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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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Answer:

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

  [tex]\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1[/tex]

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

  x ≠ 1

In interval notation, this is ...

  (-∞, 1) ∪ (1, ∞)

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

  y ≠ 7

In interval notation, this is ...

  (-∞, 7) ∪ (7, ∞)

Check the picture below.

Answer: 28 [tex]units^{2}[/tex]

Step-by-step explanation:

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the amount of money invested in stocks, y represent bonds and z represent CDs, hence:

x + y + z = 215000     (1)

Also:

0.0225z + 0.02y + 0.092x = 8087.5    (2)

And:

y = 15000 + z    (3)

The solution of the equation is:

x = 50000, y = 90000 and z = 75000

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

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C

1, -9 , 81 , -729 .....

ratio :-

R1 = -9/1 = -9

R2 = 81/-9 = -9

R3 = -729 / 81 =-9

so ,. R1= R2= R3

Answer: u - 8 = -9

Step-by-step explanation:

Given equation

-7u - 5 = 2

Add 5 on both sides

-7u - 5 + 5 = 2 + 5

-7u = 7

Divide -7 on both sides

-7u / (-7) = 7 / (-7)

u = -1

Substitute values into the goal expression

u - 8 = (-1) - 8 = [tex]\Large\boxed{-9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is -9.

First, let's find the value of u.

Now, substitute in the expression.

a. The price-earnings ratio of Maytag Company's stock is 17.

b. The stock yield of Maytag Company's stock is 3.48%.

The price-earnings ratio is a financial measurement of the worth of Maytag Company.

The price-earnings (P/E) ratio is computed as the current stock price divided by the company's earnings per share.

The P/E ratio shows the potential investor how much to pay per share for each $1 of earnings.

The stock yield is a financial measurement that shows the dividends paid relative to the market value per share.

Earnings per share = $2.60

Current share price = $46

Annual dividend = $1.60

a. Price-earnings ratio = Price per share/earnings per share

= 17 ($46/$2.60).

b. Stock yield = Annual dividend per share/Current stock price x 100

= 3.48% ($1.60/$46 x 100)

Thus, while the price-earnings ratio is 17, the stock yield is 3.48%.

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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 normal distribution, it is found that the percentages are given as follows:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The prorportion of students who receive an A is one subtracted by the p-value of Z = 1.8.

Looking at the z-table, Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359.

3.59% of the grades will be A.

For B, it is the p-value of Z = 1.8 subtracted by the p-value of Z = 1.1, hence:

0.9641 - 0.8643 = 0.0998.

9.98% of the grades will be B.

For C, it is the p-value of Z = 1.1 subtracted by the p-value of Z = -1.2, hence:

0.8643 - 0.1151 = 0.7492.

74.92% of the grades will be C.

For D, it is the p-value of Z = -1.2 subtracted by the p-value of Z = -1.9, hence:

0.1151 - 0.0287 = 0.0864.

8.64% of the grades will be D.

For F, it is the p-value of Z = -1.9, hence 2.87% of the grades will be F.

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Answer:

shift left 3

Step-by-step explanation:

(x+3)²

x = -3

therefore translation by (-3,0)

The negative number shows it move to the left

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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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

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

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.

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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The average force exerted by the block exists at -375 N.

Given:

Initial Velocity, u = 50m/s

Displacement, s = 10cm = 0.10m

Mass, m = 0.03Kg

Using the relation,

[tex]$v^{2}-u^{2}=2 a s[/tex]

Substitute the values in the above equation, we get:

[tex]$&0^{2}-50^{2}=2 \mathrm{a}(0.10) \\[/tex]

[tex]$ \mathrm{a}= -12500 \mathrm{~ms}^{-2}[/tex]

We know that, f = ma

Putting the values, we get:

f = (0.03)(-12500)

f = -375 N

The average force exerted by the block exists at -375 N.

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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.

The Lateral area of the cube = 900 in.²

The Surface area of the cube = 1,350 in.².

A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:

a = edge length of cube.

The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:

a = edge length of cube.

Edge length of cube (a) = 15 in.

Lateral area = 4a² = 4(15²)

Lateral area = 4(225)

Lateral area of the cube = 900 in.²

Surface area = 6a² = 6(15²)

Surface area = 6(225)

Surface area of the cube = 1,350 in.².

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Answer:

C

Step-by-step explanation:

The red dotted line we see is the asymptote, which is a line that the functions will never cross.

The asymptotes we see currently is:

x = -3

and

x = 2

We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:

(x-2) (x+3)

If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.

Answer:

C

Step-by-step explanation:

there are 2 vertical asymptotes at x = - 3 and x = 2

then the factors on the denominator will be (x + 3) and (x - 2)

then

f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]

The linear equation that represent the left balance of sanjaya’s y after visiting x number of days is:

y = 10x + 500.

A linear function is modeled by:

y = mx + b

In which:

From the data given, we have that:

Hence the balance is given as follows:

y = 10x + 500.

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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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The number of ways that the dancers can line up is; 518400 ways

The fundamental counting theorem is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n1 * n2 * n3.....*nₙ

Total = 12

Dancers on Green = 6

Dancers on blue = 6

Number of ways for those wearing green = 6!

Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.

Number of ways to arrange those wearing blue = 6!

Thus;

Number of ways that the dancers can line up = 6! * 6! = 518400 ways

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Answer:

1  (double root)

Step-by-step explanation:

Given quadratic equation:

[tex]9x^2+6x+1=0[/tex]

To find the solutions to the given quadratic equation, factor the equation.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=9 \cdot 1=9[/tex]

[tex]\implies b=6[/tex]

Therefore, the two numbers are: 3 and 3.

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 9x^2+3x+3x+1=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 3x(3x+1)+1(3x+1)=0[/tex]

Factor out the common term (3x + 1):

[tex]\implies (3x+1)(3x+1)=0[/tex]

Therefore:

[tex]\implies(3x+1)^2=0[/tex]

This means that the curve has one root with multiplicity 2. So the curve touches the x-axis and bounces off the axis at one point. (See attached graph).

Apply the zero-product property:

[tex]\implies 3x+1=0 \implies x=-\dfrac{1}{3}[/tex]

Therefore there is one real solution of the given quadratic equation.

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The intersection of the two intervals in the number line will be = 4, 5,  6,.......+∞ = (-∞,6).

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-∞),9)

The given intervals are;

First interval  = (-∞, 6)

Second interval  = (-∞, 9)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

The second interval includes, 4, 5,.....,+∞

Which gives the intersection as 4, 5, 6,7, 8,9......+∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

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Answer:

87 adults

174 children

70 students

Step-by-step explanation:

Answer:

X = 81

Step-by-step explanation:

600 × 0.45 = 270

270 × 0.3 = 81

X = 81