What is the velocity of a car that traveled a total of 75 km north in 1.5 hours

The number of randomly selected Americans that must be surveyed is equal to 38 if the confidence interval is 97.5% with a 0.16 margin of error.

First, we calculate the critical value as follows;

a = (1 - 0.975) = 0.025 = 0.025 / 2 = 0.0125 = (1 - 0.0125) = 0.9875

Z - Critical value = NORM.S.INV (0.9875) = 1.96

As margin of error(ME) = 0.16

Therefore;

n = pq(Z²) / ME²

n = 0.5 × 0.5 (1.96)² / (0.16)²

n = 0.25 × 3.8416 / 0.0256

n = 0.9604 / 0.0256

n = 37.515

Rounding it to the nearest whole number;

n = 37.515 = 38

Hence 38 randomly selected Americans must be surveyed if the estimated confidence interval is 97.5% and the margin of error is 0.16.

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To check the if a table represents a linear function we have to find the rate of change between the first two ordered pairs can be compared to the rate of change between the first and last ordered pairs to see if they are the same.

Well, a straight line is proportional to a linear function (on a graph). And the answers to the numbers can't be the same. If the X input is 5, for instance, and the Y output is 7, then Another non-linear X input of 5 and Y output of 8 follows.

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

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Step-by-step explanation:

The awnser is -6+6 because it would end up being 0, which is not positive nor negative

The system of inequalities is:

y ≤ -0.05*x^2 + 6x

y >  1.5x + 45

(30, 90) is not a solution of that system, while (60, 160) is a solution.

We know that the revenue y is given by:

y ≤ -0.05x^2 + 6x

And we know that the costs are 1.5x + 45, and the revenue must be larger than that, so we also have the inequality:

y >  1.5x + 45

So the system is:

y ≤ -0.05*x^2 + 6x

y >  1.5x + 45

Now, the point (30, 90) means that we need to replace x by 30 and y by 90, replacing that in the second inequality, we will get:

90 > 1.5*30 + 45 = 90

90 > 90

This is false, so the point is not a solution of this inequality, meaning that the point is not a solution of the system.

For the second point we do the same: x= 60, y = 160, replacing that in the second inequality we get:

160 > 1.5*60 + 45 = 135

160 > 135

This is true, now we need to check with the other inequality.

160 ≤  -0.05*60^2 + 6*60 = 180

This is also true.

So the point (60, 160) is a solution to the system.

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Answer:

30,90= not a solution
60,160= a viable solution

Step-by-step explanation:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Answer:

perfect square trinomial methodIf a polynomial has three terms, x2 + 12x + 36, which factoring method can be considered? Summary: If a polynomial has three terms, x2 + 12x + 36, the perfect square trinomial method can be considered to find the factor of the expression.

The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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csc(θ)= 12/7√2,tan(θ)= 12/7√2` is the value of csc(θ) and tan(θ).

Given, `sec(θ)= 7/11`To find:`csc(θ) and tan(θ)

`Formula used: `secθ = hypotenuse / adjacent`, `

cscθ = hypotenuse / opposite` and

`tanθ = opposite / adjacent`

We know that `sec(θ) = 7/11`

Let's draw a right-angle triangle to solve this problem,

In the given triangle, let `θ` be the acute angle, the hypotenuse is `11`, and the adjacent side is `7`.

Therefore, the opposite side will be `√(11² - 7²) = √(121-49) = √72

As we know, `cscθ = hypotenuse / opposite

Therefore, `cscθ = 11 / √72 = 11√72/72

To simplify the value of `cscθ`, we will multiply and divide `√2` in the denominator.

So, `cscθ = (11/72) * √72 * √2/√2 = 11√144/72√2` = `11/6√2

Also, `tanθ = opposite / adjacent`=`√72 / 7

To simplify the value of `tanθ`, we will multiply and divide `√2` in both numerator and denominator.

So, `tanθ = √72 * √2 / 7 * √2`=`√144 / 7√2` = `12/7√2

Hence, the correct answer is option `(e)` `csc(θ)= 12/7√2,tan(θ)= 12/7√2`.

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The type of data that must be used in the arithmetic operation is numeric. Thus, the  required answer to the provided question is Option B

Arithmetic operation means the method to find basic calculations like addition, subtraction, multiplication, and division on the given command.

For instance = 5 + 3 = 8

the above-given example is a perfect form of arithmetic operation that focuses on the using ability of numeric data to initiate calculations without any errors in the process. Furthermore, there are no variables involved that can hamper the process of calculation.

therefore, we can safely say that arithmetic operations can't survive without the numeric data and it will be impossible to perform calculations.

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The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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The population 20 years from now will be approximately 38.78 million.

Therefore, the correct option is:

c. 38.82 million

To find the population 20 years from now using the continuous growth formula, we can substitute t = 20 into the equation:

\(P = 25e^(0.022t)\\P = 25e^(0.022 * 20)\\P = 25e^(0.44)\)

Using a calculator or computer software, we can evaluate e^(0.44) ≈ 1.551.

P ≈ 25 * 1.551 ≈ 38.775

Rounded to two decimal places, the population 20 years from now will be approximately 38.78 million.

Therefore, the correct option is:

c. 38.82 million.

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There are 11 prime dates in it.

The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29

Relative prime:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Hence There are 11 prime dates in the month of June.

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Answer: 10

Step-by-step explanation:

Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.

Triangle TSR is congruent to Triangle QRS by the ASA (Angle-Side-Angle) congruence criterion.

Given: Angle TSR and Angle QRS are right angles.

Given: Angle T is congruent to Angle Q.

Given: Line segment SR is congruent to line segment RS (reflexive property).

By Step 1: Angle TSR is congruent to Angle QRS (right angles are congruent).

By Step 2: Angle T is congruent to Angle Q (given).

By Step 3: Line segment SR is congruent to line segment RS (reflexive property).

By ASA congruence criterion: Triangle TSR is congruent to Triangle QRS (Angle-Side-Angle).

Therefore, Triangle TSR is congruent to Triangle QRS.

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The probability that John will roll more than 4 times until the dice roll sums to 8 three times is 4 times = 1 - (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

To find the probability that John will roll more than 4 times until the dice sum to 8 three times, we need to calculate the probability of him rolling 4 or fewer times and subtract it from 1.

Let's calculate the probability of John rolling 4 or fewer times. To do this, we need to find the probability of him rolling the sum of 8 three times or more within 4 rolls.

First, let's find the total number of possible outcomes for rolling two dice, which is 36 (6 possibilities for each dice).

Next, let's find the number of favourable outcomes for rolling the sum of 8 three times or more within 4 rolls.

We can use combinations to calculate this. For the first roll, the possible combinations that result in a sum of 8 are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). So, there are 5 favourable outcomes for the first roll.

For the second roll, we need to find favourable outcomes given that the first roll was not a favourable outcome. We need to subtract the outcomes that were already counted.

So, there are 4 favourable outcomes for the second roll. Similarly, for the third roll, we subtract the outcomes that were already counted and find 3 favourable outcomes.

Finally, for the fourth roll, we subtract the outcomes that were already counted and find 2 favourable outcomes.

To find the probability, we divide the number of favourable outcomes by the total number of possible outcomes. Probability of rolling the sum of 8 three times or more within

4 rolls = (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

Now, we can find the probability of rolling more than 4 times by subtracting this probability from 1.

Probability of rolling more than

4 times = 1 - (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

The probability that John will roll more than 4 times until the dice roll sums to 8 three times is the result obtained in the calculation above.

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Answer:

The slope is -1

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

nice phone case

Answer:

There are 14,512 people in the town in 2005.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The base 2 logarithm of 64 is 6 or log264 = 6.

On solving the provided question, we can say that -  the inverse of the given y = 3x+2, function is ( y - 2 )/3 = x

A function that "undoes" another function is known as an inverse function in mathematics. In other words, if f(x) generates y, then y set to f's reciprocal will result in x. . The inverse of the function f(x) = 2x + 3 is represented as f-1(x), which is equal to (x - 3)/2.

Here,

the given equation is -

function, f(x)  = 3x + 2

=> y = 3x+2

=> y-2 = 3x

=> ( y - 2 )/3 = x

so,

therefore the inverse of the given function is ( y - 2 )/3 = x

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Step-by-step explanation:

Since the new poison kills half the population every 2 months, we can say that the remaining half will survive for another 2 months. Therefore, after 2 months, the rodent population will be half of 1,000,000, which is 500,000.

After another 2 months, the remaining half of the 500,000 will survive, which is 250,000.

After another 2 months, the remaining half of the 250,000 will survive, which is 125,000.

After 6 months, the rodent population will be 125,000.

Since 12 months is six 2-month periods, we can repeat this process again. After another 2 months, the rodent population will be 62,500.

After another 2 months, the rodent population will be 31,250.

After another 2 months, the rodent population will be 15,625.

Therefore, after 12 months, the rodent population will be 15,625.

Answer:

x = 0, 2π/3, 4π/3, 2π.

Step-by-step explanation:

cos 2x = 2cos^2x - 1 so

2cos^2x - 1 = cos x

2cos^2x - cos x - 1 = 0

(2cosx + 1)(cos x - 1) =0

cos x = -1/2, 1.

When cos x = 1, x = 0, 2π

when cos x = -1/2, x = 2π/3, 4π/3.

Answer:

a. $250

b. 50x + 200

Step-by-step explanation:

a. For the first month, you have to account for the cost to start which is $200, and the adition of the $50 for each month.

b. the 200 is only a one time fee so you add it on to months(x)

Answer:

a. 250$

b. 200+50x

Step-by-step explanation:

#1 What is the total cost to use the cell phone plan for one month?

GIVEN:

Startup price=$200

Charge per month=50$

SOLVE:

The total cost for one month will be the startup price+ charging price for one month.

200+50=250$

#2 What is the total cost for x months?

The total cost for x months will be the startup price+charging price for x months.

200+50x

Hope this helps!! :)

Please let me know if you have any questions

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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Answer:

\({:}\longrightarrow\)\(\sf {\dfrac {1}{2}} \div {\dfrac {3}{4}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {1}{{\cancel{2}}}}\times {\dfrac{{\cancel {4}}}{3}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {2}{3}}\)

Answer:

Step-by-step explanation:

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

Exact Form:

x=3/2

Decimal Form:

x=1.5

Mixed Number Form:

x =1 1/2

Answer:

5 could be the common denominator

Step-by-step explanation:

Answer:

B = 53 degrees

Step-by-step explanation:

37+90=127

180-127=53

If the measure of the angle ∠A is 37°. Then the measure of the angle ∠B will be 53°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

In the right triangle ΔABC, the measure of the angle ∠A is 37°.

Angle A and angle B are complementary angles. Then the equation is given as,

∠A + ∠B = 90°

37° + ∠B = 90°

∠B = 90° - 37°

∠B = 53°

If the measure of the angle ∠A is 37°. Then the measure of the angle ∠B will be 53°.

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The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.

To solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;

8x - 4y = -4

add 4y to both sides

8x - 4y + 4y= -4 + 4y

8x = - 4 + 4y

also to make y the subject;

- 4 + 4y = 8x

add 4 to both sides

- 4 + 4 + 4y = 8x + 4

4y = 8x + 4

factorize the right hand side

4y = 4(2x + 1)

divide through by the coefficient of y

4y/4 = [4(2x + 1)]/4

y = 2x + 1

Hence, the equation 8x - 4y = -4 has y = 2x + 1

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