A polygon with side lengths of 6, 9, and 15 forms a triangle. TrueFalse

The value of the perpetuity today, with an annual interest rate of 8%, is $4,125.25.

To calculate the present value of a perpetuity, we can use the formula: Present Value = Cash Flow / Interest Rate.

In this case, the cash flow is $500 per year, and the interest rate is 8% (or 0.08 in decimal form). Plugging these values into the formula, we get: Present Value = $500 / 0.08 = $6,250.

However, this calculation gives us the present value of the perpetuity starting from today. Since the payments start 5 years from today, we need to discount the value by the present value of $1 received 5 years from today.

Using the formula for the present value of a single amount, we find that the present value of $1 received 5 years from today, with an 8% interest rate, is approximately 0.6806.

To calculate the present value of the perpetuity starting 5 years from today, we multiply the present value of $6,250 by the discount factor of 0.6806: Present Value = $6,250 * 0.6806 ≈ $4,250.25.

Therefore, the value of the perpetuity today, with an 8% annual interest rate and payments starting 5 years from today, is approximately $4,125.25.

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We can write\(:∫0¹(1-x^q)^1/pdx = ∫1⁰(1-v)^1/pv^(1/q - 1) dv.\)

To prove that \(∫0¹(1-x^p)^1/qdx=∫0¹(1-x^q)^1/pdx,\) we use the substitution u = x^p and u = x^q respectively.

Using the substitution method, we have the following:  Let\(u = x^p,\) then \(du/dx = px^(p-1)\)and \(dx = (1/p)u^(1/p - 1) du.\)

Hence we can write\(:∫0¹(1-x^p)^1/qdx = ∫0¹(1-u)^1/qu^(1/p - 1) duLet v = (1 - u), then dv/dx = -du and dx = -dv.\)

Therefore, we can write:\(∫0¹(1-u)^1/qu^(1/p - 1) du = ∫1⁰(1-v)^1/qv^(1/p - 1) dvS\)

Since p and q are both positive, 1/p and 1/q are positive, which implies that the integrals are convergent. Now let us apply the same technique to the other integral. I\(f v = x^q, then dv/dx = qx^(q-1) and dx = (1/q)v^(1/q - 1) dv.\)

Hence we can write:∫\(0¹(1-x^q)^1/pdx = ∫1⁰(1-v)^1/pv^(1/q - 1) dv.\)

Using the identity\((1 - u)^1/q = (1 - u^q)^(1/p),\)

we can write:\(∫0¹(1-x^p)^1/qdx = ∫0¹(1 - (x^p)^q)^(1/p)dx = ∫0¹(1 - x^q)^(1/p)dx∫0¹(1-x^q)^1/pdx = ∫0¹(1 - (x^q)^p)^(1/q)dx = ∫0¹(1 - x^p)^(1/q)dx.\)

Hence, we have shown that \(∫0¹(1-x^p)^1/qdx = ∫0¹(1 - x^q)^(1/p)dx.\)

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The correct option is D. Asking 80 owners their attitude toward a new design would be an example of a sample.

If a target population is defined as all 2,134 pickup truck owners residing in Tippecanoe County, then asking 80 owners their attitude toward a new design would be an example of a sample.

Because the survey is conducted on a limited group of people who represent the larger population. Therefore, the survey conducted on the sample represents the population as a whole. The sample is a representative subset of the entire population, which can be used to infer statistics and characteristics of the whole population. A statistical frame is a technique used to choose a representative sample of the population.

Asking only owners listed in the telephone directory would not be an example of a statistical frame. Instead, it would be an example of a bias selection because it excludes owners who are not listed in the telephone directory. Asking 100 owners their attitude toward a new truck style would not be an example of a consensus as consensus is a general agreement among the people.

However, the survey conducted on a sample can be used to find out a general consensus. Universal testing is not feasible because it would involve surveying each and every member of the population, which is both time-consuming and expensive.

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The complete question is:

a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Answer: D. Subtracting 9 from each side

Step-by-step explanation:

Always start with numbers without variables first before doing anything with x. And make sure one side must not equal 0 unless you're doing polynomials.

Answer:

x = -1

Step-by-step explanation:

Answer:

x= - 1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

LCM (k, n) = 10 and HCF(k, n) = 2

Step-by-step explanation:

The given parameters are;

The time after which Keshav takes  a break = k hours

The value of k = The first smallest prime natural number

Therefore, by mathematical definition, k = 2

The time after which Noel takes a break = n hours

The value of n = The fifth smallest composite natural number

The first five composite numbers are given as follows;

4, 6, 8, 9, and 10

Therefore, the fifth smallest composite natural number = 10 = n

The LCM (k, n) = LCM (2, 10) = Least common multiple of 2 and 10 is given as follows;

Dividing by 2, we get;

2/2 = 1,  10/2 = 5

Dividing the result by 5, we get;

5/5 = 1

Multiplying the devisors together gives;

5 × 2 = 10

Therefore, the LCM of 2 and 10 = 10

LCM(2, 10) = LCM (k, n) = 10

The HCF(k, n) = HCF of 2 and 10 = The highest common factor that divides both 2 and 10 is given as follows;

Dividing 2 and 10 by 2 gives;

2/2 = 1 and 10/2 = 5

Therefore, HCF(k, n) = The highest common factor of 2 and 10 = HCF(2, 10) = 2

Answer:

8+3x=20

4 hours

Step-by-step explanation:

8+3x=20

3x=12

x=4

The only combination you will not find in a valid deductive argument is "false premises and a true conclusion."

A deductive argument is considered valid when the conclusion logically follows from the premises. In other words, if the premises are true, the conclusion must also be true. Therefore, in a valid deductive argument, the premises and conclusion must have a consistent truth value.

Let's examine the given answer choices:

1. True premises and a false conclusion: This combination would result in an invalid deductive argument because the conclusion contradicts the truth of the premises. For example:

Premise 1: All mammals are warm-blooded.

Premise 2: Elephants are mammals.

Conclusion: Elephants are cold-blooded.

2. True premises and a true conclusion: This combination represents a valid deductive argument. If the premises are true and the conclusion logically follows, the argument is valid.

3. False premises and a false conclusion: This combination may or may not represent a valid deductive argument. Although the premises and conclusion have the same truth value, it does not necessarily mean that the argument is valid. It is possible for a deductive argument with false premises and a false conclusion to be valid, as long as the reasoning is sound.

4. False premises and a true conclusion: This combination represents an invalid deductive argument. The truth of the conclusion cannot be guaranteed if the premises are false. Therefore, this combination is the one you will not find in a valid deductive argument.

In a valid deductive argument, you will not find the combination of false premises and a true conclusion. This combination would render the argument invalid because the conclusion would not be guaranteed to follow logically from the false premises.

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Cannot determine total pets polled.

The problem provides information about Abigale and Armen's poll results regarding the number of pets their classmates have. Abigale's poll results are shown in a dot plot, and Armen's poll results are listed. The total number of students polled by both Abigale and Armen is 27.

From Abigale's poll, we can see that most students have either 1 or 2 pets, with a few having 3 or 4 pets. From Armen's poll, we see that the number of pets ranges from 0 to 5, with most students having either 1 or 2 pets. To determine the total number of pets owned by all the students polled, we need to add up the number of pets reported by each student.

Since we don't have the specific number of pets for each student in Armen's poll, we cannot determine the total number of pets owned by all students polled. Therefore, the main answer is that we cannot determine the total number of pets owned by all students polled based on the information provided.

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

Heavenly,  we need the forumula for the area of a triangle, do you know it?

Step-by-step explanation:

Area of a triangle is (1/2 ) * B*H

where B = base

H = height

then

A = 1/2* B * H

A is given to be 20

B = b

H = b+4

plug all those into the formula,

20 = (1/2)*b*(b+4)

use your algebra skillz  :P

20 = 1/2 *( \(b^{2}\) + 4b)

20*2 = \(b^{2}\) + 4b

40 = \(b^{2}\) + 4b

0 = \(b^{2}\) + 4b-40

rewrite the above so it's in x format

\(x^{2}\) + 4x -40 = 0

use the quadratic formula to find  x  , and for our problem, remember that x represents the base,  or b,  but don't mix it up with the b in the quadatic fomula,  with the b of the triangle, which is the base,  they are differnt "b"s   :P

X = (b±\(\sqrt{b^{2}-4*a*c }\) ) / 2*a

a = 1

b = 4

c = -40

x = (4±\(\sqrt{4^{2}-4*1*(-40) }\)  ) /2*1

x = ( 4±\(\sqrt{16+160}\) ) / 2

x = (4±\(\sqrt{176}\) ) / 2

x = (4±13.266499)/2

x= 2±6.633249

x = 2 + 6.633249 = 8.633

b= 8.633 cm

The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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Answer:

13. 23 boat rides; 22 are full, and the first one has 301 passengers.

12. $11,067.50

Step-by-step explanation:

13,105 people in a day, divided by 582 per ride.

13,105/582 = 22 (with a remainder)

582 x 22 = 12,804

So, the remainder is

13,105 - 12,804 = 301

23 rides, with 22 full and the first one having 301 people.

----------------------------------------------------------------------------------------------

There are 879,575 tickets sold across 755 theatres. Per theatre,

879,755 / 755 = 1,165 tickets per theatre

1,165 x $9.50 = $11,067.50 per theatre.

Note that since the t- statistic (0.96) is less than the critical value     (2.571),we fail to reject the null hypothesis.

First,we calculate the differences in   weight for each mouse.

Mouse 1   19.8 - 19.6 = 0.2

Mouse 2  19.2 - 19.3 = -0.1

Mouse 3  19.5 - 19.4 = 0.1

Mouse 4   21.6 - 21.7 = -0.1

Mouse 5  22.6 - 22.6 = 0.0

Mouse 6  19.7 - 19.6 = 0.1

Next, we calculate   the mean and standard deviation of the differences.

Mean difference ( x) -  (0.2 - 0.1 + 0.1 - 0.1 + 0.0 + 0.1) / 6

=0.0333

Standard deviation (s) calculated using the differences =  0.0866

Calculating the t-statistic we say

t = ( x - μ) / (s / √n )

t = ( 0.0333 - 0) / (0.0866 / √6)

= 0.94189386183

≈ 0.94

Critical   value for a one - tailed t-test with α = 0.05 and degrees of freedom ( df) = n - 1

= 6 - 1

= 5.

Using a t - table , the critical value is   approximately 2.571. Since the t-statistic (0.96) is less than the critical value (2.571), we fail to reject the null hypothesis.

Interpretation - there isn't enough evidence to support the scientist's claim.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

A scientist claims that pneumonia causes weight loss in mice. The table shows the weights? (in grams) of six mice before infection and two days after infection. At

alpha=0.05?,

is there enough evidence to support the? scientist's claim? Assume the samples are random and? dependent, and the population is normally distributed.

Table

Mouse

1

2

3

4

5

6

Weight​ (before)

19.819.8

19.219.2

19.519.5

21.621.6

22.622.6

19.719.7

Weight​ (after)

19.619.6

19.319.3

19.419.4

21.721.7

22.622.6

19.619.6

The average rate of change tell you in this context the volume of water in the base as the volume changes from 2.5 cups to 4.25 cups.

The average rate of change is a mathematical concept used to describe how a change in one quantity affects another quantity.

To calculate the average rate of change, we need to know the height of water in the vase at two different volumes. Let's call the height of water at a volume of 2.5 cups "h1" and the height of water at a volume of 3.25 cups "h2". Then, the average rate of change over the interval from 2.5 cups to 3.25 cups is calculated as:

=> (h2 - h1) / (3.25 - 2.5) = (h2 - h1) / 0.75

This average rate of change tells us how much the height of water changes, on average, for every one cup increase in the volume of water in the vase.

In other words, the average rate of change provides us with a measure of the "slope" of the relationship between the height of water and the volume of water in the vase over the interval from 2.5 cups to 3.25 cups.

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The given function is

To find the minimum of this function, we have to find the vertex of the parabola V(h,k). Where

Where a = 2, and b = 16. Replacing these values, we have

Then, we find k

So, the vertex is at (-4, -2).

Answer:

x=-75/46

Step-by-step explanation:

\(10 - 5 + \frac{x}{3} - 8x + \frac{5}{2} = 20\)

The LCM of the denominator is 6 because both 2 and 3 can go into 6.

\(10 - 5 + \frac{2x}{6} - 8x + \frac{15}{6} = 20\)

Multiply all terms by 6 to drop the fraction. Make sure to multiply both sides of the equation

\(60 - 30 + 2x - 48x + 15 = 120\)

Put all x values on one side

\(2x - 48x = 120 - 60 + 30 - 15\)

\( - 46x = 75\)

\(x = - \frac{75}{46} \)

Answer:

158.4

Step-by-step explanation:

The equation which represents the provided function after it has been translated 5 units up and 9 units to the right is (1.6)ˣ⁻⁹+5.

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

The provided function in the problem is,

\(f(x) = (1.6)^x\)

The function has translated 5 units up. Thus, substrate 5 units inside the function.

\(g(x) = (1.6)^{x-5}\)

The function has translated units to the right. Thus, add 9 units outside the function as,

\(g(x) = (1.6)^{x-5}+9\)

Thus, the equation which represents the provided function after it has been translated 5 units up and 9 units to the right is,

\(g(x) = (1.6)^{x-5}+9\)

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Answer:

C

Step-by-step explanation:

ur wlcm

Answer: To estimate how many Hershey's Kisses can be made with 200 gallons of liquid chocolate, we need to make a number of assumptions and estimates based on the available information.

First, we need to determine how much liquid chocolate is required to make a single Hershey's Kiss. This information is not readily available, but we can estimate based on the weight of a single Kiss and the density of chocolate. According to Hershey's website, a single Hershey's Kiss weighs about 4.5 grams. The density of chocolate varies depending on the type of chocolate and the specific recipe, but we can assume a density of around 1.2 grams per milliliter.

To convert 200 gallons to milliliters, we can use the conversion factor 1 gallon = 3785.41 milliliters. So:

200 gallons x 3785.41 milliliters/gallon = 757,082 milliliters

Assuming a density of 1.2 grams per milliliter, 757,082 milliliters of liquid chocolate would weigh:

757,082 milliliters x 1.2 grams/milliliter = 908,498 grams

Dividing this total weight of chocolate by the weight of a single Hershey's Kiss (4.5 grams) gives an estimate of the total number of Kisses that could be made with 200 gallons of liquid chocolate:

908,498 grams ÷ 4.5 grams/Kiss ≈ 201,778 Kisses

Of course, this is a rough estimate that makes a number of assumptions and simplifications. In reality, the actual number of Hershey's Kisses that could be made with 200 gallons of liquid chocolate would depend on a variety of factors, including the specific recipe and production process, as well as the size and shape of the Kisses themselves. However, this estimate provides a reasonable starting point for further analysis and exploration.

Step-by-step explanation:

The given statement "if the total change of a function f along a curve c is zero, then c must be a contour of f" is true because a contour of a function f is a curve along which the function has a constant value.

When the total change of a function f along a curve c is zero, it means that the function's value has not changed throughout the curve.

This indicates that the curve c must be a contour of the function f, as the function has a constant value along the curve.

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Answer:34

Step-by-step explanation:

Answer:6/10

Step-by-step explanation:

Answer:

x=1 y=2

Step-by-step explanation:

Answer:

y= -2x+4

So the y intercept is 4, as its the c in this equation

I think that makes your x intercept as either 8 or 2...

Step-by-step explanation:

The number of rides is an illustration of a linear function.

The expression for the number of rides is: \(\mathbf{x = -\frac{100}{m}}\)

The function is given as:

\(\mathbf{y = mx + b}\)

Where:

The given parameters are:

\(\mathbf{y =0, b = 100\ and\ m < 0}\)

So, we have:

\(\mathbf{0 = mx + 100}\)

Subtract 100 from both sides

\(\mathbf{mx = -100}\)

Divide both sides by m

\(\mathbf{x = -\frac{100}{m}}\)

So, the expression for the number of rides is: \(\mathbf{x = -\frac{100}{m}}\)

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Answer:

The answer to your question thinking that you're multiplying is -6

Step-by-step explanation:

The value of the expression b²+ c², when b = 2 and c = –3, is 13.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

We have an expression,

b²+ c².

The value of the expression when b = 2 and c = –3,

= (2)²+ (-3)²

= 4 + 9

= 13

Therefore, the value is 13.

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The complete question:

What is the value of the expression b²+ c², when b = 2 and c = –3?

Answer:

x=5

Step-by-step explanation:

-3=x-8

8-3=x

x=5

Answer:

Jamie has $12.50 of her allowance left if the books cost $2.50 each.

Step-by-step explanation:

To calculate this, first calculate the total cost of the books:

5 books x $2.50/book = $12.50.

Then subtract the cost of the books from the amount Jamie has saved:

$38 - $12.50 = $25.50.

Finally, subtract the cost of the books from the amount Jamie has saved to get the amount she has left:

$25.50 - $12.50 = $12.50.

Answer:

$25.50

Step-by-step explanation:

We know Jamie bought 5 books, each worth $2.50, d. We need to know the cost of all five, so we’ll go ahead and multiply 5 times $2.50 to get $12.50.

Since we know how much the books cost, all we have to do now is subtract the amount she spent from her allowance. $38.00 - $12.50 is 25.50, the amount of money Jamie has left.

Use the way that kids use i.e trial and error method .

Solution:-

The set given by

\(\\ \rm\longmapsto \left\{32+n,\dfrac{n}{8},\sqrt{n+225}\right\}\)

Lets understand

Come to 2nd one.

Come to third one

Lets think

Nearest squares to 225 are 196 and 289

We can't take 196 as we have to take a positive one other wise it will come in terms of i.

Take 289

\(\\ \rm\longmapsto n+225=289\)

\(\\ \rm\longmapsto n=289-225=64\)

Its divisible by 8 .

Rewrite the set

\(\\ \rm\longmapsto \left\{64+32,\dfrac{64}{8},\sqrt{225+64}\right\}\)

\(\\ \rm\longmapsto \left\{96,8,\sqrt{289}\right\}\)

\(\\ \rm\longmapsto \left\{96,8,17\right\}\)

Hence n=64