HELP 25 Points CALC multiple choice

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

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The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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The values of x and y are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for this problem are given as follows:

2 and x.

The altitude is given as follows:

6.

Hence the length x is given as follows:

2x = 6²

2x = 36

x = 18.

Applying the Pythagorean Theorem, the length y is given as follows:

y² = 18² + 6²

y² = 360

\(y = \sqrt{36 \times 10}\)

\(y = 6\sqrt{10}\)

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The partial fraction decomposition of the expression 9x^2 - 8/3x^2 + 4 is \(\frac{9x^2}{3x^2 + 4} - \frac{8}{3x^2 + 4}\)

The expression is given as:

9x^2 - 8/3x^2 + 4

Rewrite properly as follows:

\(\frac{9x^2 - 8}{3x^2 + 4}\)

Split the expression as follows:

\(\frac{9x^2}{3x^2 + 4} - \frac{8}{3x^2 + 4}\)

Hence, the partial fraction decomposition of the expression 9x^2 - 8/3x^2 + 4 is \(\frac{9x^2}{3x^2 + 4} - \frac{8}{3x^2 + 4}\)

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The truck travels at a velocity of 360 kilometers per hour.

Let suppose that both the passenger car and the truck travel at constant velocity, we have following formula if they meet each other at a given point:

\(x = v_{P}\cdot t\) (1)

\(L-x = v_{T}\cdot t\) (2)

\(\frac{v_{T}}{v_{P}} = r\) (3)

Where:

Now we proceed to reduce the system of linear equations:

(1) and (3) in (2):

\(L - v_{P}\cdot t = v_{P}\cdot r \cdot t\)

\(L = v_{P}\cdot (1-r)\cdot t\)

\(v_{P} = \frac{L}{(1-r)\cdot t}\) (4)

And by (3) and (4) we know the velocity of the truck:

\(v_{T} = \frac{r\cdot L}{(1-r)\cdot t}\)

If we know that \(r = \frac{4}{5}\), \(L = 225\,km\) and \(t = 2.5\,h\), then the velocity of the truck is:

\(v_{T} = \frac{\left(\frac{4}{5} \right)\cdot (225\,km)}{\left(1-\frac{4}{5} \right)\cdot (2.5\,h)}\)

\(v_{T} = 360\,\frac{km}{h}\) \(\blacksquare\)

The truck travels at a velocity of 360 kilometers per hour.

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The specified scale factor of the dilation from S to M is 3/2 therefore, the scale factor of the dilation transformation from M to S is 2/3

A dilation is a transformation in which the lengths of the sides of the image are increased or decreased in the proportion, specified by a scale factor to the dimensions of the pre-image.

The specified scale factor from triangle S to triangle M = 3/2

3/2 = 1.5

Therefore, the length of the sides of triangle M are 1.5 times the lengths of the sides of triangle S

Let L represent the length of a side of triangle S, we get;

The length of the corresponding side on triangle M = 1.5 × L

The scale factor from triangle M to triangle S is found by taking the ratio of the corresponding sides of triangle S and M as follows;

Scale factor, SF, from M to S  = Length of a side on triangle S ÷ Length of the corresponding side on triangle

Therefore;

\(SF = \dfrac{L}{1.5\cdot L} = \dfrac{1}{1.5}\)

1.5 = 3/2, therefore;

\(SF = \dfrac{1}{1.5} = \dfrac{1}{\frac{3}{2} } =\dfrac{2}{3}\)

Therefore, the scale factor from M to S is 2/3

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Answer:
10

Step-by-step explanation:

-3x+7x-8=34+9x-2

(Combine like terms)

4x-8=32

(Add 8 to each side)

4x=40

(Divide by 4)

X=10

Sales tax is a percentage of the sale price of an item that is then added on to the total price of the item.

Example:

let's say you are buying an item priced at $10.00 and the sales tax rate is 6%. Sales tax rates can vary from state to state and even within counties or cities.

The measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angle triangle with hypotenuse as 14.5 meters and

opposite side as 6.3 meters.

We can write sine of the angle (θ) as -

sin(θ) = P/H

sin(θ) = Opposite side/Hypotenuse

sin(θ) = 6.3/14.5

(θ) = sin⁻¹(6.3/14.5)

Therefore, the measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

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The new coordinates of the point N after the given dilation transformation is; (-2, 6)

From the attached image, we see the given triangle MNP. We see that it's coordinates are;

M(-1, -2)

N(0, 2)

O(2, -2)

Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.

Thus, triangle MNP will be dilated according to the rule  (x,y), where point P is the center of dilation.

Given the coordinate N = (0, 2)

The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:

(x, y) = (2x - 2), (2x + 2)

Thus;

N = (0, 2) → N'(2(0) - 2), (2(2) + 2)

= N'(-2, 6)

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Answer:48 counters

Step-by-step explanation:8x3=2, 3x8=24, 24+24+48

Answer:

ill help u if you answer my recent questing

Step-by-step explanation:

Answer:

Third answer.

Step-by-step explanation:

To simplify, we can factor 'x' from the equation, giving us:

\(\frac{x(1)}{x(4 + x)} = \frac{1}{x+4}\)

However, we must put a domain restriction to ensure that the denominator will not equal 0. This means that 'x+ 4' cannot equal zero. Therefore, x ≠ -4.

The third answer is correct.

9514 1404 393

Answer:

  (-∞, -1/3) U (3, ∞)

Step-by-step explanation:

The given inequality is equivalent to two inequalities (joined with OR).

-(3x -4) +3 ≥ 8

  -3x +7 ≥ 8 . . . . . . eliminate parentheses

  -3x ≥ 1 . . . . . . . subtract 7

  x ≤ -1/3 . . . . . divide by 3

3x -4 +3 ≥ 8

  3x ≥ 9 . . . . . add 1

  x ≥ 3 . . . . . . divide by 3

Then the solution to the inequality is the union of these intervals:

  x ∈ (-∞, -1/3) ∪ (3, ∞)

This sequence is not convergent because the nth term does not approach a single limit as n approaches infinity. The limit does not exist, so the answer is DNE.

This sequence does not converge to a single limit because the nth term of the sequence, an, has a coefficient of n, which means that the value of an increases without bound as n increases. This means that the value of an does not approach a single limit as n approaches infinity, and so the limit does not exist. Therefore, the answer for the limit as n approaches infinity is DNE.

This sequence does not converge to a single limit because the nth term of the sequence, an, has a coefficient of n, which means that the value of an increases without bound as n increases. As n increases, the value of an increases, and so the value of an does not approach a single limit as n approaches infinity. This means that the limit does not exist, and so the answer for the limit as n approaches infinity is DNE.

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Answer:

60.48

Step-by-step explanation:

Answer:51.52

Step-by-step explanation:

Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

Answer:

Figure it out yourself

Step-by-step explanation:

the p-value is between 0.05 and 0.1, which means we can conclude that there is weak evidence against the null hypothesis at the 5% level of significance.the answer is 0.05 < p < 0.1.

To find the p-value for a chi-square test for homogeneity, we need to use the chi-square distribution table with the appropriate degrees of freedom and compare the computed chi-square statistic to the critical value at the desired level of significance.

The degrees of freedom for a chi-square test for homogeneity is given by the formula df = (r - 1) * (c - 1), where r is the number of rows and c is the number of columns in the contingency table. In this case, we have three populations and one categorical variable with three values, so the contingency table has 3 rows and 3 columns. Therefore, the degrees of freedom is df = (3 - 1) * (3 - 1) = 4.

Using the chi-square distribution table with 4 degrees of freedom and looking up the value of chi-square at 2.05, we can see that the corresponding p-value is between 0.1 and 0.05. Specifically, the p-value is between 0.05 and 0.1, which means we can conclude that there is weak evidence against the null hypothesis at the 5% level of significance.

Therefore, the answer is 0.05 < p < 0.1.

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Answer:

\(x=8.5\)

Step-by-step explanation:

By the definition of a midpoint, \(TU=UV\).

\(6=2x-11 \\ \\ 2x=17 \\ \\ x=8.5\)

Answer:

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square.

Step-by-step explanation:

f the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. for Example: ΔABC, if c2=a2+b2 then ∠C is a right triangle, ΔPQR being the right angle. hope this helps

Answer:

B)

Step-by-step explanation:

Because it says that Alex wants to spend exactly $30 so you want to have 30 as the total (  = 30 )

and it says 18 plus, you only add 18 one time ( 18 + )

and then it says 0.12 per mile, so you need to do something times 0.12 + 18 and get exactly 30. so you do ( 0.12x ) in this case we're not solving it we're just doing the equation so it's just 0.12x instead of a specific number

Put it all together and you get 18 + 0.12x = 30

Hope this helps dude

Answer:

36720 different desserts

Step-by-step explanation:

(1020x3)x12=36720

Answer:

Q1 -64 Q2 6

Step-by-step explanation:

-4*-4*-4 =-64

so -4^3 = -64

6^1=6

Answer:

B)

Step-by-step explanation:

In radical form, the expression is \(\sqrt[12]{6^7}\) .

The correct option is B.

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

Given:

An exponential expression

\(6^{7/12}\).

We can write \(6^{7/12}\) in radical form,

as follows:

\(6^{7/12}\) = (6⁷\()^{1/12}\)

Since (6\()^{1/12}\)  is the 12th root of 6, we have:

6⁷\()^{1/12}\)  = \(\sqrt[12]{6^7}\)

Therefore, the expression (6⁷\()^{1/12}\)  in radical form is \(\sqrt[12]{6^7}\) .

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Solution

- Frank's base pay is $1810 per month. He is given an extra 3% commission on the merchandise he sells each month

- We are told that His sales were $89300 for last month. This implies that He should receive 3% of this amount.

- Thus, we can calculate Frank's commission as follows:

- The commission Frank receives is $2679

- Thus, Frank's Gross pay is:

- Frank's Gross Pay is $4,489

Final Answer

- Frank's Gross Pay = $4,489

- Frank's Commission = $2,679

We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.

First of all, we will use z-score formula to find z-score corresponding to 146 and 163.

\(z=\frac{x-\mu}{\sigma}\)

\(z=\frac{146-150}{5}\)

\(z=\frac{-4}{5}\)

\(z=-0.8\)

\(z=\frac{163-150}{5}\)

\(z=\frac{13}{5}\)

\(z=2.6\)

Our next step is to find percentage of data scores falls between both z-scores.

\(P(-0.8<z<2.6)=P(z<2.6)-P(z<-0.8)\)

Using normal distribution table, we will get:

\(P(-0.8<z<2.6)=0.99534-0.21186\)

\(P(-0.8<z<2.6)=0.78348\)

Let us convert our answer into percentage.

\(0.78348\times 100\%=78.348\%\)

Upon rounding our answer to nearest thousandths, we will get:

\(78.348\%\approx 78.35\%\)

Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately \(78.35\%\).

Answer:

0.624

Step-by-step explanation:

DeltaMath