what is f(-1) for the function given?
f(x)=x^2-3x+8

The missing side length is 17 and the side lengths 8, 15, and 17 form a Pythagorean triple.

Side lengths: 8, 15

Missing side length: 17

Yes, the side lengths form a Pythagorean triple. The side lengths 8, 15, and 17 form a Pythagorean triple because 8^2 + 15^2 = 17^2.

To answer this question, we first need to determine if the side lengths 8, 15 and the missing side length form a Pythagorean triple. To do this, we use the Pythagorean theorem which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. If this is true, then the side lengths form a Pythagorean triple.

In this case, we can plug in the side lengths 8 and 15 into the Pythagorean theorem. 8^2 + 15^2 = 17^2. Since the equation is true, this means that the side lengths 8, 15 and 17 form a Pythagorean triple. Therefore, the missing side length is 17.

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Answer:

Option B

Step-by-step explanation:

To find the increased amount, we have to subtract the original value from the Increased value.

           \(\sf \boxed{\bf Increased \ percentage = \dfrac{increased \ value - original \ value}{Original \ value}*100}\)

                                                  \(\sf = \dfrac{(75-65)}{65}*100\\\\\\=\dfrac{10}{65}*100\\\\= 15.38 \%\\\\= 15 \%\)

Answer:

C

Step-by-step explanation:

I'm back!!!

Translating algebraic language into normal language is always difficult to explain, but I'll try my best.

If I told you, "What is 65 less than 100", You would probably say 35. If I say, "I make 65 dollars less than you" Then we're taking your salary and decreasing it by 65 to find my salary. So we do take your salary/100 (n) and decrease it by my salary/65, and the operation for that is subtraction, so you would do n-65, and that difference will be 65 LESS than n.

Let me know if you have any questions

The population function of the Western Lowland Gorillas can either represent population growth or population decay

The question is incomplete, as the resources to model the population of the Western Lowland Gorillas are not given.

However, the following is a general guide to solve the question.

An exponential function is represented as:

\(y = a(1 \pm r)^x\)

Where:

Given that the population of the Western Lowland Gorillas decreases, then the rate of the function would be 1 -r (i.e. an exponential decay)

Take for instance:

\(y = 2000 * 0.98^x\)

By comparison.

a = 2000 and 1 - r = 0.98

The above function can be used to model the population of the Western Lowland Gorillas

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Answer:

Peter is 20 years old

Step-by-step explanation:

John= 2(Peter's age) (j=2p)

Peter= (Alice's age + 5) (P= A+5)

Okay, so let's substitute the equations now:

John= 2(Alice + 5)

So the equation for 5 years from now is:

2(A+5) + 5 = 3a (because he is 3 times as old as alice)

so, let's solve for that equation:

2a + 10 + 5 = 3a

subtract 2a from both sides:

15= a

so, Alice is going to be 15 years old, so now we can solve for Peter's age:

P= A + 5

P= 15 + 5

P = 20

Peter is 20 years old

I hope this helps! :)

Answer:

A. 136 stars

B. 340 stars

Answer:

At 10 pm he counted 136 stars and at 12 pm he counted 340

Step-by-step explanation:

for 10 pm:

68 x 2

for 12 pm:

68 x 5

Answer:

42 minutes

Step-by-step explanation:

12÷3 = 4

This means Josephine goes 4 m/h

If she goes 4 m/h for 10.5 miles then it will take her 42 minutes to do so.

Please give brainliest if I helped! :)

The domain of h(x) is all real numbers except 0 and 7. We can express this in interval notation as (-∞,0) U (0,7) U (7,∞).

To find the domain of the function h(x) = (x - 3) / (x(x - 7)), we need to determine the values of x for which the function is defined.

Step 1: Identify any restrictions on the domain. In this case, we have a fraction with x(x - 7) in the denominator.

Step 2: Set the denominator equal to zero and solve for x to find the values where the function is undefined.
x(x - 7) = 0
x = 0 and x = 7

Step 3: The domain includes all real numbers except for the values that make the denominator zero. In interval notation, the domain of h(x) is:

(-∞, 0) ∪ (0, 7) ∪ (7, ∞)

So, the domain of the function h(x) = (x - 3) / (x(x - 7)) is (-∞, 0) ∪ (0, 7) ∪ (7, ∞).

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a) The revenue R as a function of p is given by R(p) = -5p^2 + 100p.

b) This equation has two solutions: p = 0 and p = 20. Since R is nonnegative, the domain of R is the set of all values of p greater than or equal to 20, or {p | p ≥ 20}.

c)  The price that maximizes revenue is $10.

d)  The maximum revenue is $500.

a) The revenue R is given by R = xp. Since x = -5p + 100, we can substitute this into the equation for R to get:

R(p) = p(-5p + 100) = -5p^2 + 100p

Therefore, the revenue R as a function of p is given by R(p) = -5p^2 + 100p.

(b) We are given that the revenue R is nonnegative. To find the domain of R, we need to find the values of p that make R nonnegative. We can do this by finding the zeros of the quadratic equation -5p^2 + 100p = 0:

-5p(p - 20) = 0

This equation has two solutions: p = 0 and p = 20. Since R is nonnegative, the domain of R is the set of all values of p greater than or equal to 20, or {p | p ≥ 20}.

(c) To find the price p that maximizes revenue, we can take the derivative of R(p) with respect to p, set it equal to zero, and solve for p:

R'(p) = -10p + 100 = 0

-10p = -100

p = 10

Therefore, the price that maximizes revenue is $10.

(d) To find the maximum revenue, we can substitute p = 10 into the equation for R(p):

R(10) = -5(10)^2 + 100(10) = $500

Therefore, the maximum revenue is $500.

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The height of the taller building is 18.6 meters

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Therefore, the height of the taller building is the sum of the height of the smaller building and upper part of the taller building.

tan 53 = opposite / adjacent

tan 53 = x / 10

cross multiply

x = 10 tan 53

x = 10 × 1.32704482162

x = 13.2704482162

x = 13.3 m

tan 28 = y / 10

y = 10 tan 28

y = 5.31709431661

y = 5.3

Therefore, the height of the taller building is 13.3 + 5.3 = 18.6 meters.

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The correct option b. $3,338; is the amount spent by Stephen on purchasing the shares.

For the data given in question-

On every tenth share, Stephen's broker received a commission of $12.50.

= (328 / 10) x $12.50

= 32.8 x $12.50

= $410

Add all four values

= $538.9 + $1444.3 + $944.3 + $410

= $3,338

Thus, the amount spent by Stephen on purchasing the shares is  $3,338.

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Answer:

  the can with the 5-inch radius will cost more

Step-by-step explanation:

The cost will be given by the formula ...

  cost = 1.40 × (top & bottom area) + 0.90 × (lateral area)

In terms of radius and height the areas are ...

  top & bottom area = 2πr²

  lateral area = 2πrh

So, the total cost of a can with radius r and height h is ...

  c(r, h) = 1.40·2πr² +0.90·2πrh

Filling in the given values and doing the arithmetic, we find the costs to be ...

  c(4, 5) = $253.84

  c(5, 4) = $333.01

The cost of the can with the 5-inch radius is the greatest.

Answer:

The cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.

Step-by-step explanation:

First Can:

Top and Bottom Surface Area = 2(pi(4)^2) = 2(16pi) = 32 pi = 100.53 square inches

Cost for top and bottom surface area = 1.40 * 100.53 = $140.74

Curved Surface Area = 2pi*r*h = 2*pi*4*5 = 40 pi = 125.66 square inches

Cost for Curved Surface Area = 125.66 * 0.90 = $113.10

Total Cost = $140.74 + $113.10 = $253.84

Second Can

Top and Bottom Surface Area = 2(pi(5)^2) = 2(25pi) = 50 pi = 157.08 square inches

Cost for top and bottom surface area = 1.40 * 157.08 = $219.91

Curved Surface Area = 2pi*r*h = 2*pi*5*4 = 40 pi = 125.66 square inches

Cost for Curved Surface Area = 125.66 * 0.90 = $113.10

Total Cost = $219.91 + $113.10 = $333.01

So, the cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.

The function that is likely the best fit is given as follows:

Logarithmic regression.

The function of a best fit is a logarithmic regression, as the function starts with a fast increasing rate until it approaches the vertical asymptote.

As for the other options, we have that:

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Expression f(1) < f(14) shows that, the temperature 14 hours after 9 am is less than the temperature at 9 am.

Temperature is a way to express thermal energy and serves as a gauge for how warm or cold something is. Scientists measure temperature using a variety of techniques, tools, and scales.

Three distinct degrees are used to determine temperature.

For the given question:

Outside temperature t hours is given by function f(t) at 9 am.

Let 1 hour be the time at 9 am as f(1)

Then, temperature f(t), 14 hours after 9 am will be given as f(14)

Now,

f(1) < f(14)

The above expression shows that temperature 14 hours after 9 am is less than the temperature at 9 am.

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The given pair of events are independent when your first coin flip results in heads. and your second coin flip results in heads.

Events that occur independently of any other events are referred to as independent events. if we flip a coin in the air and get the head, we will then flip the coin again, but this time we will get the tail. The occurrence of both events is unrelated in either instance. Tossing the coin the first time does not affect the outcome of the second toss.

Note that the events are not mutually exclusive as it is possible that both the first and the second toss are headed.

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Answer: Multiply the centimeters number by 10.

Step-by-step explanation: There are 10 millimeters in every centimeter.

Answer:

x = 120 degrees

Step-by-step explanation:

a hexagon has a total of 720 degrees

720- 130-140-150-90-90= 120

The probability that the mean contents of the bottles in a six-pack is less than 295 ml is approximately 0.1587, or 15.87%.

To solve this, use the standard normal distribution and the cumulative distribution function (CDF) of the normal distribution.

Standardize the value of 295 ml by subtracting the mean of the distribution (298 ml) and dividing by the standard deviation (3 ml):

Z = (295 - 298) / 3 = -1

The CDF of the standard normal distribution gives us the probability that a random variable from a standard normal distribution is less than or equal to a certain value. Using a standard normal table or a calculator with normal distribution functions, we find that the probability that a standard normal random variable is less than or equal to -1 is approximately 0.1587.

Since the contents of the bottles are normally distributed with mean 298 ml and standard deviation 3 ml, we can use the standard normal distribution and the standard score Z to approximate the probability of observing a mean contents of less than 295 ml in a six-pack of bottles. This probability is approximately 0.1587, or 15.87%.

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Step-by-step explanation:

\(f(x) = \cot(x) \)

Can be written as

\(f(x) = \frac{ \cos(x) }{ \sin(x) } \)

So let's see these answers.

Part A is wrong, when x=0, the graph is undefined(infinite discontinuity), so (0,0) is not on the graph

B is correct,for every pi radians, the function is undefined for it.

C is incorrect, The function has a zero at pi/2

D is incorrect, the function is defined when cos(x)=0

E is correct, the range of cot(x) is all real numbers.

So B and E are correct.

A link but not a function, for instance, is the set of ordered pairs (1, 2), (2, 4), (3, 6), and (1, 5) because the input variable 1 is connected to two distinct output values (2 and 5).

Mathematics is the study of integers, their variants, arithmetic, as well as the study of the region's anatomy, structures, and the both their actual and imagined locations. A function explains the relationship between a number of factors, each of which has a corresponding outcome. A function is made up of a variety of components that, when put together, produce a unique outcome for each input.

Here,

Certainly, a function is a particular kind of relation that links each input value to precisely one output value.

A function, then, is a collection of ordered pairs (x, y), in which each x-value is matched by precisely one y-value.

This implies that there is only yet another output y that is connected to any particular input x.

Sometimes the result y is referred to as the dependent variable, and sometimes the input x is referred to as the independent variable.

Relations are not all tasks, it should be noted. If a relation gives more than one output value to a specific input value or if it fails to assign an output to a specific input value, it may not be a function.

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There will be total of 722 winning hands are in total.

Let's consider the two conditions for winning separately:

3 or more face cards:

There are 12 face cards in a standard deck of 52 cards, so there are \(${12 \choose k}$\) ways to choose k face cards out of 5, where k = 3, 4, or 5.

The total number of winning hands in this case is \({12 \choose 3} + {12 \choose 4} + {12 \choose 5} = 220\)

All non-face cards with even numbers:

There are 16 even-numbered non-face cards in a standard deck,

So there are \(${16 \choose k}$\) ways to choose k of these cards, where k = 0, 2, 4.

The total number of winning hands in this case will be:

\({16 \choose 0} + {16 \choose 2} + {16 \choose 4} \\= 1 + 45 + 456 \\= 502\)

The total number of winning hands is the sum of the number of hands that satisfy each condition,

So there are a total of 220 + 502 = 722 winning hands.

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The equation rewritten as a Bernoulli equation is y = 1/∛(-2t - (1/3)t^3 + C), where C is the constant of integration.

1.1) To solve the given first-order differential equation using the substitution y = vt:

Substituting y = vt into the equation dy/dt = 2y^2 + t^2:

dv/dt * t = 2(vt)^2 + t^2.

Expanding the equation:

t * dv/dt = 2v^2t^2 + t^2.

Dividing both sides by t:

dv/dt = 2v^2t + t.

Now, we have a separable differential equation. We can rewrite it as:

dv/v^2 = 2t dt.

Integrating both sides:

∫(dv/v^2) = 2∫t dt.

This simplifies to:

-1/v = t^2 + C,

where C is the constant of integration.

Solving for v:

v = -1/(t^2 + C).

Substituting y = vt:

y = -t/(t^2 + C).

Therefore, the general solution for y using the substitution y = vt is y = -t/(t^2 + C), where C is an arbitrary constant.

1.2) To rewrite the equation as a Bernoulli equation:

The given differential equation is:

dy/dt = 2y^2 + t^2.

We can rewrite it in the form of a Bernoulli equation by dividing both sides by y^2:

dy/y^2 = 2 + t^2/y^2.

Now, we introduce a substitution u = 1/y:

du = -dy/y^2.

Substituting this into the equation:

-du = 2 + t^2(u^2).

Rearranging the equation:

du/u^2 = -(2 + t^2) dt.

This is now a Bernoulli equation, where n = -2.

To solve the Bernoulli equation, we can introduce a substitution v = u^(1-n) = u^3:

dv = (1-n)u^(n-1) du.

Substituting this into the equation:

dv = 3u^2 du.

Our equation now becomes:

3u^2 dv = -(2 + t^2) dt.

Integrating both sides:

∫3u^2 dv = -∫(2 + t^2) dt.

This simplifies to:

u^3 = -2t - (1/3)t^3 + C,

where C is the constant of integration.

Substituting back u = 1/y:

(1/y)^3 = -2t - (1/3)t^3 + C.

Taking the reciprocal of both sides:

y = 1/∛(-2t - (1/3)t^3 + C).

Therefore, the equation rewritten as a Bernoulli equation is y = 1/∛(-2t - (1/3)t^3 + C), where C is the constant of integration.

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750$

idont have a explanation

Answer:

9

Step-by-step explanation:

Sean and Greg share a 24-ounce bucket of clay

Sean uses 3/8 of the bucket

= 3/8 ×24

= 9 ounce

Greg uses 1/4 if the bucket

= 1/4 ×24

= 6 ounce

= 9+6

= 15 ounce

Therefore the quantity left in the bucket can be calculated as follows

= 24-15

= 9

Hence 9 ounces are left in the bucket

Answer:

976 cm^2.

Step-by-step explanation:

The surface area = 2 * area of the triangular side + 2 * area of the rectangular sides + area of the rectangular base.

= 2 + 1/2 * 24 * 14 + 2 * 25 * 10 + 14*10

= 336 + 500 + 140

= 976 cm^2.

The  total surface area of this triangular prism is 976 square cm

The total surface area is the sum of the area of the faces of a figure.

The given shape is made up of three rectangles and 2 triangles.

Surface area = 2[25*10] + (14 * 10) + (24 * 14)

Surface area = 2(250) + 140 + 336

Surface area = 976 square cm

Hence the  total surface area of this triangular prism is 976 square cm

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Answer:

p2 - 12p - 27

Step-by-step explanation:

mark me brainiest

Answer: ( P - 9 ) ( p - 3)

......Should be ur answer. have a wonderful day kind person!!!!!

PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

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c.)

When a coin is tossed, there is a probability of 1/2 getting a tail.

The word INDIANAPOLIS has 12 letters in total, with 2 Ns. This gives us a probability of 2/12.

Therefore:

d.) P(heads, then D or I)

When a coin is tossed, there is a probability of 1/2 getting a heads).

There would be a probability of 5/12 when getting a D or an I.

Therefore:

The probability that the first candy selected is butterscotch and the second candy is taffy can be calculated as the product of the probabilities of these two events occurring.

First, let's calculate the probability of selecting a butterscotch candy as the first candy. There are 9 butterscotch candies out of a total of 15 candies, so the probability is 9/15.Next, for the second candy to be taffy, we need to consider that one butterscotch candy has already been selected and removed from the box. Therefore, there are 14 candies remaining in the box, including 2 taffy candies. Hence, the probability of selecting a taffy candy as the second candy is 2/14.

To find the probability of both events occurring, we multiply the probabilities together: (9/15) * (2/14) = 18/210.Simplifying this fraction, we get 3/35.Therefore, the probability that the first candy selected is butterscotch and the second candy is taffy is 3/35, which is approximately 0.086 or rounded to three decimal places.

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Answer:

D

Step-by-step explanation:

Rolling a die and getting a certain number will not change the chances of you getting the same number a second time. A normal die will always have a 1/2 chance of rolling an even number. However, the other answer choices will make the likelihood of getting the same type of event again slimmer as you remove one of the objects from being chosen again. An example for the first option would be drawing an ace from a deck of 52 cards where you only have 4 aces, so the chance on the first draw would have been 4/52 or a 7.7% chance while the next draw will be a 3/51 or 5.9% chance.