Suppose p and q vary inversely and p = 14 when a = 4 Find p when q = 8 please show work

The first four terms and the stated term, with an as the first term, are given the arithmetic sequence: 11 + 9n, a6.

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With the given compound interests, Investment B results in greatest total amount.

What exactly is compound interest?

Compound interest is interest charged on a loan or deposit. It is the most widely utilised idea in our everyday lives. The compound interest for an amount is determined by both the principal and the interest earned over time. This is the primary distinction between compound and simple interest.

Compound interest calculation formula:

A=P(1+r/n)ⁿˣ

Where,

A Equals Amount

P stands for principal.

r = interest rate

n is the number of times interest is compounded each year.

x = time (in years)

Alternatively, the formula may be written as follows:

CI = A – P

Where CI stands for Compound Interest.

Now,

For A

principal = $3000, Rate = 7% compounded semiannualy and time = 7 years

amount=3000(1+7/200)¹⁴

A=3000*1.61

=$4856

For B

 principal = $5000, Rate = 3.2% compounded quaterly and time = 4 years

amount = 5000(1+3.2/400)¹⁶

A=5000*1.13

=$5680

hence,

           Investment B results in greatest total amount.

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In geometry, two triangles are said to be congruent if they are the same size and shape. This means that all corresponding angles and sides are equal.

To prove that two triangles are congruent, we must use one of the five congruency tests: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).The SSS test states that if all three sides of two triangles are equal, then the triangles are congruent. The SAS test states that if two sides and the included angle of two triangles are equal, then the triangles are congruent. The ASA test states that if two angles and the included side of two triangles are equal, then the triangles are congruent. The AAS test states that if two angles and a non-included side of two triangles are equal, then the triangles are congruent. Lastly, the HL test states that if the hypotenuse and a leg of a right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are congruent.In order to prove that two triangles are congruent, we must show that one of the five congruency tests is true. To do this, we can use techniques such as the Reflexive Property, the Symmetric Property, and the Transitive Property. We can also use logical reasoning, such as if two angles are equal and their corresponding sides are proportional, then the triangles must be congruent.

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What is the definition of congruent triangles?

Answer:

Y=3x+2

Graph the line using the slope and y-intercept or two points

Slope: 3 Y-intercept: (0,2)

Point 1: (0,2) Point 2: (1,5)

-4x+2y=8

Graph the line using the slope and y-intercept or two points

Slope: 2 Y-intercept: (0,4)

Point 1: (0,4) Point 2: (1,6)

Answer: x=92x=−7

Step-by-step explanation:x=−b±b2−4ac2a=−±2−4√2Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

Answer:it’s 3

Step-by-step explanation:

so what u do is multiply

The complete question:

The stem-and-leaf plot shows the test scores for a chemistry class.

How many students had a score greater than 90 points?

A. 6

B. 7

C. 8

D. 9

Solution:

The number of students had a score greater than 90 points is 7. So option B is correct.

A stem-and-leaf plot is a type of data visualization that shows the distribution of a set of data. It is particularly useful for small to medium-sized data sets. In a stem-and-leaf plot, each data point is split into two parts: the stem and the leaf. The stem is the leftmost digit or digits of the data point, and the leaf is the rightmost digit.

To the left of the vertical bar are the tens places.

As we want to find the scores greater than 90, we start at the row in the stem and leaf plot with a 9 to the left.

To the right are 6 values - 1, 2, 3, 4, 6, and 7.

So there are six scores here higher than 90:

91, 92, 93, 94, 96, and 97.

Now we move lower to 10 in the tens place.

There is one score there - 100. (That smart kid.)

Total up the six scores in the 9 row and the 1 in the 10 row to get 7 scores higher than 90 in this stem and leaf plot.

Hence, the number of students is 7

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The length of the garden which is in the shape of a rectangle with a perimeter of 18 meters and whose length is 3 meters more than twice the width, is 7 metres.

Let's name the width "w" and the length "l" of the rectangle.

We know from the problem description that the rectangle's perimeter is 18 metres, thus we can formulate an equation:

2l + 2w = 18

We also know that the length is 3 metres longer than the breadth, thus we can solve the following equation:

l = 2w + 3

We may plug the second equation into the first to remove the letter "l" and get an equation with only one variable:

2(2w + 3) + 2w = 18

When we simplify this equation, we get:

6w + 6 = 18

When we subtract 6 from both sides, we get:

6w = 12

When we divide both sides by 6, we get:

w = 2

We can use the second equation to get the length now that we know the width is 2 metres:

l = 2w + 3 = 2(2) + 3 = 7

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Answer: approx 13.54 (full decimal : 13.416666667)

Step-by-step explanation:

Area = Base Area x Height   OR    Length x Width x Height

5/3 x 13/4 x 5/2

5 x 13 x 5 = 325

3 x 4 x 2 = 24

325/24 = approx 13.54

The area of the trapezoid is given as 40 cm square

The formula for the trapezoid is given as

A = (a + b) / 2 * h

the question did not tell us the sides hence I have taken

a = 6

b = 10

h = 5 cm

such that we would have

6 + 10 / 2 * 5

8 * 5

= 40 cm square

Hence the area of the trapezoid is given as  40 cm square

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The number of balls that he can make is given as follows:

249 balls.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

Considering the radius of 3 inches, the volume of each ball is given as follows:

V = 4π x 3³/3

V = 113.1 in³.

He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:

28260/113.1 = 249 balls.

(rounding down, as there will not be enough material for the 250th ball).

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Answer:

AB = a - 8b

Step-by-step explanation:

AB = AO + OB

    = - OA + OB

     = - (4a + 7b ) + (5a - b )

    = - 4a - 7b + 5a - b ← collect like terms

     = a - 8b

Answer:

2 * (M - 14) = 64

Step-by-step explanation:

Twice mean s two times the rest of M

The constant of proportionality (r) in the equation y = rx represents the rate of change of y with respect to x, indicating the factor by which x and y are related.

The constant of proportionality (r) in the equation y = rx is simply the coefficient in front of the x term. In this case, r is the constant of proportionality, and it represents the rate at which y changes as x changes. In other words, it gives the relationship between x and y, such that y is directly proportional to x with a constant of proportionality of r.

So, in the equation y = rx, the value of r is the constant of proportionality.

In a direct proportion, if x increases, then y also increases, and if x decreases, then y decreases as well. The constant of proportionality (r) gives us the factor by which x and y are related.

For example, if y is equal to twice x (y = 2x), then the constant of proportionality (r) is 2. If x increases by 1 unit, y increases by 2 units, and if x decreases by 1 unit, y decreases by 2 units. The constant of proportionality in this case is 2.

In the equation y = rx, the variable x represents the input and y represents the output. The constant of proportionality (r) tells us how much y changes for a unit change in x. It can be thought of as the ratio of the change in y to the change in x. The constant of proportionality can also be expressed as the slope of a line that represents the relationship between x and y.

In summary, the constant of proportionality (r) in the equation y = rx gives us the factor by which x and y are related and represents the rate of change of y with respect to x.

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The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.

[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]

[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]

[tex]3.8\sqrt{2}x^{5+3+9}[/tex]

[tex]3.8\sqrt{2}x^{17}[/tex]

[tex]24\sqrt{2}x^{17}[/tex]

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For the polynomial "8d⁻² - 4d³" , the standard form is  "-4d³ + 8d⁻²"  , the degree is "3"  and the leading coefficient is  "-4" and the number of terms is "2"  .

The polynomial is ⇒ 8d⁻² - 4d³.

To write the polynomial in standard form, we first rearrange the terms by putting the terms with the highest degree first ;

So , the standard form is ⇒ -4d³ + 8d⁻²  ;

The degree of the polynomial is 3, because it is the highest power of the variable "d" in the polynomial "-4d³ + 8d⁻²" .

The leading coefficient of the polynomial is "-4" , because it is the coefficient of the term with the highest degree.

The polynomial has 2 terms, so it is a binomial.

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The given question is incomplete , the complete question is

Write the polynomial " 8d⁻² - 4d³ " in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.

The value of the equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex] after taking the integral is  [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].

What is meant by the integral of an equation?

Calculating areas, volumes, and their extensions require the use of integrals, which are the continuous equivalent of sums. One of calculus' two fundamental operations is integration, which involves computing integrals. The other essential operation is differentiation. The area under the graph of a function for some interval can be expressed numerically as the integral (definite integral), or a new function can be created whose derivative is the original function (indefinite integral).

Given equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex]

Multiply and divide the equation by eˣ

The equation becomes [tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx[/tex]

Now substitute eˣx = a

Differentiating both sides

[eˣ + xeˣ]dx = da

eˣ[1+x]dx = da

Substituting the above in the equation

[tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx = \frac{da}{a(1+a)}[/tex]

Now add and subtract a in the numerator

[tex]\frac{1 da}{a(1+a)} = \frac{a-a+1}{a(1+a)} da = \frac{a+1-a}{a(1+a)} da = \frac{1}{a} da - \frac{1}{a+1} da[/tex]

Now taking integral

[tex]\int \frac{1}{a} da -\int \frac{1}{a+1} da = ln(a) - ln(a+1) + c = ln ( \frac{a}{a+1} ) + c[/tex]

Now substituting back the value of a = eˣx

Therefore the value of the equation after taking the integral is  [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].

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To translate the sentence into an equation, we can let c represent the value we want to find. The difference between c and 25 is 75, so we can write this as:

c - 25 = 75

To solve the equation, we can add 25 to both sides:

c - 25 + 25 = 75 + 25

c = 100

So the value of c is 100.

Answer:

Step-by-step explanation:

The statements that are true regarding the graph of this linear function are:

The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.

The slope of the line, 25, is the amount of money she makes per hour of work.

The statement:

The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours. is not true.

And the statement:

The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours. is not true because the y-intercept is not 0, it's -25, which represents the amount of money she owes to her sister.

Answer:

B, C, A.

Step-by-step explanation:

In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.

Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)

Next, we can use the perimeter equation of the triangle, which is

KL + LM + KM = 27, to find the value of x:

x - 4 + x + 4 + 2x - 1 = 27

4x = 36

x = 9

So, the lengths of the sides of the triangle are

KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.

Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)

cos A = 74 / 60

A = cos^-1 (74/60) = approximately 49.7°

Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:

B + C = 180° - 49.7° = 130.3°

B / sin B = LM / sin A

B = sin^-1 (sin B / sin A) * LM / sin A

C = 130.3° - B

The angles of triangle KLM in order from least to greatest are approximately:

B, C, A.

The number of possible requests for free samples is 5^1 = 5. This means that the customer has 5 different requests that they can make for free samples.

The number of possible requests for free samples can be calculated using the combination formula. The combination formula is used to calculate the number of combinations with repetitions of size “n” taken from a set of “r” elements . The formula is: [tex]C(n,r) = n^r[/tex] In this case, n = number of requests (1 request) and r = number of free samples offered (let’s say, 5). Therefore, the number of possible requests for free samples is[tex]5^1 = 5.[/tex]This means that the customer has 5 different requests that they can make for free samples.

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All the angles of the given parallelogram found using the properties of the parallelogram are 38°,38°, 142° and 142°.

What is meant by a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. On the same side of the transversal, the interior angles are supplementary. 360 degrees is the sum of all interior angles. The qualities of a parallelogram are shared by the shapes of a square and a rectangle.

Given the two opposite angles of parallelogram as (4x-50)° and

(60 - x)°.

We are asked to find all the angles of the parallelogram.

As said earlier, opposite angles of parallelogram are equal.

So,

4x-50 =  60 - x

5x = 110

x = 22

So the opposite angles are:

4x-50 = 4*22- 50 = 38°

Adjacent angles are supplementary. So,

38 + y = 180

y = 142°

Sum of all angles of parallelogram should be 360°.

38+38+142+142 = 360°.

Therefore all the angles of the parallelogram are 38°,38°, 142° and 142°.

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The number of vegetable seeds Frank is going to plant is 3b + 1

From the question, we are to determine the number of vegetable seeds Frank is going to plant on the gardens

From the given information, we have that

"Frank in going to plant b vegetables in one garden"

and

"2b+1 vegetables seeds in a another"

To determine the number of vegetable seeds he would be planting in the gardens, we would find the sum of the vegetable seeds he is planting in the first garden and the second garden

That is,

b + (2b + 1)

= b + 2b + 1

= 3b + 1

Hence, the number of seeds is 3b + 1

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B .The value of f(x) is increasing for each unit decrease in x  about the graph is correct.

What is the graph of exponential function?

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines

Exponential function f(x) is given

According to given graph, The value of f(x) is increasing for each unit decrease in x

Therefore, The statement, The value of f(x) is increasing for each unit decrease in x about the graph is correct.

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The correct order of the ratios from the least to the greatest is given below:

4/2, 11 to 2, 22:3, 30/4, 36:5

Least to greatest: 4/2 = 2, 11:2 = 5.5, 22:3 = 7.33, 30:4 = 7.5, 36:5 = 7.2

15/4, 19 to 5, 53/15, 4:1, 18 to 6

Least to greatest: 15/4 = 3.75, 19:5 = 3.8, 53:15 = 3.53, 4:1 = 4, 18:6 = 3

7:11, 8:12, 6:10, 1/2, 7:4

Least to greatest: 7:11 = 0.6364, 6:10 = 0.6, 8:12 = 0.6667, 1/2 = 0.5, 7:4 = 1.75

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Therefore,

The ratios listed in the question are ordered from least to greatest by converting each ratio into a decimal and comparing the values.

In each case, the fraction is divided, the ratio of two numbers is expressed as a decimal, and then the decimals are ordered from least to greatest.

For example, in the first list, the ratio "11 to 2" is expressed as the decimal 11/2, which is equal to 5.5. The other ratios are similarly expressed as decimals and then ordered to get the final answer.

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Rachel's Coffee Shop used 33 pounds of type A coffee at a cost of $4.20 per pound, and four times as many pounds of type B coffee at a cost of $5.50 per pound, to create a blend costing a total of $864.60.

Let's use the variable "x" to represent the number of pounds of type A coffee used in the blend.

The amount of type B coffee used in the mix was four times that of type A, therefore we can write:

number of pounds of type B coffee = 4x

The total cost of the blend is given as $864.60, so we can write an equation based on the cost:

[tex]4.2x + 5.5(4x) = 864.60[/tex]

Simplifying and solving for x, we get:

[tex]4.2x + 22x = 864.60[/tex]

[tex]26.2x = 864.60[/tex]

[tex]x = 33[/tex]

As a result, the mix contained 33 pounds of type A coffee.

To check our answer, we can substitute x = 33 into the equation we used to solve for it and verify that the total cost is indeed $864.60.

[tex]4.2(33) + 5.5(4*33)[/tex]

= [tex]138.6 + 726.0[/tex]

= [tex]864.6[/tex]

The total cost matches, so our answer is correct.

Therefore, Rachel's Coffee Shop used 33 pounds of type A coffee in the blend.

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The complete question is:

A blend made by Rachel's Coffee Shop combines two different kinds of coffee. Rachel pays $4.20 per pound for type A coffee and $5.50 for type B coffee. This month's blend cost $864.60 and included four pounds more of type B coffee than type A. How many pounds of coffee of type A were consumed?

The inequality that represents the cost c per 14 squares for a new carpet with a budget of $700 is: c ≤ 700/14 = 50 Therefore, the answer is:

The inequality is c ≤ 50.

Assuming that the price of the carpet is constant per square foot, we can write the following inequality to represent the cost c per 14 squares:

c/14 ≤ 700

This inequality states that the cost per 14 square feet (c/14) cannot exceed $700, which is the total amount of money available to purchase the carpet.

To write an inequality representing the cost of a new carpet per 14 square feet, we need to first define the cost per square foot. Let's say the cost per square foot is $x. Then, the cost of the carpet for 14 square feet would be 14x.

Since we have a budget of $700, we can write the inequality:

14x ≤ 700

This inequality represents that the cost of the carpet for 14 square feet should be less than or equal to $700. We can solve for x by dividing both sides by 14:

x ≤ 50

This means that the cost per square foot of the carpet should be less than or equal to $50 for it to fit within the budget of $700.

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Answer:

(a) P(A ∩ E) = 0.03

(b) P(A) = 0.39

(c) P(A | E) = 0.1

Step-by-step explanation:

The first level of the tree gives the following probabilities

P(E) = 0.1

P(E') = 1 - P(E) = 0.9

The second level gives conditional probabilities

P(A|E) = 0.3  this is the top most branch from the root

P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03      Answer(a)

To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities

For event E happening, P(A ∩ E) = 0.03 which is computed in A

However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36

Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)

P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch

This is 0.1   answer (c)

The correct answer is,

x = 39

y =21

A different type of quadrilateral known as parallelogram has both pairs of its opposite sides parallel and equal.

The figure shows a parallelogram ABCD with the parameters AB II CD and AD II BC. Furthermore, AB = CD and AD = BC.

In a parallelogram, the opponent angles are equal.. So it means that side /A is equal to side /C, let's equate the two angles and solve for x;

5y - 3 = x + 3y

2y - x = 3                            ........(1)

Also, consecutive angles of a parallelogram are supplementary,

therefore,

/C + /D = 180

x + 3y + 2x = 180

3x + 3y = 180

x + y = 60                                  .......(2)

Now, add equations (1) and (2)

(2y-x) + (y+x) = 3 + 60

3y = 63

y = 21

now put this value of y in (2) we get,

x + y = 60

x + 21 = 60

x = 39

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The possible values of the length of the rectangle is x > 34, the correct option is A.

For a rectangle with length and width L and W units, we get:

Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]

Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given that width is 8 inches less than the length x

Sum of length and width more than 60

Now, the length is x

Width is x-8

x-8+x>60

2x>60

x>30

Therefore, the length of rectangle will be  x > 34

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The graph of the function is horizontal when the value of the Porsche stays even.

Staying even means that the value of the car does not change, hence it is constant.

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