Suppose log 2 = r, log, 3= s, and log 5 = t. Which algebraic expression represents log 75?

The coordinates of the focus of the parabola y = -(1/8)x² - 2x - 4 is (-8, 2).

y = -(1/8)x² - 2x - 4

Given by the equation y = -(1/8)x² - 2x - 4,

To find the focus of the parabola we first need to put the equation in standard form:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola, and a is a constant that determines the shape and size of the parabola.

Completing the square on the x terms, we get:

y = -(1/8)(x² + 16x + 64) - 4 + 8

= -(1/8)(x + 8)² + 4

Comparing this to the standard form, we see that the vertex is (-8, 4) and a = -1/8.

Since the coefficient of x² is negative, the parabola opens downwards.

The focus of the parabola is located at a distance of 1/(4a) units from the vertex, on the axis of symmetry, which is a vertical line passing through the vertex.

Substituting the value of a, we get:

= 1/(4a)

= 1/(4(-1/8))

= 2

Therefore, the focus of the parabola is located 2 units below the vertex, on the line x = -8.

So the focus has coordinates (-8, 2).

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Answer: The total sum of all monthly payments required to pay off this loan is $410,932.

To calculate this, we need to first find the amount of the loan that is not covered by the deposit. The deposit is 20% of $300,000, or $60,000, so the remaining amount of the loan is $300,000 - $60,000 = $240,000.

Next, we need to calculate the monthly payment on the loan. We can use the formula for a fixed-payment loan to do this:

Payment = (Loan amount x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))

The monthly interest rate is the annual interest rate divided by 12, or 0.0394 / 12 = 0.003283.

The number of months is the number of years times 12, or 30 x 12 = 360.

Plugging these values into the formula gives:

Payment = ($247,249 x 0.003283) / (1 - (1 + 0.003283)^(-360)) = $1,151.80

Finally, we can find the total sum of all monthly payments by multiplying the monthly payment by the number of months:

Total payments = $1,151.80 x 360 = $410,932 (rounded to the nearest whole number).

Step-by-step explanation:

The Volume of Cone is 84.8 m³.

We have,

d = 9 m

r= 4.5 m

H = 4 m

So, Volume of Cone

= 1/3 πr²h

= 1/3 (3.14) (4.5)² (4)

= 1/3 (3.14) (20.25) (4)

= 84.8 m³

Thus, the volume is 84.8 m³.

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Answer:

d y                              x+1

-----   = (l x+1 l + 2) x -----------------------

d x                            (l x+1 l + 2) x lx+1l

The solution is the missing angle is 74.

Here, we have,

The sum of all the angles of a triangle (of all types) is equal to 180°.

The sum of the length of the two sides of a triangle is greater than the length of the third side.

In the same way, the difference between the two sides of a triangle is less than the length of the third side.

here, we have,

from the given diagram, we get,

the given angles are 55 and 51

let,  the missing angle be x

we know that,

The sum of all the angles of a triangle (of all types) is equal to 180°.

so, x+55+51 = 180

or, x + 106 = 180

or, x = 74

Hence, The solution is the missing angle is 74.

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a) The slope shows that the appropriate dose c for an older child increase by 6.225 mg if the child is one year older.

b) The dose for newborn baby is: 6.225 mg

The equation of a line in slope intercept form is:

y = mx + c

where: m is slope and c is y-intercept

(a) Let a be an age of an child in years. Then:

c = 0.0417Da + 0.0417D

Where D is a constant

Since D = 150 mg, then we have:

The slope of the graph = 0.0417(150)

= 6.225 mg/year

The slope shows that the appropriate dose c for an older child increase by 6.225 mg if the child is one year older.

(b) Newborn baby:  a=0

Thus:

c(0) = 0 + 6.225

= 6.225 mg

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Domain where x is not equal to 3 and a range where y is not equal to 2 for function  (x+5)/(x-3)

Domain = Set of all input values of a function.

range = set of all output values of a function.

Given: Domain:  x≠3 ; range = y≠2

We do not include a value for domain if it makes the expression indeterminant .

Since all the functions in options are fractions, here the denominator does not equal to 0.

But in option C and D, the denominator can be zero if x=3.

So , domain for then it x ∈ R-3

for option C if 2=2(x+5)/(x-3)

x-3=x+5

-3=5 which is not possible

Where as in option D, 2=(x+5)/(x-3)

2x-6=x+5

x=11

Hence, domain where x is not equal to 3 and a range where y is not equal to 2 for function  (x+5)/(x-3)

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Which function has a domain where x does not =3 and a range where y does not =2? A. f(x)=(x-5)/(x+3) B. f(x)=2(x+5)/(x+3) C. 2(x+5)/(x-3) D. (x+5)/(x-3)

The expansion and simplification of the expression, (3x - 2)(2x² + 5x - 1) is 6x³ + 11x² - 13x + 2.

In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms.

Therefore, let's expand and simplify the expression.

Hence,

(3x - 2)(2x² + 5x - 1)

Therefore, let's multiply

(3x - 2)(2x² + 5x - 1)  = 6x³ + 15x² - 3x - 4x² - 10x + 2

6x³ + 15x² - 3x - 4x² - 10x + 2 = 6x³ + 15x² - 4x² - 3x - 10x + 2

6x³ + 15x² - 4x² - 3x - 10x + 2 = 6x³ + 11x² - 13x + 2

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Answer:

18

Step-by-step explanation:

AC=AB

BC^2=AB^2+AC^2

162+162=324

Square root of 324 is 18.

The point (-25, 15) lies in the third quadrant above the x-axis and left to the y-axis.

The four quadrants are formed by the intersection of the x-axis and the y-axis on a Cartesian plane. The point (-25, 15) is represented by the coordinates (-25) and (15) on the x and y-axis, respectively. Since the x-coordinate is negative, the point lies to the left of the y-axis.

Similarly, since the y-coordinate is positive, the point lies above the x-axis. Therefore, the point (-25, 15) is located in the third quadrant, which is below the x-axis and to the left of the y-axis. In this quadrant, both the x and y-coordinates are negative.

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Answer:

The cost per ounce of the small cup is $0.269

Step-by-step explanation:

To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.

Cost per ounce = Cost of the cup ÷ Number of ounces in the cup

Cost of the cup = $2.69

Number of ounces in the cup = 10 oz

So,

Cost per ounce = $2.69 ÷ 10 oz

Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)

Therefore, the cost per ounce of the small cup is $0.269.

Answer:

Step-by-step explanation:

The category that had the highest relative frequency is given as follows:

Have chores.

To obtain the relative frequencies for each item, we must add the rows/columns that represent the items in this problem.

Hence the relative frequencies for each item are given as follows:

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John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.

If John wants to make a 30% profit on the price he paid for the bike, he needs to sell it for:

$270 + 30% of $270 = $270 + $81 = $351

To offer a 10% discount on the marked price, he needs to calculate the price that includes the discount. Let's call this price "x".

90% of the marked price "x" is the same as the price he wants to sell the bike for ($351):

0.9x = $351

x = $390

Therefore, John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.

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The value of reserve rate is 5%

Given that;

Solitary savings bank received initially amount of $2000.

Now, Let x% percent be kept as reserve then (100-x)% will be loaned out which would be deposited in other bank.

The other bank would keep x% of (100 - x) and again loan the remaining amount.

Thus the total deposits of this cycle would be a geometric series as

⇒ 2000[1 + (100 - x)% + (100 - x)²%+(100-x)² +...]

Here common ratio is,

(100 - x) / 100 = 1 - 0.01x <

for all possible x

This series is infinite and sum of this would be

= sum of geometric series

= 2000 (1/ (x/100)

= 200000/x

This is given as, 40000

Hence, equate and simplify to get;

⇒ x = 5%

So, The value of reserve rate is 5%

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Using trigonometric relations we can see that:

6) θ = 30°

7)   θ = 60°

We can see a right triangle where we want to find the value of θ, we know the hypotenuse and the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opp cath)/hyp

Replacing what we know:

sin(θ) = 6/12 = 1/2

Then we know that θ = 30°

For the second one we know the adjacent cathetus and the hypotenuse, here we need to use the cosine relation:

cos(θ) = 5/10

cos(θ) = 1/2

then θ = 60°

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The spreadsheet formula that will calculate the post-split number of outstanding shares in C3 will be C3*(B2/C2).

Assuming the split ratio has been inputted in cells B2 and C2, one can easily ascertain the post-split number of outstanding shares in cell C3 by simply using the following formula:

=C3 × (B2/C2).

In this case, the equation multiplies the pre-split quantity of outstanding shares by the ratio written down in cells B2/C2 for the determination of resulting post-split number of outstanding shares that are in cell C3.

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Answer:twelve million, three hundred and four thousand, six hundred and fifty two

Step-by-step explanation:

There is sufficient evidence to suggest that the proportion of homes with only a landline phone is less than 7.4%.

Null hypothesis: p ≥ 0.074

proportion of homes with only a landline phone is greater than or equal to 7.4%

Alternative hypothesis: p < 0.074 (proportion of homes with only a landline phone is less than 7.4%)

where p is the true proportion of homes in the population that have only a landline phone.

(b) Compute the test statistic and p-value assuming the null hypothesis is true, using a significance level of α = 0.05.

To compute the test statistic, we first need to calculate the sample proportion:

p cap= 0.0577

The test statistic is given by:

z = (p cap - p) / √p(1-p)/n

where n is the sample size. Substituting the values, we get:

z = (0.0577 - 0.074) / √0.074(1-0.074)/13323)

= -12.28

the p-value is less than 0.0001, which is much smaller than the significance level of 0.05.

Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of homes with only a landline phone is less than 7.4%.

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The set of ordered pairs of the polygon is:

(0.75, -0.75), (-1, 0.5), (0, 1.25)

Option B is the correct answer.

We have,

From the figure,

We have,

The polygon has three points.

The points are in ordered pairs.

We see that,

Each number has four units.

So,

1 unit = 0.25 units

Now,

The coordinates of the polygon are:

(3 units, -3 units) = (0.75, -0.75)

(0, 5 units) = (0, 1.25)

(-4 units, 2 units) = (-1, 0.50)

Thus,

The set of ordered pairs of the polygon is:

(0.75, -0.75), (-1, 0.5), (0, 1.25)

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Answer:

the simplified expression is 4x - 4y

Step-by-step explanation:

1. Rewrite!

12x - 7y - 8x + 3y

2. Combine like terms:

12x - 8x - 7y + 3y

3. Solve both sides to simplify

12 x - 8x = 4x

and

-7y + 3y = -4y

So, 4x - 4y is your answer.

The possible outcomes for each of the given events are:

A {1, 3, 5, 7}

B {3, 4, 5, 6}

The possible outcomes for the experiment are {1, 2, 3, 4, 5, 6, 7, 8}.

The two given events are:

A "The marble selected is an odd number"

The outcomes for this event are the odd numbers that are outcomes for the experiment, then the outcomes here are {1, 3, 5, 7}

The second event is:

B "The marble selected has a number from 3 to 6."

The possible outcomes here are {3, 4, 5, 6}

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The problem with Foofy's conclusion is that she drew a general conclusion from a sample without considering potential biases or confounding factors. To make the report better, she could provide more context, acknowledge potential biases, and make it clear that her conclusion only applies to her sample.

The problem with Foofy's conclusion is that it is based on a biased sample. She only surveyed mothers who were employed outside the home, which does not represent all working women. Therefore, her conclusion cannot be generalized to all working women.

To make the report better, Foofy could specify that her conclusion only applies to mothers who are employed outside the home, rather than all working women.

Additionally, she could improve the study's sampling method by randomly selecting a more representative sample of working women, rather than only surveying mothers who are employed outside the home.

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Answer: 3

Step-by-step explanation:

The scale factor is the proportional ratio from one figure to another.

Notice the corresponding lengths are CE≅JS, TC≅TJ, and TE≅TS.

Comparing CE and JS, the length for CE is 4, and the length for JS is 12.

[tex]4*3=12[/tex]

This means the scale factor is 3. To be sure, let's try the other side.

TC and TE have the same lengths. They are both 5 in length. TS is 15 in length.

[tex]5*3=15[/tex]

This confirms that the scale factor is 3.

The meaning of the absolute value of -5.5 is given as follows:

The temperature decreases 5.5 degrees.

The absolute value of a number is the number without the signal, for example:

|-2| = |2| = 2.

The number in this problem is given as follows:

-5.5.

Hence:

Hence the second option is the correct option in the context of this problem.

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(1) F(s) = 5+1 / (s^2 + 28s + 2)

To perform partial fraction expansion, we first need to factor the denominator:

s^2 + 28s + 2 = (s + 14 - sqrt(194))(s + 14 + sqrt(194))

We can then write:

F(s) = A / (s + 14 - sqrt(194)) + B / (s + 14 + sqrt(194))

where A and B are constants to be determined.

Multiplying both sides by the denominator and simplifying, we get:

5+1 = A(s + 14 + sqrt(194)) + B(s + 14 - sqrt(194))

Setting s = -14 - sqrt(194), we get:

5+1 = B(2sqrt(194))

Solving for B, we get:

B = (5+1) / (2sqrt(194))

Setting s = -14 + sqrt(194), we get:

5+1 = A(2sqrt(194))

Solving for A, we get:

A = (5+1) / (2sqrt(194))

Thus, the partial fraction expansion of F(s) is:

F(s) = [(5+1) / (2sqrt(194))] / (s + 14 + sqrt(194)) + [(5+1) / (2sqrt(194))] / (s + 14 - sqrt(194))

To find the inverse Laplace transform, we can use the table of Laplace transforms or MATLAB. Using MATLAB, we get:

ilaplace(F(s)) = (5+1) / (2sqrt(194)) * (exp(-14t) / sqrt(194)) * (cosh(sqrt(194)t) + sinh(sqrt(194)t))

(2) F(s) = s^2 + 3s + 1 / (s + 2)(s^2 + 8s + 1)

To perform partial fraction expansion, we first need to factor the denominator:

s^2 + 8s + 1 = (s + 4 - sqrt(15))(s + 4 + sqrt(15))

We can then write:

F(s) = A / (s + 2) + B / (s + 4 - sqrt(15)) + C / (s + 4 + sqrt(15))

where A, B, and C are constants to be determined.

Multiplying both sides by the denominator and simplifying, we get:

s^2 + 3s + 1 = A(s + 4 - sqrt(15))(s + 4 + sqrt(15)) + B(s + 2)(s + 4 + sqrt(15)) + C(s + 2)(s + 4 - sqrt(15))

Setting s = -4 + sqrt(15), we get:

-4 + sqrt(15) = A(-4 + sqrt(15) + 4 + sqrt(15))

Solving for A, we get:

A = (-4 + sqrt(15)) / (2sqrt(15))

Setting s = -4 - sqrt(15), we get:

-4 - sqrt(15) = A(-4 - sqrt(15) + 4 + sqrt(15))

Solving for A, we get:

A = (-4 - sqrt(15)) / (-2sqrt(15))

Setting s = -2, we get:

-1 = B(-2)(-2 + 4 + sqrt(15))

Solving for B, we get:

B = (-1) / (2sqrt(15) + 4)

Setting s =