Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.

Experimental Probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

Theoretical probability is equal to the number of favorable outcomes divided by the total number of possible outcomes.

In your case, when tossing a coin 15 times, you get the Pr(Heads)=2/5, this probability is experimental and the result is found by repeating an experiment.

Answer: correct option A.

Answer:

Difference in cash and plan = $155 - $149.50 = $5.50

Interest Rate = 3.68%

Step-by-step explanation:

Given:A food processor for $149.50 cash, or $5.00 down and $10.00 per month for 15 months

A food processor by cash = $149.50

Payment plan =  Down payment + $10*15 months

= $5 + $10*15

= $5 + $150

Payment plan = $155

Difference in cash and plan = $155 - $149.50 = $5.50

Now we have to find the interest rate

= (difference/original)*100

= (5.50/149.50)*100

Interest Rate = 3.68%

Answer:

Step-by-step explanation:

Answer:

B. [tex]x^2(4x^2 + 2x -9) -3x(4x^2 + 2x - 9)[/tex]

Step-by-step explanation:

The distributivity establish that in order to multiply these two polynomials, first you have to multiply [tex]x^2[/tex] by every element in  [tex]4x^2 + 2x - 9[/tex] and then multiply [tex]-3x[/tex] by every element in [tex]4x^2 + 2x - 9[/tex] as well.

That is exactly what the option B. says, since

in the expresion [tex]x^2(4x^2 + 2x - 9) - 3x(4x^2 + 2x - 9)[/tex] [tex]x^2[/tex] is being multiplied  by every element in  [tex](4x^2 + 2x - 9)[/tex] and also [tex]-3x[/tex] is being multiplied by every element in  [tex](4x^2 + 2x - 9)[/tex].

Answer:
D) 4x - 17
E) -b - 6a
F) -2(7x + 34)

Explanation:
For question D, we divide each term in the first binomial by 3x and simplify:
(12x² / 3x) - (51xy / 3x)
12 / 3 = 4, x² / x = x         51 / 3 = 17, x / x = 1, y / 1 = y
4x - 17(1)y
4x - 17y is left as a quotient

For question E, we do distribute -3a to the binomial in the numerator and do the same, divide each term in the binomial by -6a and simplify:

-3a(-2b - 12a) = -3a(-2b) - 3a(-12a) = 6ab + 36a²

(6ab + 36a²) / -6a =
(6ab / -6a) + (36a² / -6a)
6 / -6 = -1, a / a = 1, b / 1 = b         36 / -6 = -6, a² / a = a
-1(1)(b) + (-6)(a)
-b - 6a is left as a quotient

For question F, we distribute the 4 and 3x to their respective binomials and then combine like terms where applicable:
4(x² - 8x) + 3x(-6x - 12)
4(x²) + 4(-8x) + 3x(-6x) + 3x(-12)
4x² - 32x - 18x² - 36x
4x² - 18x² - 32x - 36x
-14x² - 68x, both terms have a greatest common factor (GCF) of -2 which can be divide out of them to further simplify:
-2(7x + 34)

Final answer:

To find tan theta when cos theta = 1/4, use the Pythagorean identity to find sin theta and then divide sin theta by cos theta to get tan theta, which is (sqrt(15)).

Explanation:

To find tan theta when given that cos theta = 1/4 and knowing that theta is between 0 and 90 degrees, we can use the Pythagorean identity for trigonometric functions, which states that sin^2 theta + cos^2 theta = 1. Since we have cos theta, we can solve for sin theta.

First, square cos theta to get cos^2 theta:

cos^2 theta = (1/4)^2 = 1/16

Now, apply the identity:

sin^2 theta = 1 - cos^2 theta = 1 - 1/16 = 15/16

Take the square root to find sin theta (choosing the positive root since theta is between 0 and 90 degrees):

sin theta = √(15/16) = √15/4

Finally, use the definition of tan, which is sin theta / cos theta:

tan theta = sin theta / cos theta = (√15/4) / (1/4) = √15

The measure of spread that would be most appropriate to measure the amount of money that high school students spend on fast food per month is the range.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The amount of money that high school students spend on fast food each month can vary between $50 and $200, there is a considerable range of possible values.

Additionally, some students may not eat fast food at all, which could further increase the variability in the data.

The range is the difference between the maximum and minimum values in a dataset and provides a simple and straightforward measure of the variability of the data.

Therefore, the measure of spread that would be most appropriate to measure the amount of money that high school students spend on fast food per month is the range.

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The value for the sum of the squared residuals is SS(residuals) = (1 - r²) SS(y).

Residual value is defined as the difference of the value that we predicts with that of the observed value.

Given that,

The distance between the y value in the data and the y value predicted from the regression equation is known as the residual.

Sum of the squared residuals is used to measure the variance level in a regression model.

We know that,

r² = 1 - [SS(residuals) / SS(total)]

[SS(residuals) / SS(total)] = 1 - r²

SS(residuals) = (1 - r²) SS(total)

SS(residuals) = (1 - r²) SS(y)

Hence the value is SS(residuals) = (1 - r²) SS(y).

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Answer:

The answer is option C= 252

Step-by-step explanation:

To get the coefficient of [tex]x^{5}y^{5}[/tex] we will put r = 5, in the below given general term.

The general term is : nCr [tex]x^{r}[/tex] [tex]y^{n-r}[/tex]

We get:

Coefficient is = 10C5 = [tex]\frac{10!}{5!*5!}[/tex]

= 252

So, option C is correct.

The question is

if p(x)= 2x³-3x+5, what is the remainder of p(x) divided by (x-5)

We use the synthetic division to find the remainder,

x-5=0

x=5

Now, write the coefficients of polynomial.

5 | 2  0  -3    5

   | ↓ 10  50  235

-------------------------------

     2 10  47  | 240→ is the remainder.

Quotient= 2x²+10x+47

Remainder= 240

The remainder of [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] is

Explanation:

If division of a polynomial by a binomial result in a remainder of zero means that the binomial is a factor of polynomial.

The polynomial is [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and [tex]\left( {x - 5} \right).[/tex]

The numerator of the division is [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and the denominator is

Solve the given polynomial [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] by the use of synthetic division.

Now obtain the value of [tex]x[/tex] from the denominator.

[tex]\begin{aligned}x - 5 &= 0\\x&= 5\\\end{aligned}[/tex]

Divide the coefficients of the polynomial by [tex]5.[/tex]

[tex]\begin{aligned}5\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5} \,}} \right.  \hfill\\\,\,\,\,\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,50\,\,\,\,\,\,\,\,\,\,\,\,\,\,235}\hfill\\\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,47\,\,\,\,\,\,\,\,\,\,\,\,\,\,240\hfill\\\end{aligned}[/tex]

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is [tex]240[/tex].Therefore, the remainder of the synthetic division is [tex]240.[/tex]

The remainder of [tex]p\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] is [tex]\boxed{240}.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

Answer:

76

Step-by-step explanation:

The length of the curve to the nearest foot is 628 feet.

To find the length of the curved edge, which is an arc of a circle, one can use the formula for the arc length [tex]\( L \)[/tex] of a circle, given by the product of the radius [tex]\( r \)[/tex] and the radian measure [tex]\( \theta \)[/tex] of the central angle that intercepts the arc:

[tex]\[ L = r \cdot \theta \][/tex]

In this case, the radius [tex]\( r \)[/tex] is given as 1600 feet, and the central angle [tex]\( \theta \)[/tex] is given as [tex]\( \frac{\pi}{8} \)[/tex] radians.

Plugging in the values, we get:

[tex]\[ L = 1600 \text{ feet} \cdot \frac{\pi}{8} \text{ radians} \][/tex]

To find the numerical value, we use the approximation [tex]\( \pi \approx 3.14159 \)[/tex]:

[tex]\[ L \approx 1600 \cdot \frac{3.14159}{8} \] \[ L \approx 1600 \cdot 0.39269906 \] \[ L \approx 628.3185 \][/tex]

Since we are asked to round to the nearest foot, we consider the value 628.3185 feet. Rounding this to the nearest whole number, we get:

[tex]\[ L \approx 628 \text{ feet} \][/tex]

Therefore, the length of the curve to the nearest foot is 628 feet.

Answer:

This one is Right...

Step-by-step explanation:

Answer:

its 60

Step-by-step explanation:

Mary should buy 6 bags of 1 pound trail mix to provide each of the 15 club members with a 2/5 pound bag, resulting in no leftovers.

The task is to determine how many 1 pound bags of trail mix Mary should buy if each of the 15 members of her hiking club is to receive a 2/5 pound bag of trail mix without any leftovers.

First, calculate the total amount of trail mix needed by multiplying the number of members by the amount each member will receive: 15 members × 2/5 pound per member = 6 pounds.

Since trail mix is sold in 1 pound bags, Mary should buy 6 of these bags to provide the right amount of trail mix for her hiking club members without any leftovers.

Answer:

The answer is C on EDGEN.

Step-by-step explanation:

C. 11