2p + 3 = 5 - 6p
what is the value of p in the equation?

Answer:

Step-by-step explanation:

(a)If log₄​x = 5, the base is 4 and the logarithm is 5 , then x = 1024. (b) If log₆​x = 8 the base is 6 and the logarithm is 8  then x = 1679616.

(a) In the equation log₄​x = 5, the base is 4 and the logarithm is 5. To solve for x, we need to rewrite the equation in exponential form. In exponential form, 4 raised to the power of 5 is equal to x. Therefore, x = 4^5 = 1024.

(b) In the equation log₆​x = 8, the base is 6 and the logarithm is 8. Rewriting the equation in exponential form, 6 raised to the power of 8 is equal to x. Hence, x = 6^8 = 1679616.

In both cases, we used the property of logarithms that states: if logₐ​x = y, then a raised to the power of y equals x. By applying this property, we can convert the logarithmic equations into exponential form and find the values of x.

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The new point after rotation of point  (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.

For example (5,3) here 5 will be for the x and 3 will be for the y.

Another example is (9,0) here 9 is for x and 0 is for y.

Given,

Point A =  (-7, -3)

Let's say after rotation this point moves to a new coordinate (x, y) which is point B

Let's say the origin is O

Slope of line segment AO = (-3-0)/(-7-0) = 3/7

Slope of line segment BO = (y - 0)/(x - 0) = y/x

Now,

Since both lines are perpendicular to each other so

Slope AO × Slope BO = -1

3/7 × y/x = -1 ⇒ 3y = -7x

Now if we observe the result then it will be clear that if we put x = 3 than y = -7 will be the new coordinate.

Hence, The new point after rotation of point  (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).

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1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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Solution:

Given:

A 52-card deck

There are four suits in a standard deck of cards, Clubs, Hearts, Spades, and Diamonds.

There are 13 diamond cards.

Hence,

Probability is calculated by;

Thus, the probability of drawing a diamond on the first draw is;

Since two draws are made with replacement, the cards are completed back again before the next draw.

Hence, the probability of drawing a diamond on the second draw is;

Therefore, the probability of drawing a diamond each time;

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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9.38

please don't trust this answer

We know that Uta invested $345 at an interest rate of 9% per year, so P = $345 and r = 0.09. Uta's money was invested for c. 6 years in the simple interest investment account.

To solve this problem, we can use the formula I = P r t, where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time in years.
We also know that she withdrew $531.30 from her account after several years, which means that the interest earned was $531.30 - $345 = $186.30.
Plugging in these values into the formula, we get:
186.30 = 345 x 0.09 x t
Simplifying, we get:
186.30 = 31.05t
Dividing both sides by 31.05, we get:
t = 6 years

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Answer:

It’s 64 x 9 equals 576

Step-by-step explanation:

The answer is 9 feet

The value height of shed is 9 feet.

The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases.

Here, Vol. of rectangular prism = 576 ft³

          base area = 64 ft²

Volume of rectangular prism = area of base X height

      576 = 64 X h

        h = 576 / 64

       h = 9 ft.

Thus, the value height of shed is 9 feet.

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Answer:

x        1            2             6            12         25

f(x)     22        34           82          154       310

f(3)= 46 means that in the third month, the online magazine provider will charge a total of $46.00

Step-by-step explanation:

For finding the missing f(x) values:

Plug in the x-values that are given into the original equation: f(x)= 12x + 10

ex: f(1)= 12(1) + 10 => 22

For finding the missing x value, set the original equation to the given f(x) value

ex: 34 = 12x + 10 => 2

Using the half life of palladium, mass seven weeks after start was 0.7931 gm.

The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.

The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.

The  half life of palladium 100 = 4 days

after 24 days sample has reduced to a mass of 5mg

standard exponential function is

\(P = P_o e^{kt}\)

plugging P = P₀ /2

\(P_o/2 = P_o e^{4k }\)

\(1/2 = e^{4k }\)

ln (1/2) = 4k

k = -0.1733

function becomes

\(P = P_o e^{- 0.1733 t }\)

plugging P = 5 and t = 24

\(5 = P_o e^{( - .1733\times 24 ) }\)

P₀ = 320.10

In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.

For the second part of the problem:

7 weeks = 5 × 7 =49 days

plugging t = 49

\(P = 320.10 e^{(-.1733 * 35 ) }\)

mass 7 weeks after = 0.7431 mg

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

I think D but I honestly might be wrong

Step-by-step explanation: cross multiply

5 x 2. : 18

6. 23. : 115

The correct answer is option D: Chen read for less time because an hour a day for 7 days is equal to 210 minutes.

To determine the correct answer, we need to use the unitary method. This method involves converting the units of measurement into a common unit and then comparing them.

In this case, we need to convert hours into minutes to compare the reading time of Sierra and Chen.

An hour is equal to 60 minutes. Therefore, 1 hour a day for 7 days is equal to

=> 60 minutes * 7 days = 420 minutes.

However, we need to divide this number by 2 because Chen only read for half an hour a day. Hence, Chen read for 210 minutes

=> (420 minutes / 2).

Now that we have both the reading times in minutes, we can compare them. Sierra read for 220 minutes while Chen read for 210 minutes. As 220 > 210, it is clear that Sierra read for more time.

In conclusion, option D is the correct answer as Chen read for less time because an hour a day for 7 days is equal to 210 minutes. The unitary method is useful in comparing measurements with different units and it provides us with accurate results.

Complete Question:

Sierra read for 220 minutes in 1week. Chen read for an hour a day for 7 days. Which explanation is correct?

A. Sierra read for more time because 220 is greater than

B. Sierra read for less time because minutes are less than hours.

C. They read for the same amount of time because 1 week is equal to 7 days.

D. Chen read for less time because an hour a day for 7 days is equal to 210 minutes.

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If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3  and number of 6 cent stamps used is 12 .

Let number of 41 cents stamps used be = x ;

and let number of 6 cents stamps used be = y ;

converting amount 41-cents in dollars is = $0.41  ;

and converting amount 6-cents in dollars is = $0.06  ;

the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;

this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 195  ;

⇒ y = (195 - 41x)/6 ;

We will test this equations for values of x and y , the number of stamps must be whole numbers .

If x = 1 , then value of y is = 25.66

If x = 2 , then value of y is = 18.833

If x = 3 , then value of y is = 12

If x = 4 , then value of y is = 5.166 .

the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .

Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .

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Answer:

D) 3 units

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The following are the ways of illustrating a relation and a function using Mapping or Arrow Diagram EXCEPT

B. One-to-many correspondence

A relation represents a function when each input value is mapped to a single output value.

This means that there cannot be an one-to-many correspondence, which would mean that a single input would be mapped to multiple outputs.

This means that the correct option in the context of this problem, the one with a false statement, is given by option B.

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She can select one freshman and one sophomore in 72 ways.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Phyllis who wants to select one freshman and one sophomore to attend a conference. She teaches 8 freshman and 9 sophomores

Total number of possible combinations are -

C[8,1] x C[9,1]

8!/(7! x 1!) x 9!/(8! x 1!)

8 x 9

72

Therefore, she can select one freshman and one sophomore in 72 ways.

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The simplified expression for the complex expression is -56-52i

What is a complex expression?

A complex expression is an expression of the form a+ ib where a , b are constant and i is the imaginary number known as iota. In a + ib a is the real part and b is the imaginary part.

We are given two complex number as (8-8i) and (8+4i)

We have to simplify the given expression

As Complex number are added multiplied subtracted same as real number we can simplify the expression easily

2(8-8i)-9(8+4i)

We multiply the constants inside the bracket

16-16i-72-36i

Separating the terms and simplifying them we get

-56-52i

Hence the simplified expression is -56-52i

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Answer:

T = 3.5m

T is trash in pounds

m is members of family

Step-by-step explanation:

Answer:

If you are solving for V, the answer is \(v = 1, -1\)

Step-by-step explanation:

Take the root of both sides and solve.

Hope this helps!

Step-by-step explanation:

For solving this problem, we will use √ab=√a√b. Therefore, the value of 3√27 is 9√3. Note: In the above solution, we factored 27 which is inside the root.

To evaluate the line integral using Green's Theorem, we need to find the curl of the vector field and then calculate the double integral over the region enclosed by the curve. Answer :  the critical points of the function z = (x^2 - 4x)(y^2 - 5y) are (x, y) = (0, 0) and (x, y) = (0, 4)

Given the vector field F = (xy^2, x^5), we can find its curl as follows:

∇ × F = (∂Q/∂x - ∂P/∂y)

where P is the x-component of F (xy^2) and Q is the y-component of F (x^5).

∂Q/∂x = ∂/∂x (x^5) = 5x^4

∂P/∂y = ∂/∂y (xy^2) = 2xy

Therefore, the curl of F is:

∇ × F = (2xy - 5x^4)

Now, we can apply Green's Theorem:

∮C P dx + Q dy = ∬D (∇ × F) dA

where D is the region enclosed by the curve C.

In this case, C is the rectangle with vertices (0,0), (3,0), (3,5), and (0,5), and D is the region enclosed by this rectangle.

The line integral becomes:

∮C xy^2 dx + x^5 dy = ∬D (2xy - 5x^4) dA

To evaluate the double integral, we integrate with respect to x first and then with respect to y:

∬D (2xy - 5x^4) dA = ∫[0,5] ∫[0,3] (2xy - 5x^4) dx dy

Now, we can calculate the integral using these limits of integration and the given expression.

As for the second part of your question, to find the critical points of the function z = (x^2 - 4x)(y^2 - 5y), we need to find the points where the partial derivatives with respect to x and y are both zero.

Let's calculate these partial derivatives:

∂z/∂x = 2x(y^2 - 5y) - 4(y^2 - 5y)

      = 2xy^2 - 10xy - 4y^2 + 20y

∂z/∂y = (x^2 - 4x)(2y - 5) - 5(x^2 - 4x)

      = 2xy^2 - 10xy - 4y^2 + 20y

Setting both partial derivatives equal to zero:

2xy^2 - 10xy - 4y^2 + 20y = 0

Simplifying:

2y(xy - 5x - 2y + 10) = 0

This equation gives us two cases:

1) 2y = 0, which implies y = 0.

2) xy - 5x - 2y + 10 = 0

From the second equation, we can solve for x in terms of y:

x = (2y - 10)/(y - 1)

Now, substitute this expression for x back into the first equation:

2y(2y - 10)/(y - 1) - 10(2y - 10)/(y - 1) - 4y^2 + 20y = 0

Simplifying and combining like terms:

4y^3 - 32y^2 + 64y = 0

Factoring out 4y:

4y(y^2 - 8y +

16) = 0

Simplifying:

4y(y - 4)^2 = 0

This equation gives us two cases:

1) 4y = 0, which implies y = 0.

2) (y - 4)^2 = 0, which implies y = 4.

So, the critical points of the function z = (x^2 - 4x)(y^2 - 5y) are (x, y) = (0, 0) and (x, y) = (0, 4).

To classify these critical points, we can use the second partial derivative test or examine the behavior of the function in the vicinity of these points.

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Answer:

D

Step-by-step explanation:

Selection Bias because they are selecting people who are not Right handed.

Answer:

Step-by-step explanation:

D.SELECTION BIAS

The statement holds true for the base case and it holds true for any k=n assuming it holds true for k=n, we can conclude that the statement holds true for all positive integer values of k. Hence, if we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in k binomial trees of the smaller orders.

The statement to be proven is: "If we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{k}$\) binomial trees of the smaller orders."

We will prove this statement by mathematical induction.

Base case k=1 :

Inductive step:

Suppose the statement holds true for some \($\mathbf{k}=\mathbf{n}$\), i.e., if we remove the root of an \($\mathbf{n}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{n}$\) binomial trees of the smaller orders. We need to show that it also holds true for \($\mathbf{k}=\mathbf{n}+1$\)

using definition of mathematical induction.

Consider a \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, which can be formed by joining two \($\mathrm{n}^{\text {th }}$\) order binomial trees. If we remove the root of this \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, we are left with two nth order binomial trees. By the induction hypothesis, each of these \($\mathbf{n}^{\text {th }}$\) order binomial trees will result in n binomial trees of the smaller orders. Hence, the result of removing the root of the \($(n+1)^{\text {th }}$\) order binomial tree will be n + n = 2n binomial trees of the smaller orders, which implies that the statement holds true for \($\mathrm{k}=\mathrm{n}+1$\) as well.

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The inverse of (- 2 . 3 ) is (1 / - 2.3 ).

In mathematics, the inverse of a number refers to the concept of taking its reciprocal; for instance (2 . w ) results in its reciprocal as ( 1/ 2. w ). When a number is multiplied by its inverse the result yields 1, meaning that the product of the number and its inverse, i.e. reciprocal always equals 1.

As per the given number which is (-2.3) and its inverse is ( 1 / -2.3 ), when these two numbers are multiplied together they result in 1. Such as:

(-2.3) x ( 1 / -2.3 ) = 1

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Answer:

A

Step-by-step explanation:

third angle=180-(35+73)=180-108=72°

I would conduct a research about students who are enrolled and currently studying at 11th grade.

Enrolled Students means students who have been found eligible, under criteria acceptable to the Association

I'll use stratified random sampling.

Stratified random sampling is different from simple random sampling. It involves random selections of data from a whole population. Each possible sample is therefore equally likely.

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The research would investigate the quality of life of barangay residents. Specifically, the research would aim to understand the daily lives of barangay residents, their access to basic services, and their general satisfaction with life.

The sampling technique used would be a stratified random sampling, in which the barangay would be divided into distinct strata based on various demographic characteristics (e.g. income level, gender, age) and a sample of individuals would be selected from each stratum.

A technique is a specific way to carry out an activity, typically one that requires practical abilities. tests carried out utilizing a new technique. Similar words: approach, system, technique, and method More technical euphemisms.

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In regression analysis, the technique used to determine the best-fitting line by minimizing the vertical distances of all the points from the line is called the least squares method.

This method aims to find the line that minimizes the sum of the squared differences between the observed values and the predicted values.

By minimizing these vertical distances, the least squares method provides an optimal fit for the data and allows for the estimation of the coefficients of the regression line.

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