David keeps a range of stationery in his study. one could find pencils, erasers and pens in his study.5/7 of his stationery consists of pencils and 1/6 of the remaining stationery consists of erasers. there are 20 pens in his study. how many units of stationery does he have?

Answer:

b = 10

b = 17

Step-by-step explanation:

Hello!

Usually, when you want two different integer solutions, you probably want the quadratic to be factorable.

So what we want to know is that b should be the sum of the factors in 16.

Factors of 16: 1, 2, 4, 8, 16

Factor pairs:

Factor Sums:

These are our possible b-values.

Check:

Let's try 17 first:

Now 10:

And finally, 8:

Since x = 4 is a repetitive integer, we cannot use 8 as a value for b.

The answers are b = 10, and b = 17.

The 7th term of the geometric sequence is given as follows:

384/15625.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.

The nth term of a geometric sequence is given by the equation presented as follows:

\(a_n = a_1q^{n-1}\)

The common ratio for this problem is given as follows:

q = (12/5)/6 = 12/5 x 1/6 = 12/30 = 2/5.

The first term is of:

\(a_1 = 6\)

Hence the rule for the nth term is given as follows:

\(a_n = 6\left(\frac{2}{5}\right)^{n - 1}\)

Hence the 7th term is given as follows:

\(a_7 = 6\left(\frac{2}{5}\right)^{7 - 1}\)

\(a_7 = \frac{384}{15625}\)

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Answer: 23

Step-by-step explanation:

Answer:

$24.91

Step-by-step explanation:

The original price of the item before the 6% sales tax was added is $25.

To find the original price of an item that costs $26.50 including 6% sales tax, we need to work backward and remove the tax from the total cost.

First, we can calculate the amount of tax that was added to the original price by using the formula:

tax amount = original price x tax rate

where the tax rate is expressed as a decimal,

so 6% =6/100= 0.06. Thus, 6% becomes 0.06

So, in this case, the tax amount is:

tax amount = original price x 0.06

We can simplify this equation to:

tax amount = 0.06 original price

Next, we can add the tax amount to the original price to get the total cost:

total cost = original price + tax amount

We know that the total cost is $26.50, so we can substitute this value into the equation:

$26.50 = original price + 0.06 original price

Simplifying this equation, we can factor out the original price:

$26.50 = original price (1 + 0.06)

Dividing both sides by 1.06 gives:

original price = $26.50 / 1.06

Simplifying this, we get:

original price = $25

Therefore, the original price of the item before the 6% sales tax was added is $25.

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9514 1404 393

Answer:

  4

Step-by-step explanation:

We assume that point X is the intersection point of the medians. Then ...

  MQ = 3XQ

  3x -3 = 3(2x -6)

  3x -3 = 6x -18 . . .  eliminate parentheses

  15 = 3x . . . . . . . . . add 18-3x

  5 = x . . . . . . . divide by 3

Now, we can find XQ:

  XQ = 2x -6 = 2(5) -6

  XQ = 4

Answer:

Step-by-step explanation:

In order to solve this question we use ratio and proportion

From the question

In 25 days geese fly 1355 miles

So we have

if in 25 days they fly 1355 miles

Then in one day they will fly

\( \frac{1355 \times 1}{25} = \frac{1355}{25} \\ \)

We have the final answer as

Hope this helps you

The definite integral given is 2e1/x5 x6 dx.

To solve this integral, we need to use integration by parts. We will use u = 2e1/x5 and dv = x6 dx. Using integration by parts, we have:

∫ udv = uv - ∫vdu

Therefore, we have:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) ∫e1/x5 dx

We can solve this last integral by using the substitution x5 = u. Doing so, we have:

∫ e1/x5 dx = (1/5) ∫ eudu

Using integration by parts, we have:

∫ eu du = eu u - ∫ ueu du

Therefore, we have:

∫ e1/x5 dx = (1/5) [eu u - ∫ ueu du] = (1/5) [eu u - u2 eu/2]

Substituting x5 = u, we have:

∫ e1/x5 dx = (1/5) [ex5 x5 - x10 ex5/2]

Finally, we can substitute this result into the original integral and get the answer:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) [(1/5) [ex5 x5 - x10 ex5/2]]

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Answer:

3

Step-by-step explanation:

Find the value of x for which n(x) = 0.

-6x+18 = 0

6x = 18

x = 3

Answer:

28,000

Step-by-step explanation:

Answer:

28,000

Step-by-step explanation:

if u multiply 6,827 by 4 u get 27,303  and 208, 000 is way off so is 240, 000 24,000 is off by 3,303 and 28, 000 is off by 697. so it's 28,000.

Answer:

12

Step-by-step explanation:

The Pythagorean theorem is

a^2+b^2 = c^2  where a and b are the sides and c is the hypotenuse ( the side opposite the right angle)

a^2 + b^2 = c^2

Substitute the known values

5^2 + b^2 = 13^2

25+b^2 = 169

Subtract 25 from each side

25+b^2-25 =169-25

b^2 = 144

Take the square root of each side

sqrt(b^2) = sqrt(144)

b=12

Answer:

Given:

To find:

missing side b

Solution:

Using Pythagorean theorem,

(Hypotenuse² = base² + perpendicular²)

b² = c² - a²

= 13² - 5²

= 169 - 25

= 144

b = √144

= 12

Answer:

Part A:

\(x+y=27 \\4x+y = 45\)

Part B:

Number of vanilla wafers packets bought = 6  and

Number of chocolate wafers packets bought = 21

Step-by-step explanation:

Given:

Cost of each packet of vanilla wafer = $4

Cost of each packet of chocolate wafer = $1

Total number of packets bought = 27

Total money spent = $45

Part A:

To write a system of equations for the given situation.

Here, we do not know the number of packets bought for each type of wafer.

We just know that total number of packets bought and the total money spent in buying those packets.

Let us suppose,

Number of packets of vanilla wafers bought = \(x\) and

Number of packets of chocolate wafers bought = \(y\)

Total number of packets = Number of packets of vanilla wafers bought Plus Number of packets of chocolate wafers bought:

i.e. \(x+y=27 ...... (1)\)

Money spent on vanilla wafers packets = \(4 \times x\)

Money spent on chocolate wafers packets = \(1 \times y\)

Total money spent = \(4x+y = 45 ...... (2)\)

So, the system of equations is:

\(x+y=27 \\4x+y = 45\)

Part B:

To find number of packets bought for each flavor = ?

Here, we have two equations and two variables \(x\) and \(y\).

As, the coefficients of \(y\) in both the equations are same.

Let us subtract equation (1) from (2):

\(4x+y-x-y=45-27\\\Rightarrow 3x = 18\\\Rightarrow \bold{x =6}\)

By equation (1), putting the value of \(x\) and solving for \(y\):

\(6+y=27\\\Rightarrow \bold{y =21}\)

So, number of vanilla wafers packets bought = 6  and

number of chocolate wafers packets bought = 21

A rectangular tank 3600 bricks measuring 1/5m by 1/8m by 1/10m into the tank before the water overflows.

To find bricks can be put into the tank before the water overflows,  the volume of water in the tank and then determine the volume of each brick.

The volume of water in the tank  length, width, and depth:

Volume of water = length × width × depth = 3m × 2m × (3/4)m

The volume of each brick:

Volume of each brick = length × width × height = (1/5)m × (1/8)m × (1/10)m

Divide the volume of water in the tank by the volume of each brick:

Number of bricks = (Volume of water) / (Volume of each brick)

Now let's substitute the given values into the formulas and

Volume of water = 3m × 2m × (3/4)m = 9/2 m³

Volume of each brick = (1/5)m × (1/8)m × (1/10)m = 1/400 m³

Number of bricks = (9/2 m³) / (1/400 m³)

= (9/2) / (1/400)

= (9/2) × (400/1)

= 9 × 400 / 2

= 3600

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Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

To start off, we can use the fact that the total area under the probability density function (PDF) must equal 1. This is because the PDF represents the probability of X taking on any particular value, and the total probability of all possible values of X must add up to 1.

So, we can set up an integral to solve for the constant c:

integral from 0 to 1 of c(1-x) dx = 1

Integrating c(1-x) with respect to x gives:

cx - (c/2)x^2 evaluated from 0 to 1

Plugging in the limits of integration and setting the integral equal to 1, we get:

c - (c/2) = 1

Solving for c, we get:

c = 2

Now that we have the value of c, we can use the PDF to find probabilities of X taking on certain values or falling within certain intervals. For example:

- The probability that X is exactly 0.5 is:

PDF(0.5) = 2(1-0.5) = 1

- The probability that X is less than 0.3 is:

integral from 0 to 0.3 of 2(1-x) dx = 2(0.3-0.3^2) = 0.36

- The probability that X is between 0.2 and 0.6 is: integral from 0.2 to 0.6 of 2(1-x) dx = 2[(0.6-0.6^2)-(0.2-0.2^2)] = 0.56

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Using the laws of logarithms: a) log(xy^3). b) log(a^3/bc^21).c) : 8a * log(5). (d) 2 + 2a.

a) Using the laws of logarithms:

log(1000y) + 2log(x^4) = log(10^3 * y) + log(x^8) = log(10^3 * y * x^8) = log(xy^3)

b) Using the laws of logarithms:

3log(a) - log(b) - 21log(c) = log(a^3) - log(b) - log(c^21) = log(a^3/bc^21)

c) Given log(5) = a and log(36) = b, we need to find log(256) in terms of a and b.

We know that 256 = 2^8, so log(256) = 8log(2).

We need to express log(2) in terms of a and b.

2 = 5^(log(2)/log(5)), so taking the logarithm base 5 of both sides:

log(2) = log(5^(log(2)/log(5))) = (log(2)/log(5)) * log(5) = a * log(5).

Substituting back into log(256):

log(256) = 8log(2) = 8(a * log(5)) = 8a * log(5).

d) Given log(x) = a and log(y) = b, we need to find log(100x^2) in terms of a and b.

Using the laws of logarithms:

log(100x^2) = log(100) + log(x^2) = log(10^2) + 2log(x) = 2log(10) + 2log(x).

Since log(10) = 1, we have:

log(100x^2) = 2log(10) + 2log(x) = 2 + 2log(x) = 2 + 2a.

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In order to determine the integer that makes true the given expression:

______ x 7 = -14

consider that such integer must be equal to the quotient between -14 and 7:

-14/7 = -2

In fact, you have:

-2 x 7 = -14

Hence, the integer is -2

Since 7u1v1 ≠ 7v1u1, the property of conjugate symmetry is violated. Therefore, the correct option is option B.

The function is an inner product on R2 if and only if it satisfies the following four properties for any vectors u, v, and w in R2 and any scalar c :Linearity: u, v = v, u Conjugate symmetry: u, u ≥ 0, with equality only when u = 0.

Thus, in this case, the function is not an inner product on R2 because it does not satisfy the property of conjugate symmetry.

Conjugate symmetry, also known as complex conjugate symmetry, is a property of complex numbers.

Given a complex number z = a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)), the conjugate of z is denoted as z* and is defined as z* = a - bi.

Conjugate symmetry refers to the relationship between a complex number and its conjugate. Specifically, if a mathematical expression or equation involves complex numbers, and if z is a solution to the equation, then its conjugate z* is also a solution.

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Answer:

3/4x+3-2x= −5 /4 x+3

Step-by-step explanation:

yw <3 IMAO

The response variable is the amount of tax, whereas the explanatory variable is whether the student believes global warming is a serious issue or not.

An explanatory variable is a variable that can influence another variable or cause changes in the response variable. It is the variable that is controlled or manipulated to study its effect on the dependent variable (response variable) and is an independent variable in statistical analysis. The response variable is a dependent variable or an output variable that changes based on the influence of other variables (explanatory variable).The researchers wanted to compare the mean response on gasoline taxes (the first question) for those who answer yes and for those who answer no to the second question. Therefore, the response variable is the amount of tax the student is willing to add to a gallon of gasoline. This response variable is an indication of how much students are willing to pay to mitigate global warming. On the other hand, the explanatory variable is whether the student believes that global warming is a serious issue or not. This variable will help determine if students' perception of global warming has any effect on their willingness to pay for mitigative measures.

In conclusion, the response variable in the given scenario is the amount of tax, while the explanatory variable is students' perception of global warming.

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Answer:

$5.50

Step-by-step explanation:

If we are finding the price of each item and they are the same price each, we can just do division! 2,673/486=5.5, so $5.50 is the price for each item.

hope this helped!! <3

Answer: 22

Step-by-step explanation:

Ok, so the way I do it I multiply then divide.

For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday

For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.

So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)  

(6x-5)-(-x-4)

6x-5=x+4

6x-x=4+5

5x=9

If a forest covers 51,000 acres. A survey finds that 0.4​% of the forest is​ old-growth trees. The number of  acres of​ old-growth trees that are​ there is: 204 acres.

Using this formula to find the number of acres that are there.

Number of acres = Number of forest covers acres × Forest old growth tree percentage

Where:

Number of forest covers acres = 51,000 acres

Forest old growth tree percentage = 0.4% or 0.004

Let plug in the formula

Number of acres = 51,000 acres × 0.004

Number of acres = 204 acres

Therefore we can conclude that the number of acres  is 204 acres.

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Answer:

560x^3y^4.

Step-by-step explanation:

The (r+1)th term of (a + b)^r = nCr a^(n-r) b^r

We want the fifth term so r = 5 - 1 = 4:

(4 + 1)th term = 7C4 x^(7-4) (-2y)^4

= 35x^3 16y^4

= 560x^3y^4.

Answer:

1,200 more

Step-by-step explanation:

because 1,200 + 2000=3,200

When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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Formula:

\(\frac{1}{2}(Big Arc- Small Arc)\)

\(\frac{1}{2} (118-26)\)

\(\frac{1}{2}(92)\\\)

=46

m∠DPR = 46°

I hope it helps! :)