answer pls
3278+32+3213+89321+31398

Answer:

Let total non-fiction books = 3x

And total fiction books = 5x

After reading 6 non-fiction books, remaining non-fiction books = 3x-6

After reading 13 fiction books, total fiction books remaining fiction books = 5x-13

(3x-6)/(5x-13) = 3/4

Solving for x, we get x = 5

So total non-fiction books = 15 and fiction books=25

So total number of books bought = 40

The integral ∫ 4e^x dx simplifies to 4e^x + C, where C is the constant of integration.

To evaluate the integral ∫ 4e^x dx, we can use the power rule for integration.

The power rule states that ∫ x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.

In this case, we have the integral ∫ 4e^x dx, where the function inside the integral is e^x.

Using the power rule, we can integrate e^x as follows:

∫ e^x dx = e^x + C,

where C is the constant of integration.

Now, we can apply the integration of e^x to the original integral:

∫ 4e^x dx = 4 ∫ e^x dx.

Applying the integration of e^x, we have:

4 ∫ e^x dx = 4(e^x) + C.

Therefore, the integral ∫ 4e^x dx simplifies to 4e^x + C, where C is the constant of integration.

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Answer:

D. 1960

Step-by-step explanation:

Diameter=6units

Area:-

3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

The Policeman’s rate of change is $10 per hour and the firefighter's rate of change is $10 per hour

The Policeman’s rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

On the line of the policeman, we have the following point

(x, y) = (4, 40)

So, the rate of change is

Rate = y/x

This gives

Rate = 40/4

Evaluate

Rate = 10

The firefighter's rate of change

On the line of the firefighters, we have the following point

(x, y) = (4, 60)

So, the rate of change is

Rate = y/x

This gives

Rate = 60/4

Evaluate

Rate = 15

Hence, the rate is $15 per hour

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The null and alternative hypotheses for this scenario can be formulated as follows:

Null Hypothesis (H0): The mean depression scores of the bullies and bully-victims are equal.

Alternative Hypothesis (H1): The mean depression scores of the bullies and bully-victims are not equal.

We can represent these hypotheses symbolically as:

H0: μbullies = μbully-victims

H1: μbullies ≠ μbully-victims

where μbullies and μbully-victims are the population means of depression scores for bullies and bully-victims, respectively.

Note that we do not assume any prior knowledge or expectation regarding which group may have a higher mean depression score. The null hypothesis assumes that the mean depression scores are equal, and the alternative hypothesis allows for the possibility that they are not equal in either direction.

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The length of the third side of the right triangle is approximately 16.49 units.

Pythagoras' theorem is a fundamental principle in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

In the given question,

In a right triangle, the height is the perpendicular line segment that connects the base to the opposite vertex (the point where the two legs of the triangle meet).

We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

So, in this case, we have:

Base = 13

Hypotenuse = 21

Let the height be h.

Using the Pythagorean theorem, we have:

21² = 13² + h²

441 = 169 + h²

Subtracting 169 from both sides, we get:

272 = h²

Taking the square root of both sides, we get:

h = √(272)

Simplifying, we get:

h = 16.49 (rounded to two decimal places)

Therefore, the length of the height of the right triangle is approximately 16.49 units.

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The other rules for derivatives can be used to check the answer found by using the limit definition. To find the derivative of a function, like f(x) = x/n, where n ≠ 0, using the limit definition of a derivative, we must take the limit of the quotient f(x+h) - f(x) / h as h approaches 0.

However, other rules for derivatives, like the power rule, can also be used to find the derivative of f(x) = x/n and can be used to check the answer found by using the limit definition.

Power law:

According to the derivative power rule, d/dx (xn) = n xn - 1.

Rule of sum and difference

This rule states that when there is a sum or difference, the differentiation process can be dispersed to the functions. d/dx (f(x) g(x)) = d/dx (f(x)) d/dx (g(x)), for example.

Product law:

To determine the derivative of the product of two functions, apply the product rule. It states that f(x) d/dx (g(x)) + g(x) d/dx (f(x)) = d/dx (f(x)) (f(x)) g(x)). It can be expressed mathematically as (uv)' = u v' + v u'.

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Answer:

y=60 degrees

x=90 degrees

Step-by-step explanation:

If you look at x, you can tell by it's angle that it is 90 degrees. A square has 4 sides with 90 degrees on each side, that angle is 1/4 of a square, making it a 90 degree angle, and a triangle has 3 sides, all 60 degrees, if you look at y, you can see that angle is 1/3 of a triangle, giving it a 60 degree angle.

Hope this helps!

Answer:

A.

Step-by-step explanation:

An irrational number is a number that goes on forever without repeating. The square root of 2 does exactly this.

Answer:

the y intercept represents the point on the y axis in which the line crosses on a graph.

From th given graph, the line is passing through the points,

The expression to calculate the slope of a line passing through two points is,

Substitute values in the above expression.

Thus, the slope of the line y is -1/3.

Answer:

your answer should be 15

Step-by-step explanation:

The policyholder's dwelling is insured for $238,000 and the flood-related damages are valued at $170,000. Since the policyholder has a flood policy, the damages will be paid on a replacement cost basis, not actual cash value.

Therefore, the amount the policyholder will receive on their claim is the full replacement cost of their dwelling, which is $240,000. So the answer is option B. Your answer: A. $110,000

Here's the step-by-step explanation:

1. Since this is a flood claim in Rockport, Texas, the policyholder's flood policy will come into play.
2. The policyholder's duplex is insured for $238,000, and the replacement cost of the dwelling is $240,000. However, the insured amount ($238,000) is what will be considered for the claim.
3. The flood-related damages are valued at $170,000, but the actual cash value of these damages is $110,000.
4. Since the actual cash value of the damages is lower than the insured amount, you will pay the policyholder the actual cash value of the damages, which is $110,000.

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Answer:

we have x=1, y=0 and x=-3, y=4

Step-by-step explanation:

We need to solve the equations: \(y=x^2+x-2 \ and \ y=-x+1\)

Let:

\(y=x^2+x-2--eq(1)\\ y=-x+1---eq(2)\)

Putting value of eq(2) into eq(1)

\(-x+1=x^2+x-2\\Solving:\\x^2+x-2+x-1=0\\x^2+2x-3=0\\Factorising:\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x-1)(x+3)=0\\x-1=0 \ or \ x+3=0\\x=1 \ or \ x=-3\)

Now finding values of y for x=1 and x=-3

\(For \ x=1, \\y=-x+1 \\y=-1+1 \\y=0\\For \ x=-3\\ y=-x+1\\y=-(-3)+1 \\y=3+1\\y=4\)

So, we have x=1, y=0 and x=-3, y=4

Answer:

(l*b)

length*breadth

=is answer.

The equation of the line that is perpendicular to y = -(1/5)x - 1 and passes through the point (15, 0) is y = 5x - 75.

To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal of a slope is the opposite of its reciprocal.

The given line y = -(1/5)x - 1 is in slope-intercept form (y = mx + b), where 'm' represents the slope and 'b' represents the y-intercept. From this equation, we can see that the slope of the given line is -1/5.

To find the slope of a line perpendicular to this, we take the negative reciprocal of -1/5. The reciprocal of -1/5 is -5/1, and the negative of that is 5. Therefore, the slope of the line we're looking for is 5.

Now that we have the slope (5) and the point (15, 0) through which the line passes, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1),

where (x1, y1) is the given point and 'm' is the slope

Substituting the values into the equation, we have:

y - 0 = 5(x - 15)

y = 5x - 75

Finally, we have the equation of the line that is perpendicular to y = -(1/5)x - 1 and passes through the point (15, 0): y = 5x - 75.

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The probability that the three pieces can be assembled into a triangle is 25%

Let the length of the stick be 1, so each break can occur at a position in the interval [0,1]. Let x and y be the two breaks in the stick. Then the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is the probability of the triangle.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for  y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for  y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square,

Thus, the probability that the three pieces can be assembled into a triangle is 25%

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Answer:

0

Step-by-step explanation:

Angle x+45  = (145-55) / 2

2x + 90 = 90

2x = 0

x = 0

There is no way to accurately answer this question as there are too many variables to consider, such as the population size and crime rate of the state.

There is no way to accurately answer this question as there are too many variables to consider. The population size of the state would be an important factor in calculating the number of murders per 100,000 residents. The population size of the state would determine how many people are in the state with an automatic weapon and therefore how many potential murders could occur. Additionally, the crime rate of the state would be an important factor in determining the number of murders per 100,000 residents as it would indicate whether or not there would be a higher propensity for crime in the state. Additionally, the availability of other weapons, such as handguns or knives, would also be a factor as it could reduce or increase the number of murders with automatic weapons. All of these factors, as well as others, make it impossible to accurately determine the number of murders per 100,000 residents in a state with 1 thousand automatic weapons.

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Your answer for A is correct.

For B, I would keep the base of the logarithm as simple as possible.

\(y = 100 \cdot 3.24^x \implies \dfrac y{100} = 3.24^x \implies \log_{3.24}\left(\dfrac y{100}\right) = \log_{3.24}(3.24)^x \\\\ \implies x = \log_{3.24} \left(\dfrac y{100}\right)\)

In part A, the function told us the number of students with cell phones (dependent variable) after some number of years post-2000 (independent variable). Our new function turns this around and tells us the time in years after 2000 (dependent) based on how many student have cell phones (independent).

For C, if we set \(y=7200\) students, then we can estimate the time it takes for the all students to acquire cell phones by solving for \(x\).

\(x = \log_{3.24}\left(\dfrac{7200}{100}\right) = \log_{3.24}(72) \approx 3.63794\)

If you're using a typical calculator, it probably won't have buttons for logarithms of any base other than 10 or the natural base \(e\). To work around that, use the change-of-base identity

\(\log_{3.24}(72) = \dfrac{\log_{10}(72)}{\log_{10}(3.24)} = \dfrac{\ln(72)}{\ln(3.24)}\)

At any rate, it would take about 3.64 years for all students to get a cell phone, according to this model.

Answer:

x < -6

Step-by-step explanation:

\(\frac{x}{4} < -1.5\)

to isolate x, multiply both sides by 4

\((4) \frac{x}{4} < -1.5 (4)\)

which gives you:

x < -6

The package which the company should choose if it costs the same to produce the two products is the cylinder because it has about 27.5 in.3 less wasted space than the prism.

The term "cost of production" refers to all the costs that are involved when a company offers a service or manufactures a product.

Costs of production relate to the different expenses that a firm faces in producing a good or service.

This refers to the amount which is used to produce a good.

With this in mind, we can see that there are the given dimensions for the square prism and cylinder from the complete question.

Hence, because they cost the same, choosing the cylinder is the best choice because of the less wasted space than the prism.

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Answer:

It's A

Step-by-step explanation:

The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer:

114

Step-by-step explanation:

L=9.5 inches  W=1.5 inches H= 8 inches

V=LWH=9.5*1.5*8=114

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Answer:

74

Step-by-step explanation:

21, 22, 20, 74, 25, 22, 29, 26, 26, 22, 21, 22

An outlier is a piece of data that is significantly different from the other pieces of data

All of the data is in the twenties except 74.  It is significantly different

It is an outlier

Hello!

\(\boxed{ \bf The~outlier~in~the~data~set~is~74.}\)

__________________________________________________

An outlier is basically a number that is much greater or smaller than the rest of the numbers in the data set. In this case, all of the numbers are twenty-something, except for 74. There is a huge difference between 74 and these numbers.

Answer:

x = 55

Step-by-step explanation:

61+3×X=226

61+3x=226-61

3x=165

x= 165/3

x= 55