Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff did not spend more than $14 on the hot dogs and the bottle of water. Which inequality can be used to find h, the number of hot dogs that Jeff could have bought? A.3h−2≤14 B.3h+2≤14 C.3h−2≥14 D.3h+2≥14

Solution:

Given:

The sum of exterior angles of a polygon is 360°.

The formula for calculating the size of an exterior angle is;

Hence,

Therefore, the measure of each exterior angle of a regular polygon with 80 sides is 4.5 degrees.

f(x) is well-defined for all x in the domain of R, we have shown that R is a well-defined function.

To prove that R is a well-defined function, we need to show that for each x in the domain of R, there exists a unique y in the range of R such that (x, y) is in R.

Let x be an arbitrary real number. We need to find a unique y such that (x, y) is in R. By definition, (x, y) is in R if and only if x2 + y2 = 1. Solving for y, we get:

y = ±√(1 - x^2)

Since the range of R is R, we need to choose the appropriate sign for ± in order to ensure that there exists a unique y in R for each x in R. Since the range of R is not restricted, we can choose either the positive or negative square root, depending on the sign of x, to ensure that y is in R. Therefore, we define the function f: R → R as:

f(x) = √(1 - x^2) if -1 ≤ x ≤ 1

f(x) = undefined otherwise

To learn more about number visit:

brainly.com/question/17429689

#SPJ11

Answer:

9: x = 3

   y = 1

10: x = -2

     y = 4

Hope it helps and have a great day! =D

~sunshine~

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

Learn more about probability here

https://brainly.com/question/32117953

#SPJ4

Use the Law of Sines to solve the triangle. The correct option among the given options is B C = 85°, a = 5.76, b = 8.69, where c ≈ 10.38.

To solve the triangle using the Law of Sines, we can use the formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's analyze each option one by one:

A) C = 85°, a = 7.76, b = 10.69

To solve this triangle, we can use the Law of Sines as follows:

a/sin(A) = b/sin(B) = c/sin(C)

7.76/sin(35°) = 10.69/sin(60°) = c/sin(85°)

Using this equation, we can solve for c:

c = (7.76 * sin(85°)) / sin(35°) c ≈ 13.99

Therefore, the answer is not C = 85°, a = 7.76, b = 10.69.

Now let's check the other options:

B) C = 85°, a = 8.76, b = 10.69

Using the same formula, we can calculate c:

c = (8.76 * sin(85°)) / sin(35°) c ≈ 15.77

Therefore, the answer is not C = 85°, a = 8.76, b = 10.69.

C) C = 85°, a = 8.69, b = 9.69

Using the same formula, we can calculate c:

c = (8.69 * sin(85°)) / sin(35°) c ≈ 15.56

Therefore, the answer is not C = 85°, a = 8.69, b = 9.69.

The correct option among the given options is B C = 85°, a = 5.76, b = 8.69, where c ≈ 10.38.

Learn more about Law of Sines

https://brainly.com/question/30401249

#SPJ11

The general solution of the given differential equation is given by:y(t) = y_c(t) + y_p(t)y(t) = e^(-t) [C₁ cos (√6t / 2) + C₂ sin (√6t / 2)] + 2/5 cos 2t - 7/5 sin 2t.

Differential equation:y'' + 2y' + 5y = 8 sin 2tThe general solution of the given differential equation can be obtained as follows:For the complementary function:Consider the characteristic equation of the given differential equation.The characteristic equation is given by: m² + 2m + 5 = 0The roots of the above equation can be obtained using the quadratic formula as shown below:m = [-b ± √(b² - 4ac)] / 2aOn substituting the values of a, b, and c in the above formula, we get:m = [-2 ± √(2² - 4 × 1 × 5)] / 2 × 1On simplifying the above expression, we get:m = [-2 ± i √6]/2The complementary function is given by: y_c(t) = e^(-t) [C₁ cos (√6t / 2) + C₂ sin (√6t / 2)]where C₁ and C₂ are constants of integration.

For the particular integral:Let the particular integral be of the form y_p = A sin 2t + B cos 2t + C sin 2t + D cos 2tOn substituting the above particular integral in the given differential equation, we get:20 A cos 2t - 20 B sin 2t + 8 sin 2t + 20 C cos 2t + 20 D sin 2t + 20 A sin 2t - 20 B cos 2t = 8 sin 2tSimplifying the above equation, we get:20 A cos 2t - 20 B sin 2t + 20 C cos 2t + 20 D sin 2t + 20 A sin 2t - 20 B cos 2t = 8 sin 2tOn comparing the coefficients of sin 2t and cos 2t on both sides, we get:A + 5B + C = 0andC - 5D + A = 0On substituting A = 0, we get:B = -8/20 = -2/5On substituting B = -2/5, we get:C = 2/5 and A = 5DSubstituting these values of A, B, C, and D in the particular integral, we get:y_p(t) = 2/5 cos 2t - 2/5 sin 2t + 5/4 sin 2tThe general solution of the given differential equation is given by:y(t) = y_c(t) + y_p(t)y(t) = e^(-t) [C₁ cos (√6t / 2) + C₂ sin (√6t / 2)] + 2/5 cos 2t - 7/5 sin 2t.

Learn more about differential equation here:

https://brainly.com/question/25731911

#SPJ11

If the coin is fair, the expected gain would be $5. However, without information about the probabilities, we cannot determine the exact expected gain or loss.

To calculate the expected gain or loss, we need to determine the probability of getting a tail or a head when tossing the loaded coin.

Let's assume that the probability of getting a tail is represented by p and the probability of getting a head is represented by q. Since these are the only two possible outcomes, we know that p + q = 1.

Given that we win $20 for a tail and lose $10 for a head, we can calculate the expected gain or loss using the following formula:

Expected gain or loss = \((p \times $20) + (q \times -$10)\)

Since the question doesn't provide any information about the probabilities, we cannot provide an exact calculation for the expected gain or loss. However, if we assume that the coin is fair (50% chance of getting a tail and 50% chance of getting a head), we can substitute the values into the formula:

Expected gain or loss = \((0.5 \times $20) + (0.5 \times -$10) = $10 - $5 = $5\)

Therefore, if the coin is fair, the expected gain would be $5. However, without information about the probabilities, we cannot determine the exact expected gain or loss.

Learn more about probabilities

https://brainly.com/question/29381779

#SPJ11

Answer:

Step-by-step explanation:

-6+6=0 -3+3=0

This is because the signs are different so you count back starting with the negatives.

-6,-5,-4,-3,-2,-1,0

Answer:

B) 6 positive tiles

Step-by-step explanation:

The demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

The demand function is the function

\(Q=a-bP\)

Here, Q is linear demand curve, a factor which influence the demand, b is slope and P is price.

A concert-promoting company has been selling an average of 175 T-shirts at performances for $23 each. Thus, the total selling price is,

\(P=175\times23\\P=4025\)

The company estimates that for each dollar that the price is lowered, an additional 25 shirts will be sold.  Thus, the total number of

\(23=175-25b\\23-175=-25b\\b=\dfrac{152}{25}\\b=6.08\)

Put the values in, the function for X number of shirt and y price,

\(y=175-6.08x\)

Hence, the demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

Learn more about the demand function here;

https://brainly.com/question/14408984

#SPJ1

Stan's average speed for the total trip is 55 miles per hour.

Given,

Stan drove 300 miles in 5 hours 20 minutes

Again, Stan drove 360 miles in 6 hours 40 minutes

To find,

Stan's average speed in miles per hour for the total trip

Solution

We can start the problem by calculating the total distance and the total time for the trip. Then we can use the formula for average speed which is;

Average speed = Total distance / Total time

First, let's calculate the total distance covered by Stan in the entire trip;

Total distance covered = 300 + 360= 660 miles

Now, let's calculate the total time taken by Stan in the entire trip;

Total time taken = 5 hours 20 minutes + 6 hours 40 minutes= 12 hours

Now, let's use the formula for average speed and calculate the average speed for the entire trip;

Average speed = Total distance / Total time= 660 / 12= 55 miles per hour

Therefore, Stan's average speed for the total trip is 55 miles per hour.

learn more about average speed here:

https://brainly.com/question/13318003

#SPJ11

Answer:Its F

Step-by-step explanation:

Answer:

Letter i

Step-by-step explanation:

BeCuAsE A rAtIoNaL NuMbEr Is A NuMbEr ThAt CaN Be MaDe InTo A FrAcTiOn AnD I CaNt Be MaDe InTo A FrAcTiOn.

When two players A and B alternately flip a fair coin, the probability  E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

Two players, A and B, turn a fair coin in succession (A tosses the coin first, then B tosses the coin, then A, then B and so on). The order of the heads and tails is noted. If there is a head followed by a tail, the game is done, and the person who throws the tail wins (HT sub-sequence).

We must ascertain the game's estimated duration. Allow T coin tosses for the game to proceed. Find E (T).

\(E(T) = first instance of HT in seriesE(T) =0.5×(1+2)+0.5×(1+E(T))\\0.5×E(T)=0.5×4\\E(T) =4\)

As a result, when two players A and B alternately flip a fair coin, The E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ4

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."

for more questions on logistic growth

https://brainly.com/question/2102628

#SPJ11

Answer:

Linear ;

Increasing ;

51 ;

Kindly check explanation

Step-by-step explanation:

The relationship between homework a d test scores is linear, this can be deduced based on the straight trend line which could be drawn through the points on the scatter plot.

The relationship is increasing, the linear trend is positive ; also from the function derived for the plot, the slope Coefficient is positive.

C.)

Given the plot function :

y = 7x + 30

The score for 3 hours of homework :

x = 3

y = 7(3) + 30

y = 21 + 30

y = 51

Test score = 51

D.) 30 represents the intercept vamie of the graph, the value of y when x = 0 ;

With respect to the context, it means the test score for a student with 0 hours of homework (student with no homework hours at all). Will be 30.

tan=sin/cos so tan=3/5/4/5=3/4

Answer:

SOH CAH TOA

3/5 opposite over hypotenuse

4/5 adjasent over hypotenuse

tan= opposite over adjasent which is 3/4

Step-by-step explanation:

The option C, 3(5X - 8) is equivalent to the polynomial 15X-24.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given expression is, \(15X-24\)

which is \(= (3 \times 5 \times X) + (3 \times 8)\)

Here, taking out 3 in common, results in:

\(= 3 \times (5X - 8)\)

\(= 3(5X-8) \text{ - Option C}\)

To learn more about Polynomial, visit:

brainly.com/question/20121808

#SPJ4

Given statement solution is :- When the weight of apples is increased by a factor of 4, the total cost also increases by a factor of 4. The correct answer is 4, not 8.

To determine the factor by which the total cost increases when the weight of apples is increased by a factor of 4, let's examine the relationship between the weight and total cost in the given ratio table.

Weight (lb) | Total cost (S)

1 | 2

4 | 8

6 | 12

10 | 20

To find the factor by which the total cost increases, we need to compare the change in total cost to the change in weight. Let's consider the first and last entries in the table:

Initial weight: 1 lb

Initial total cost: 2 S

Final weight (increased by a factor of 4): 4 * 1 lb = 4 lb

Final total cost: 8 S

The change in weight is from 1 lb to 4 lb, which is a factor of 4. The change in total cost is from 2 S to 8 S, which is also a factor of 4.

Therefore, when the weight of apples is increased by a factor of 4, the total cost also increases by a factor of 4. The correct answer is 4, not 8.

For such more questions on Cost increase factor

https://brainly.com/question/10986392

#SPJ8

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (6, 1)

m = \(\frac{1-3}{6-(-2)}\) = \(\frac{-2}{6+2}\) = \(\frac{-2}{8}\) = - \(\frac{1}{4}\) → A

Answer:

p = 125

Step-by-step explanation:

Given p is inversely proportional to q³ then the equation relating them is

p = \(\frac{k}{q^3}\) ← k is the constant of proportion

To find k use the condition p = 9 when q is 5, then

9 = \(\frac{k}{5^3}\) = \(\frac{k}{125}\) ( multiply both sides by 125 )

k = 1125

p = \(\frac{1125}{q^3}\) ← equation of proportion

When q = 3, then

p = \(\frac{1125}{3^3}\) = \(\frac{1125}{9}\) = 125

Answer:

x=15

Step-by-step explanation:

5x= 75 (divide)

75/5= 15

Answer: There is only one step to solve this equation; we use inverse operations to isolate the x by dividing 5 on both sides. We divide because 5 is being multiplied by x, and the inverse operation for multiplication is division.

5x/5 = x

75/5 = 15

The equation now looks like:

x = 15

x is equal to 15. This is your answer.

Answer: 36

Step-by-step explanation: Multiplication

Answer:

1/8

Step-by-step explanation:

The cube root of 1 is just 1.

1/8=1/8.

The proportion null hypothesis is a specific type of hypothesis that tests for significant differences in proportions between two groups.

In statistics, a hypothesis is a statement that is being tested through data analysis. The null hypothesis is a specific type of hypothesis that assumes there is no significant difference or relationship between two variables being studied. The proportion null hypothesis specifically applies to situations where the variable being studied is a proportion or percentage.

The proportion null hypothesis states that there is no significant difference in the proportions of two groups being compared. This can be represented mathematically as

H0 => p1 = p2, where H0 represents the null hypothesis, p1 represents the proportion in the first group, and p2 represents the proportion in the second group.

To test this hypothesis, researchers will collect data from both groups and calculate the proportion for each group. They will then use statistical tests to determine whether the difference in proportions is significant or could have occurred by chance. If the difference is not significant, then the null hypothesis is accepted, and it can be concluded that there is no real difference in the proportions of the two groups.

It is important to note that the proportion null hypothesis is just one type of hypothesis that can be tested in statistics.

To know more about hypothesis here.

https://brainly.com/question/29576929

#SPJ4

Answer:

Im pretty sure its 4 divided by (4/5 wrong)

Step-by-step explanation:

Answer:

4/5 ÷ 1.5  (C)

Step-by-step explanation:

4 sections out of 5 are shaded, this represents 4/5

1 section not shaded represents 1/5

4/5 ÷ 1/5   is the same as 4/5 · 5/1  which equals 4 (the amount shaded)

Answer:

4 units

Step-by-step explanation:

The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.

Answer: Your answer is 2

Step-by-step explanation: I did the k12 quiz here's proof

We should reject the null hypothesis, and we have enough evidence to support the claim.

What is the test statistic ?

Identify the null Hypothesis -

The null hypothesis contains “equal” sign (“=” or “≥” or “≤”),  the  alternative  hypothesis  is the complement to the null hypothesis. The claim is “professional pilots have IQ scores with a standard deviation less than 15”. As the claim contains the “<” sign, it is an alternative hypothesis. Thus, the null hypothesis is the complement: “professional pilots have  IQ  scores  with  a  standard deviation at least 15”.

H0: s ≥ 15

Alternative hypothesis:

“Professional pilots have IQ scores with a standard deviation less than 15.”

H0: s<15

Test statistic:

As the alternative hypothesis contains “<” sign, the test is left - tailed. α = 0.05

The sample standard deviation:

s = 9.5

The test statistic is:

x2 = (n - 1) * s22

= (12 - 1) * s2152

=4.412

P - Value or critical value(s):

For α = 0.05 and d.f. = (12 – 1) * (2 – 1) = 11 the critical value is 4.575 (determined by the table for chi - squared distribution).

As 4.412 < 4.575,

we should reject the null hypothesis, and we have enough evidence to support the claim.

Learn more about test statistic here:

https://brainly.com/question/15980493

#SPJ4

Answer:

Step-by-step explanation:

The area of a Trapezoid is

Area = (b1 + b2)*h/2

b1 and b2 are the two parallel sides of a trapezoid. In this problem, they are both given.

You are trying to find h (which is x here).

b1 = 13

b2 = 6.4

Area = 78

h = x = ?

78 = (6.4 + 13) * x / 2              Multiply both sides by 2

156 = (6.4 + 13) * x                  Combine the numbers in the  brackets

156 = 19.4 * x                          Divide by 19.4

156 / 19.4 = x

x = 8.04

Answer:

Step-by-step explanation:

Well first you would have to find the price of each shirt which is 1400/200 meaning each shirt would be $7

At this point the cost of all of the shirts would be 2000  in total

For each shirt they are earning a $3 profit so for each shirt there is a 42.85714 or you could simplify it to 43 or 42.9