=36

Thus,

[tex]x=\frac{-b\±\sqrt{\Delta} }{2a}= \frac{-4\±\sqrt{36} }{2*1}= \frac{-4\±\ 6 }{2}[/tex]. Therefore

x1=(-4-6)/2= -10/2=-5

x2= (-4+6)/2 = 2/2=1

From equation 2 : y=2+x

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The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.

A certain order of transformational occurrences is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.

We are given that ΔA'B'C' exists formed after a sequence of transformations applied to ΔABC.

The first exists a reflection across a line and the second exists a translation.

The coordinates of point C exist (-4, -2). After reflection from the line y = x, the coordinates become (2, -4).

Also, the coordinates of point C' are (12, 0).

So, to get point C' from point C, we should add 10 units to the x-coordinate and 4 units to the y-coordinate.

The translation of 10 units right and 4 units up.

Therefore, the complete transformation is

The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.

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Answer:

Step-by-step explanation:

$4.69