Determine whether y=9(-5)^x represents an exponential function

log base 16, 32 can be written as log₂⁴ 2₅.

Evaluate with logₐx, write a and x as powers of same.

a) log₁₆ 64

= log₂⁴=2⁶

b) log₈₁ 27

= log₃⁴ 3³

c) log₁₆ 32

= log₂⁴ 2₅

d) log₂₇ 243

= log₃³ 3₅

Therefore, log base 16, 32 can be written as log₂⁴ 2₅.

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Answer:

[tex] {z}^{2} - 10z + 9 = [/tex]

[tex](z - 1)(z - 9)[/tex]

The maximum cardinality of S is 20.

To increase the number of subsets within S, our goal must be to find as many non-empty subset intersections as possible. This is achieved by constructing subsets that possess only one shared element. In this particular case, any two sets contained in the collection will include the element 2000 in their intersection causing it to become a valid subset.

Now, we shall investigate whether an additional subset can be added to S. If an extension exists without including 2000, its intersection with the previous 20 subsets would negligibly have no common elements and would hence not be regarded as a valid subset for addition into S.

As a result, a total of 20 subsets represent maximum cardinality for set S per these conditions.

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The number of times more high school football players were there is 500.

Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.

Here, the number of times more high school football players were there

= 1×10⁶/2×10³

= 1×10³/2

= 1000/2

= 500

Therefore, the number of times more high school football players were there is 500.

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"Your question is incomplete, probably the complete question/missing part is:"

In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?​

Daniel incorrectly applied the square root to both terms on the left side of the equation and he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

Let's first look at the first equation that Daniel solved incorrectly:

25x²-16=9

Daniel's solution:

√(25x² )-√16=√9

5x-4=±3

5x=±7

x=±7/5

What Daniel did wrong here is that he incorrectly applied the square root to both terms on the left side of the equation.

Instead, he should have simplified the left side first, using the fact that √(a²) = |a|, before applying the square root. So the correct solution is:

25x²-16=9

25x²=25

x²=1

x=±1

Now let's look at the second equation that Daniel solved incorrectly:

z³-2=6

Daniel's solution:

z³=8

∛(z^3 )=∛8

z=±2

What Daniel did wrong here is that he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

In fact, z³ = 8 has three roots: z = 2, z = -1 + i√3, and z = -1 - i√3. So the correct solution is:

z³-2=6

z³=8

z=2

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C: the number of leaves is multiplied by 2 each week

Step-by-step explanation

The proper expression ought to be 5(2) ^ t =5(2)^{t}

where t speak to the number weeks after it planted.

On the off chance that we put to the time(t) we are going know how numerous clears out at first are. The calculation will be:

5(2)^{t}= 5(2)^{0} =5

This appear that coefficient 5 decide how much the takes off at first are.

Let see how the number going for distinctive esteem of t. On the off chance that its 1 week after plant, the leaf will ended up:

5(2)^{t}= 5(2)^{1} = 10

At that point the number of takes off 2 weeks after planted will be:

5(2)^{t}= 5(2)^{2}= 20

The number keeps twofold each week since coefficient 2 speaks to the proportion of the development of the work and the proportion decides how much takes off duplicated each week.

So, the reply will be C.

Answer:

True proportion of homeowners in the population lies between 0.333 and 0.847

Step-by-step explanation:

If 9 out of 22 randomly picked people said they rented their homes, then the remaining 13 must own their homes. Therefore, the point estimate of the proportion of homeowners is:

Point estimate = Number of homeowners / Total number of people surveyed

Point estimate = 13 / 22

Point estimate = 0.59 (rounded to two decimal places)

To calculate the 95% confidence interval for the true proportion of homeowners, we can use the following formula:

Confidence interval = Point estimate ± (Z-value x Standard error)

where the Z-value corresponds to the desired level of confidence and the standard error is given by:

Standard error = sqrt [ (Point estimate x (1 - Point estimate)) / Sample size]

For a 95% confidence interval, the Z-value is 1.96 (from the standard normal distribution). Using the point estimate obtained earlier, the sample size is 22, and we can calculate the standard error as:

Standard error = sqrt [ (0.59 x 0.41) / 22 ]

Standard error = 0.131 (rounded to three decimal places)

Substituting these values into the formula, we get:

Confidence interval = 0.59 ± (1.96 x 0.131)

Confidence interval = 0.59 ± 0.257

Confidence interval = (0.333, 0.847)

Therefore, with 95% confidence, we can say that the true proportion of homeowners in the population lies between 0.333 and 0.847.

The Ferris Wheel can carry 2100 passengers on a total of 35 rides.

According to the question,

Number of cars in the Ferry Wheel = 15

Number of passengers in each car = 4

∴ Number of passengers in 15 cars = 15×4 = 60

So, the number of passengers on the Ferry Wheel = 60

Now,

The number of passengers the Ferry Wheel carries in one ride = 60

∴ The number of passengers in 35 rides = 60×35 = 2100.

Hence the Ferris Wheel can carry 2100 passengers on a total of 35 rides.

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The probability P (X≤2). from the probability distribution is 1/3

A continuous random variable is a type of random variable that can take on any value within a specific range, often an infinite range.

It has a probability distribution function that describes the probability of the variable taking on certain values within that range.

This means that

P (X≤2) =  the f(x) value

From the graph, we have

P (X≤2) = 1/3

Hence, teh value is 1/3

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If principal of $3900 is invested at 4.25% interest, compounded annually, the investment will be worth approximately $4,756.89 after 5 years.

To calculate the future value of the investment, we use the formula for compound interest:

A = [tex]P(1 + r/n)^{(n*t)[/tex]

where A is the future value, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $3900, r = 4.25%, n = 1 (compounded annually), and t = 5. Plugging these values into the formula, we get:

A = 3900(1 + 0.0425/1)⁵

A = 3900(1.0425)⁵

A ≈ $4,756.89

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Therefore, the solutions of the equation -x² + x + 12 = 0 are x = -3 and x = 6.

In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.

Here,

The given equation is:

-x² + x + 12 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

In this case, we have:

a = -1, b = 1, and c = 12

Substituting these values into the quadratic formula, we get:

x= (-1 ± √(1² - 4(-1)(12))) / 2(-1)

x = (-1 ± √(1 + 48)) / (-2)

x = (-1 ± √(49)) / (-2)

x = (-1 ± 7) / (-2)

There are two solutions:

x = (-1 + 7) / (-2)

= -3

x = (-1 - 7) / (-2)

= 6

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The correct interpretation of the p-value is 3.34.

We are given that;

t-value=3.34

Number of customers= 200

Now,

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming that the null hypothesis is true. In this case, the p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if the true slope of the linear relationship between the two ratings is zero. The p-value is very small, which indicates that the data provide strong evidence against the null hypothesis and in favor of the alternative hypothesis.

The p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if there is no linear relationship between the two ratings.

Therefore, by probability the answer will be 3.34

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Mr. Mensah will pay 247.5 each month to the social security fund because 5.5% of 4500 is 247.5.

The total monthly salary of Mr. Mensah is 4500.

He is required to pay 5.5% of his salary into a social security fund.

Now, we have to find the amount he has to pay each month into the social security fund.

To find that, we need to find the value of 5.5 percent of 4500.

4500 ×5.5/100

45×5.5

247.5

Therefore, 5.5% of 4500 is 247.5.

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Where is the given proof

Assertion: Yes, √2 is an irrational number.

Reason: The decimal expansion of √2 is 1.41421356237 which is a non-recurring and non-terminating number.

Both (A) and (R) are true and Reason (R) is the correct explanation of Assertion (A).

Assertion: Yes, √2 is an irrational number.

Reason: The decimal expansion of √2 is 1.41421356237 which is a non-recurring and non-terminating number.

All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.

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The Complete Question

Assertion (A): V2 is an irrational number. Reason (R) : Decimal expansion of an irrational number is non-recurring and non terminating???? a) Both (A) and (R) are true and Reason (R) is the correct explanation of Assertion (A) b) Both (A) and ( R) are true but Reason (R) is not a correct explanation of (A) c) Assertion (A) is true and Reason (R) is false d) Assertion (A) is false and Reason (R) is true​

An exponential function would be more appropriate than a linear function, as exponential growth

To determine which type of function best fits the data, we can analyze the difference in the y values (Value of Investment) as x increases.

Differences between consecutive y values:

16,357.04 - 14,944.54 = 1,412.50

17,974.72 - 16,357.04 = 1,617.68

19,891.18 - 17,974.72 = 1,916.46

The differences between consecutive y values are increasing as x increases. This suggests that an exponential function would be more appropriate than a linear function.

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The total amount that the Bells will pay for their house would be $313, 680.

The cost that would be interest is $193, 680

The amount of the first payment going to mortgages is $165. 24

Find the down payment :

Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000

Then the points paid at closing :

= $ 90,000 x 0. 02 = $1,800

Total amount paid = Total mortgage payments + Down payment + Points cost

= 281, 880 + 30, 000 + 1, 800

= $ 313, 680

The total that is interest is:

Total interest paid = Total interest paid through monthly payments + Points cost

Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680

The amount of the first payment going to principal is:

Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24

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The set of coordinates that satisfy the equation are as follows:

(2, 3)

The equation given is as follows:

x - 2y = -1

2x + 3y = 12

Therefore, let's find the set of coordinates that satisfies the equation. Hence,

x - 2y = -1

2x + 3y = 12

multiply equation(i) by 2

Hence,

2x - 4y = -2

2x + 3y = 12

Therefore, subtract the equations

7y = 14

divide both sides of the equation by 7

y = 14 / 7

y = 2

Let's find x as follows

x - 2y = -1

x = -1 + 2(2)

x = -1 + 4

x = 3

Therefore, the solution is (2, 3)

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Answer:

10000

otra solución es: 10⁴

The distance between point (−7, 8) and point (5, 8) is 12 units (since they are on the same horizontal line). The distance between point (−7, 8) and point (−7, −5) is 13 units (using the Pythagorean theorem). Therefore, the point that is farther away is option D: Point (−7, −5), and it is 13 units away.

From the given data, we have:

| x   | 2   | 3   | 4   | 5   | 6   |

| --- | --- | --- | --- | --- | --- |

| p(x) |    |    |    |    |    |

We need to find the value of p(x > 3).

We know that the sum of all the probabilities is equal to 1. So, we can find the missing probability by subtracting the sum of the probabilities we know from 1.

p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = 1

We don't know the value of p(x = 2), so we can't directly calculate p(x > 3). But we can find p(x ≤ 3) and subtract it from 1 to get p(x > 3).

p(x ≤ 3) = p(x = 2) + p(x = 3)

To find p(x = 2), we can use the fact that the sum of all the probabilities is 1:

p(x = 2) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6))

Now we can substitute this into the equation for p(x ≤ 3) and solve:

p(x ≤ 3) = p(x = 2) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 4) + p(x = 5) + p(x = 6))

Finally, we can subtract p(x ≤ 3) from 1 to get p(x > 3):

p(x > 3) = 1 - p(x ≤ 3)

p(x > 3) = 1 - (1 - (p(x = 4) + p(x = 5) + p(x = 6)))

p(x > 3) = p(x = 4) + p(x = 5) + p(x = 6)

Therefore, the value of p(x > 3) is the sum of the probabilities for x = 4, 5, and 6.

(a) The value of the row operation of -2(row1) + row (2) is [-10     4    -12].

(b) The interchange of row 1 and row 2 is  [0     6    -3]

                                                                       [5    -2     6]

The value of the row operation of -2(row1) + row (2) is calculated as follows;

-2 (row 1) = 2 [5   -2    6]

-2 (row 1) = [-10     4    -12]

The addition of -2(row1) to row (2) is calculated as follows;

[-10     4    -12] + [0    6    -3]

= [-10   10  - 15]

The interchange of row 1 and row 2 is calculated as follows;

R₁ ↔ R₂

= [5    -2     6]    =   [0     6    -3]

  [0     6    -3]         [5    -2     6]

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Answer:

$74.66

Step-by-step explanation:

Plot the points on the graphing calculator (x = length of HDMI cord, y = cost). Then generate a linear regression model:

y = 3.68x + 1.06 (approximately)

x = 20, so y = 74.66

$74.66 is the correct answer.

Answer:

n = 20/3

Step-by-step explanation:

Theory about the discriminant, and how solutions are acquired via the quadratic formula

One variable quadratic equations in the form [tex]0=ax^2+bx+c[/tex] have exactly one solution when the discriminant [tex](b^2-4ac)=0[/tex].

This is because for quadratic equations of the original form, the two solutions are given by the quadratic formula:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

which is equivalent to [tex]x=\dfrac{-b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}[/tex].

The [tex]x=\dfrac{-b}{2a}[/tex] is the axis of symmetry, and the [tex]\dfrac{\sqrt{b^2-4ac}}{2a}[/tex] part is how much the solutions deviate from the axis of symmetry.  If the deviation is zero, then the two solutions are both ON the axis of symmetry, and are the same number, giving exactly one solution.

Addressing the given equation

Putting it into standard form

Given the given equation...

[tex](n-4)u^2+6=8u[/tex]

subtract 8u from both sides to obtain an equation that looks like the standard form equal to zero...

[tex](n-4)u^2-8u+6=0[/tex]

The variable here is "u" instead of "x", so the solutions to this equation would be [tex]u=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex], where [tex]a=n-4[/tex], [tex]b=-8[/tex], and [tex]c=6[/tex].

Identifying the discriminant

The discriminant then, with values of a, b, and c, substituted, becomes:

[tex]Discriminant=(-8)^2-4(6)(n-4)[/tex]

If we want the discriminant to equal zero (so that there is exactly one solution for "u"), substitute zero on the left side of the equation, and solve for n.

Solving for n

[tex]0=(-8)^2-4(6)(n-4)[/tex]

[tex]0=64-4(6)(n-4)[/tex]

[tex]0=64-24(n-4)[/tex]

Add -24(n-4) to both sides...

[tex]24(n-4)=64[/tex]

Divide both sides by 24...

[tex]n-4=\dfrac{64}{24}[/tex]

Reduce the right hand side...

[tex]n-4=\dfrac{8}{3}[/tex]

Add 4 to both sides...

[tex]n=\dfrac{8}{3}+4[/tex]

Find a common denominator...

[tex]n=\dfrac{8}{3}+\dfrac{12}{3}[/tex]

Find a common denominator...

[tex]n=\dfrac{20}{3}[/tex]

So, if [tex]n=\dfrac{20}{3}[/tex], then the equation [tex](n-4)u^2+6=8u[/tex] has exactly one solution.  Furthermore, this is the only value of "n" for which the equation has exactly one solution, because it is the only value of "n" for which the discriminant is zero.

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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Answer:

mt1= 995

mt2=975

Step-by-step explanation:

the line inside the box plot shows where the median is.

If you look at the six numbers (101, 203, 407, 512, 98, 642) you can see they range from 98 all the way to 642. the best interval to use for this group be 100.

The right interval to utilize for this set of numbers depends on the aim of the analysis.

If we want to look on the single values and small differences between them, then using interval of 10 would be more better. This would give u room to see small changes that exist between adjacent numbers.

So,  in the event that we need to look on the full range and distribution of the numbers, an interval of 100 would be more better. This would permit us to see how the numbers are shared over a larger area of values.

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See full question below

If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?

101, 203, 407, 512, 98, 642

Answer: [tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

   To find the slope of the line, we will use change in y over change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{-4--1}{3--1} =\frac{-4+1}{3+1} =\frac{-3}{4}[/tex]

The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.

Let's denote the angles of triangle ΔABC as follows:

∠A = x

∠B = y

∠C = 90° (right-angled triangle)

Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.

Since CD is the median, we know that angle ∠ECD = φ.

In right-angled triangle ΔCEB, we have:

∠CEB = 90° - y

Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:

∠CED + ∠CEB + ∠ECD = 180°

Substitute the known values:

∠CED + (90° - β) + φ = 180°

Since ∠CED and ∠A are supplementary angles, we can also write:

∠CED = 180° - x

Now substitute this value into the previous equation:

(180° - x) + (90° - y) + φ = 180°

Simplify the equation:

270° - x - y + φ = 180°

Subtract 90° from both sides:

180° - x - y + φ = 90°

From this equation, we get:

x + y = 90°

Substitute this value back into the equation involving φ:

180° - (90°) + φ = 90°

Simplify:

90° + φ = 90°

Therefore, the measure of the larger acute angle of ΔABC is:

x = 45° + φ/2 (option a)

the above answer is in response to the full question below;

Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:

a. 45⁰ + φ/2

b. 60⁰ + φ/2

c. 90⁰ - φ/2

d. 2φ

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