during one semester, the time elaine spent doing homework or participating in extracurricular activities was 20 percent less than the time she spent attending class. if she spend a total of 981 hours attending class, doing homework, or participating in extracurricular activities, how many hours did she spend attending class?

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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The number of solutions to the system is 1

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y = 4x + 8

4y = 4x - 8

Substitute y = 4x + 8 in 4y = 4x - 8

4(4x + 8) = 4x - 8

Expand the equation

16x + 32 = 4x - 8

Evaluate the like terms

12x = - 40

Divide by 12

x = -10/3

The above means that the number of solutions to the system is 1

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Answer:

the height would be around 19.2 cm

Step-by-step explanation:

hyp length = 63

base = 60

length = sqrt(63^2 - 60^2) = sqrt(369)

Answer:

  34

Step-by-step explanation:

You want the value of |m² +n²| for m = -5 and n = 3.

Put the values where the variables are in the expression and do the arithmetic.

  |m² +n²| = |(-5)² +3²| = |25 +9| = |34| = 34

The value of the expression is 34.

__

Additional comment

Here, the absolute value bars don't do anything, because the value between them is positive. If it were negative, they would remove the minus sign.

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A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance.

A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance. It is an essential type of motion used in geometry due to the rigid transformation of objects considered in the topic.

Rigid transformation is a method required to change the position, size, orientation, or dimensions of a given shape. This implies that the given shape (object) undergoes the appropriate transformation into its image. Types of rigid transformation are translation, rotation, dilation, and reflection.

Considering the given question, the quadrilateral performed a rigid motion. This was done by first reflecting it about the vertical axis, and now translating it 2 units downwards towards the horizontal axis.

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$3,717.14

Compound interest is the interest on the principal funding as well as the interest itself.

Compound Interest Formula

Compound interest can be solved by plugging known values into a formula.

In this formula, the variables stand for different values.

So, for this question, we can plug in the values we are given and solve for P.

Identifying Known Values

First, let's find the exact numbers we are going to plug in.

Solving For P

Now we can plug all of these values in.

First, simplify the values within the parentheses and in the exponent through arithmetic.

Next, divide both sides by [tex]1.005^{96}[/tex]

*Note that the answer has been rounded to the nearest hundredth.

This means that you would need to deposit $3,717.14 into the account to have $6,000 in 8 years.

Answer:

[tex]\textsf{A)} \quad (x-40)^2=-100(y-16)[/tex]

B)  Focus = (40, -9)

    Directrix:  y = 41

    Axis of symmetry:  x = 40

Step-by-step explanation:

The x-intercepts of a parabola are the points at which the curve intercepts the x-axis (when y = 0).

The x-coordinate of the vertex of a parabola is halfway between the x-intercepts.

The y-coordinate of the vertex if the minimum or maximum height of the parabola.

A jumping spider's movement is modeled by a parabola.

Define the variables:

From the information given:

Standard form of a parabola with a vertical axis of symmetry:

[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute the vertex (40, 16) and one of the x-intercept points (0, 0) into the formula and solve for p:

[tex]\implies (0-40)^2=4p(0-16)[/tex]

[tex]\implies 1600=-64p[/tex]

[tex]\implies p=-25[/tex]

Substitute the vertex and the found value of p into the formula:

[tex]\implies (x-40)^2=4(-25)(y-16)[/tex]

[tex]\implies (x-40)^2=-100(y-16)[/tex]

Given:

Substitute the given values into the formulas for focus, directrix and axis of symmetry:

Focus

⇒ (h, k+p)

⇒ (40, 16 + (-25)))

⇒ (40, -9)

Directrix

⇒ y = (k-p)

⇒ y = (16 - (-25))

⇒ y = 41

Axis of symmetry

⇒ x = h  

⇒ x = 40

Answer: [tex]a_n=12(-\frac{1}{2})^{n-1}[/tex]

Step-by-step explanation:

Let's first find the common ratio this sequence. To get to the next term, we divide by 2 and we alternate signs. Hence, the common ratio is [tex]-\frac{1}{2}[/tex].

We can now use the formula [tex]a_n=a_1(r)^{n-1}[/tex] to get the formula, where [tex]a_1[/tex] is the first term and r is the common ratio.

[tex]a_n=a_1(r)^{n-1}\\a_n=12(-\frac{1}{2})^{n-1}[/tex]

Using the Fundamental Counting Theorem, it is found that there are 124 three-digit multiples of 5 that have three different digits and at least one prime digit.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Multiples of 5 finish at 0 or 5, hence the parameters to find the number of three-digit multiples of 5, with different digits are:

[tex]n_1 = 9, n_2 = 8, n_3 = 2[/tex]

And the number is:

N = 9 x 8 x 2 = 144.

With no prime digits, 2, 3, 5 and 7 cannot be used, hence the parameters are:

[tex]n_1 = 5, n_2 = 4, n_3 = 1[/tex]

Hence 20 of the numbers have no prime digits, and 144 - 20 = 124 have at least one prime digit.

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Answer:

Step-by-step explanation:

2^0 is less than or equal to 1!, because 1<= 1

if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since

(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0

Part I: The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

Part II: The midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

From the question, we are to determine the formula for calculating the midpoint of a segment

The midpoint of a segment can be determined by using the formula,

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

II. To determine the midpoint of the segment with endpoints (-2, -1) and (0, 9)

x₁ = -2

y₁ = -1

x₂ = 0

y₂ = 9

Putting the parameters into the formula,

Midpoint of the segment = ((-2 + 0)/2, (-1 + 9)/2)

Midpoint of the segment = (-2/2, 8/2)

Midpoint of the segment = (-1, 4)

Hence, the midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

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Answer:

d - 7

Step-by-step explanation:

The word "difference" tells us that we will be using subtraction. Also, subtraction is not the same if you reverse the terms like, x - 2 and 2 - x are not the same. In your question it say "d and 7" so that's the order we use in the algebraic expression.

The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.

Number of days =  1       2     3      4      5       6            Total = 6
                              1.72  1.8    1.86 1.88  1.74   1.86                  

The average of the values is the ratio of the total sum of values to the number of values.

Since the mean of the heights of the tides,
= sum of heights / number of heights observation
=  (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters

Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

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Answer:

120

Step-by-step explanation:

5 rings 5 colors

for the first ring there are 5 colors to choose from

4 colors for the second

3 for the third

2 for the fourth

1 for the last one

so 5! = 120

The area of the circle is 78.5 square yards and the circumference of the circle is 31.4  yards

The radius of the circle is given as:

r = 5 yard

The area is calculated using

A = pi r^2

Substitute the known values in the above equation

A =3.14 * 5^2

Evaluate the exponent

A =3.14 * 25

Evaluate the product

A =78.5

Hence, the area of the circle is 78.5 square yards

The radius of the circle is given as:

r = 5 yard

The circumference is calculated using

C = 2pi r

Substitute the known values in the above equation

C =2 * 3.14 * 5

Evaluate the product

C = 31.4

Hence, the circumference of the circle is 31.4  yards

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By analyzing the end behavior of the graphed function, we conclude that the graphed function is an exponential one.

On the graph, we can see that as the independent variable (the one in the horizontal axis) tends to large negative values, the dependent variable (the one in the vertical axis) tends to zero.

And, as the independent variable increases in the positive domain, also does the dependent variable. So we have an increasing function

Finally, we can see that the range (set of the outputs) of the function is the set of values larger than zero.

These 3 are characteristics of exponential functions, so we conclude that the graphed function is an exponential one, thus the correct option is the first one.

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Answer:

Logarithmic

Step-by-step explanation:

HS Teacher

The amount we should charge Tommy is $363.

How much should we charge Tommy:

The amount charged for 1000 words = $110

The amount charged per word = $110/1000

Amount to be charged for 3300 words = $(110/1000) × 3300

= $(0.11) × 3300

= $363

The amount we should charge Tommy is $363.

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Answer: q = -2/3

Step-by-step explanation:

First, we need to apply the Distributive Law in order to proceed with the problem.

3(q + 4/3) = 2

3q + 3(4/3) = 2

We already know that 3(4/3) = 4, since the 3's cancel out. Or, 3(4/3) = 12/3 = 4.

Our new equation is,

3q + 4 = 2

Through transposition and isolation of variables, we get,

3q = -2

Dividing by 3 on both sides...

q = -2/3

Step-by-step explanation:

if I understand you correctly, then the 3 sides are

a = 20 m

b = 34 m

c = 42 m

under this assumption the best is to use Heron's Formula to get the area :

s = (a + b + c)/2

area = sqrt(s(s - a)(s - b)(s - c))

in our case

s = (20 + 34 + 42)/2 = 96/2 = 48

area = sqrt(48(48-20)(48-34)(48-42)) =

= sqrt(48×28×14×6) = sqrt(112,896) =

= 336 m²

Answer:

sorry i didnt know this D: <3

Step-by-step explanation:

Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

A linear function is modeled by:

y = mx + b

In which:

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

0.25 = 10 - 0.75t

0.75t = 9.75

t = 9.75/0.75

t = 13 hours.

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The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The function is given as:

f(x)=6x^4+ 2x^3 - 4x^2 +2

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 6

b = 2

The factors of 6 and 2 are

a = 1, 2, 3 and 6

b = 1 and 2

So, we have:

Rational roots = ±(1, 2)/(1, 2, 3, 6)

Split the expression

Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)

Evaluate the quotient

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)

Remove the repetition

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

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Step-by-step explanation:

1. Lower the confidence level.

2. Use a one-sided confidence interval. ...

3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...

4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...

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Answer:

Increase the sample size.

Usually, the more observations that you have, the narrower the interval around the sample statistic is.

Step-by-step explanation:

The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.

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By the chain rule,

[tex]g(x) = f(4 - x^2) \\\\ \implies g'(x) = -2x f'(4 - x^2) \\\\ \implies g''(x) = -2 f'(4 - x^2) + 4x^2 f''(4 - x^2)[/tex]

Observe that

[tex]4 - x^2 = 1 \implies x^2 = 3 \implies x = \pm\sqrt3[/tex]

Then

[tex]g''(\sqrt3) = -2 f'(1) + 4\left(\sqrt3\right)^2 f''(1) = -2(-5) + 4(3)(-1) = \boxed{-2}[/tex]

Check the attached file.

The length of the transverse axis is 8.

Given the equation of hyperbola:[tex]\frac{(y-2)^{2} }{16}[/tex][tex]-\frac{(x+1)^{2} }{144 }[/tex][tex]=1[/tex]

Rewrite this equation as [tex]\frac{(y-2)^{2} }{4^{2} }[/tex][tex]-\frac{(x+1)^{2} }{12^{2} }[/tex][tex]=1[/tex]

When comparing this equation to the common hyperbola equation with a vertical transverse axis is [tex]\frac{(y-k)^{2} }{a^{2} }[/tex][tex]-\frac{(x+h)^{2} }{b^{2} }[/tex][tex]=1[/tex]

[tex]h = -1[/tex]

[tex]k= -2[/tex]

[tex]a = 4[/tex]

[tex]b = 12[/tex]

The length of the transverse axis is[tex]2a = 2*4[/tex]

                                                               [tex]=8.[/tex]

The length of the transverse axis is 8.

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Answer: d = 1/3

Step-by-step explanation: 48y = 48/4 = 12. So, 2d(18) is equal to 12. 12/18 is 2/3 so 2d has to equal 2/3. That means d = 1/3.

The length of one of the remaining sides is 34.20 meters.

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Perimeter of an isosceles trapezoid =  sum of lengths of sides of a trapezoid

length of shorter base + length of longer base + (2 x legs)

108 = 11.5 + 28.1 + (2 x legs)

108 = 39.60 + (2 x legs)

108 - 39.60 =  (2 x legs)

68.40 =  (2 x legs)

leg = 68.40 / 2

= 34.20 meters

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Answer:

Step-by-step explanation:

yes

The gross pay, taxable income, withholding taxes, and net pay can be computed as follows:

a) The gross pay per pay period = $500

b) Taxable income per pay period = $425

c) Federal tax withholding per pay period = $46.75

d) FICA withholding per pay period = $26.35

e) Medicare withholding per pay period = $6.16

f) State tax wtihholding per pay period = $10

g) Net pay per pay period = $335.74

The number of hours per pay period = 40 hours

The number of pay periods in a month = 2

The total number of hours worked per month = 80 hours (40 x 2)

Earnings per hour = $12.50

a) The gross pay per pay period = $500 (40 x $12.50)

Deductions per pay period:

Health care = $25

401k = $50

The gross pay per pay period  = $500

Total deductions per pay period = $75

b) Taxable income per pay period = $425 ($500 - $75)

c) Federal tax withholding per pay period = $46.75 ($425 x 11%)

d) FICA withholding per pay period = $26.35 ($425 x 6.2%)

e) Medicare withholding per pay period = $6.16 ($425 x 1.45%)

f) State tax wtihholding per pay period = $10 ($500 x 2%)

Total withholding taxes = $89.26

g) Net pay per pay period = $335.74 ($425 - $89.26)

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