Can someone help me please

Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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Answer:

8

Step-by-step explanation:

Step-by-step explanation:

y=|x| is a vee graph starting at (0,0)

y=|x| - 3 is a vee graph starting (0,-3)

see attachment

The chief of security for the Mall of the Dakotas directed a study of theft. He selected a sample of 200 boxes that had been tampered with and ascertained that for 80 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 45 boxes, employees had stolen the goods, and for the remaining 75 boxes, he blamed poor inventory control.

In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.10 significance level. H0: The proportions are as stated. H1: The proportions are not as stated. The decision rule using a 0.10 significance level is: Reject H0 if the computed chi-square value is greater than 4.605. Compute the value of chi-square as follows: Observed Frequencies: Shoplifting: 80 Employee theft: 45 Poor inventory control: 75 Total: 200 Expected Frequencies: Shoplifting: (80+45+75) x (80/200) = 80. Employee theft: (80+45+75) x (45/200) = 36. Poor inventory control: (80+45+75) x (75/200) = 84. Total: 200The formula for chi-square is: χ2=∑((Oi−Ei)2/Ei). Using the observed and expected frequencies from above, we get: χ2 = [(80 - 80)²/80] + [(45 - 36)²/36] + [(75 - 84)²/84] = 2.4. The value of chi-square is 2.4, which is less than 4.605. Therefore, we fail to reject H0. Hence, the chief of security for the Mall of the Dakotas cannot say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely at a 0.10 significance level.

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Answer:

8x^3y^9

Step-by-step explanation:

just multiply 4 by 2. then, add each exponent. for example, there is x² and there is x, so do x² × x = x³. then do y³ × y^6 = y^9.

The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.

To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:

z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906

z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849

Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.

To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:

P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.

As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.

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Answer:

676 (in)³ is the volume of the following question

The domain of the function 8 - \((x-3)^{2}\) is R which is all the real numbers.

What is domain of a function?

The set or grouping of all potential values that may be used in the function is known as the domain.

We are given a function as 8 - \((x-3)^{2}\).

Now, in order to find the domain, we need to find the values where the function is not defined for a value of x.

But, there is no such value for x where the function is not defined.

This means that all values of x give an output.

So, the domain is the set of all the real numbers.

Hence, the domain of the given function is R.

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Answer:

nth term of geometric sequence = a(n) = \((3/4)(4/3)^{n-1}\)

Step-by-step explanation:

nth term of geometric sequence = a(n)

nth term of geometric sequence = a(n) = \(ar^{n-1}\)

Where,

a =  first term

r = common ratio

n = number of term

So,

GP: 3/4, 1, 4/3, 16/9

a = 3/4

r = 1 / [3/4] = 4/3

n = n

nth term of geometric sequence = a(n) = \(ar^{n-1}\)

nth term of geometric sequence = a(n) = \((3/4)(4/3)^{n-1}\)

The value of the given expression will be equal to 2060.

Expression in maths is defined as the collection of the numbers variables and functions by using the signs like addition,substraction, multiplication and division.

It is given that:-

=p²(m)-(np+r)

=(-8)²(32)-(2x(-8)+4)

=(64x32)-(-16+4)

=2060

Hence value of the given expression will be equal to 2060.

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Answer:

2 looks good  I & IV

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

because it is a trapezoid so, the angles and sides don’t equal in length please mark brainliest hopes this helps

Answer:

Option D.

Question:

A regular polygon is a shape with all sides equal in length. Which of these is an irregular polygon?

Explanation:

Regular polygons have all sides equal. Then an irregular polygon doesn't have equal sides.

Which of them doesn't have equal sides?

We have the next cost given function:

The average cost function is given by:

Replace:

Simplify the expression:

Derivate A(x)

Set A'(x)=0

Solve for x:

Therefore, the average cost per unit will be minimized at 100 units of production level.

Answer:

-a^2-a+12

Step-by-step explanation:

After multiplying and opening the brackets

we get

-a^2-4a+3a+12

=-a^2-a+12. ( simplifying)

hope it helps.....

Answer:

\( \boxed{\sf -a^2 - a + 12} \)

Step-by-step explanation:

⇒(-a + 3)(a + 4)

⇒-a(a + 4) + 3(a + 4)

⇒(-a)(a) + (-a)(4) + (3)(a) + (3)(4)

⇒-a² - 4a + 3a + 12

⇒-a² - a + 12

Answer:

4.5

Step-by-step explanation:

Find the amount of miles in 1 hour. 18/3=6

Now multiply 1.5x3=4.5

3/4=75

This is how i got 4.5 miles

The original two-digit number is 10x+y =62.

Here, we have,

Let's denote the tens digit as x and the units digit as y.

The original two-digit number can be expressed as

10x+y.

According to the given information, the tens digit exceeds the units digit by 4, so we have the equation:

x=y+4

The number obtained by reversing the digits of the original number is

10y+x.

The problem states that the original number exceeds twice this reversed number by 10.

Therefore, we can write another equation:

10x+y=2(10y+x)+10

Now, let's solve these equations to determine the values of x and y and find the original number.

Expanding the second equation:

10x+y=20y+2x+10

10x−2x+y−20y=10

8x−19y=10

We now have a system of two equations:

Equation 1:

x=y+4

Equation 2:

8x−19y=10

Let's solve this system of equations.

We can substitute the value of x from Equation 1 into Equation 2:

8(y+4)−19y=10

8y+32−19y=10

−11y=−22

y=2

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

x=2+4

x=6

Therefore, the original two-digit number is 10x+y=10(6)+2=62.

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The name for the triangle cartilage anterior to the auditory meatus is called the tragus.

The tragus is a small triangular cartilage that is located anterior to the auditory meatus. It is a small flap of cartilage that projects out from the side of the face and helps to protect the external auditory canal. It is located right above the lobe of the ear, and is covered with a thin layer of skin. It is known to be relatively sensitive, due to its numerous nerve endings. The tragus has a variety of functions, such as helping with hearing, as it helps to focus sound waves into the ear canal. It also helps to block out external noise, which is beneficial for those who are exposed to loud noises on a regular basis. It also helps to keep the ear canal clean, as it acts as a barrier against dirt, water, and other foreign objects. Additionally, it has an aesthetic function, as it is a defining feature of the human ear. Thus, the tragus can be seen as an important part of the structure and function of the human ear.

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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196 children's tickets and 328 adult tickets were sold.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: One night a theater sold 524 movie tickets. An adult's ticket costs $6.50 and a child's ticket cost $3.50. In all, $2881 was taken in.

Let the amount of the child's ticket be x

Let the amount of adults tickets be y

If the total number of tickets sold is 524 movie tickets, then;

x + y  = 524

x = 524 - y...(1)

If an adult ticket cost $6.50 and a child’s ticket cost $3.5 with a total of $2881 in all, then;

3.5x +  6.5 y = 2881

35x + 65y = 28810 ...(2)

Substitute equation 1 into 2:

35x + 65y = 2881

35(542-y) + 65y = 28810

18970 - 35y + 65y = 28810

30y = 9840

y = 328

Put the value of y in equation (1) and we get

x = 524 - 328

x = 196

Hence,  196 children's tickets and 328 adult tickets were sold.

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Answer:

11

Step-by-step explanation:

The sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

Acute angles are angles whose measures are greater than 0° and less than 90°. According to the statement, we must find at least a value such that sin θ = cos θ:

sin θ = cos θ                     Given

sin θ / cos θ = 1                 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property

tan θ = 1                            Definition of tangent

θ = π / 4                            Inverse trigonometric function / Result

In a nutshell, the sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:

9

Step-by-step explanation:

Let the two perfect cubes be x and y where x > y.

According to the given conditions:

\( {x}^{3} - {y}^{3} = 386...(1) \\ y = 7...(2) \\ plug \: y = 7 \: in \: equation \: (1) \\ {x}^{3} - {7}^{3} = 386 \\ {x}^{3} - 343 = 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 729 \\ x = \sqrt[3]{729} \\ x = 9\)

Thus the cube root of the larger number is 9.

Building and solving an equation, it is found that the cube root of the larger number is 9.

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

\(x^3 - y^3 = 386\)

\(x^3 - y^3 = 386\)

\(x^3 - 7^3 = 386\)

\(x^3 - 343 = 386\)

\(x^3 = 386 + 343\)

\(x^3 = 729\)

\(x = \sqrt[3]{729}\)

\(x = 9\)

Thus, the cube root of the larger number is 9.

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Answer:

The slope is 3!

Step-by-step explanation:

In the equation y=3x+2, whatever constant is with the variable "x" is the slope.

Hope this helps :)

The delivery rate for Famotidine should be set at 2/3 mL/min.

To determine the delivery rate for each scenario, we can use the formula:

Delivery rate = Volume / Time

1. Cefazolin:

Given:

- Dose: 1000 mg

- IV fluid volume: 50 mL

- Infusion time: 30 minutes

Using the formula, the delivery rate for Cefazolin will be:

Delivery rate = 50 mL / 30 min

Simplifying:

Delivery rate = 5/3 mL/min

So, the delivery rate for Cefazolin should be set at 5/3 mL/min.

2. Famotidine:

Given:

- Dose: 20 mg

- IV fluid volume: 10 mL

- Infusion time: 15 minutes

Using the formula, the delivery rate for Famotidine will be:

Delivery rate = 10 mL / 15 min

Simplifying:

Delivery rate = 2/3 mL/min

So, the delivery rate for Famotidine should be set at 2/3 mL/min.

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