Two cars entered an interstate highway at the same time at different locations and traveled in the same direction. The initial distance between the cars was 30 miles. The first car was going 70 miles per hour and the second was going 60 miles per hour. How long will it take for the first car to catch the second one?

Answer:

My guess is 2b^5

Step-by-step explanation:

This question is kinda tricky. LMK if its correct

Answer:

The destination airport identifier code.

Step-by-step explanation:

What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?

A destination identifier code should be entered.

if no stopover for more than 60 minutes is expected, enter ICAO four letter identifier in item 16 of the flight plan. and indicate when to stopover

Item 16 on an IFR flight plan is used to indicate the destination aerodrome, which is the airport where the aircraft is planning to land. For an IFR flight with an intended stopover of 30 minutes, you would enter the ICAO code or the three-let...

Item 16 on an IFR flight plan is used to indicate the destination aerodrome, which is the airport where the aircraft is planning to land.

For an IFR flight with an intended stopover of 30 minutes, you would enter the ICAO code or the three-letter identifier for the destination aerodrome in item 16.

In this case, you would enter the ICAO code or three-letter identifier for the airport where you will land after the intended stopover, and not the stopover airport itself.

Answer:

The total amount of commission on these vehicles is 1686.

Step-by-step explanation:

Given:

Miles earns a 6% commission on each vehicles he sells.

Today he sold a truck for 18500 and a car for 9600.

Now, to get the total amount of his commision on these vehicles.

Percent of commission Miles earns on each vehicles he sells = 6%.

He sold a truck for = 18500.

He sold a car for = 9600.

So, the total amount of vehicles:

[tex]18500+9600=28100.[/tex]

Now, to get the total amount of commission on vehicles:

[tex]6\%\ of\ 28100[/tex]

[tex]=\frac{6}{100} \times 28100[/tex]

[tex]=0.06\times 28100[/tex]

[tex]=1686.[/tex]

Therefore, the total amount of commission on these vehicles is 1686.

Answer:

Step-by-step explanation:

6 X 7 = 42

This is simply the sum of 6 in seven places or 7 in six places.

Answer:

Part A) The amplitude = 24

Part B) The period = 24

Part C) Vertical shift = 36

Step-by-step explanation:

The general equation of the sine function:

y = A sin (Bx) + C

Where A is the amplitude and B = 360°/Period  and C is the vertical shift

See the attached figure which represents the graph of m and f(m)

So,

Part A:

The function has minimum at 12 and maximum at 60

The difference is = 60 - 12 = 48

So, The amplitude = 48/2 = 24

Part B:

Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.

We can deduce that the function completes one cycle within 24 months

So, the period = 24

Part C:

Vertical shift is obtained at m = 0

So, f(m) = 36

36 = A sin (0) + C

C = 36 ⇒ Vertical shift

So, The amplitude = 24

The period = 24

Vertical shift = 36

Answer:

Answer:

Part A) The amplitude = 24

Part B) The period = 24

Part C) Vertical shift = 36

Step-by-step explanation:

The general equation of the sine function:

y = A sin (Bx) + C

Where A is the amplitude and B = 360°/Period  and C is the vertical shift

See the attached figure which represents the graph of m and f(m)

So,

Part A:

The function has minimum at 12 and maximum at 60

The difference is = 60 - 12 = 48

So, The amplitude = 48/2 = 24

Part B:

Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.

We can deduce that the function completes one cycle within 24 months

So, the period = 24

Part C:

Vertical shift is obtained at m = 0

So, f(m) = 36

36 = A sin (0) + C

C = 36 ⇒ Vertical shift

So, The amplitude = 24

The period = 24

Vertical shift = 36

Step-by-step explanation:

Answer:

The standard deviation of given data is 12.36  

Step-by-step explanation:

We are given the following data in the question:

40, 12, 17, 25, 9, 46, 13, 22, 16,7

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{207}{10} = 20.7[/tex]

Sum of squares of differences =

372.49 + 75.69 + 13.69 + 18.49 + 136.89 + 640.09 + 59.29 + 1.69 + 22.09 + 187.69 = 1528.1

[tex]\sigma = \sqrt{\dfrac{1528.1}{10}} = 12.36[/tex]

Thus, the standard deviation of given data is 12.36

Final answer:

The standard deviation of the provided data set (number of merchandise returns on Mondays) is approximately 14.8.

Explanation:

To calculate the standard deviation of the provided data set (40, 12, 17, 25, 9, 46, 13, 22, 16, 7), we will follow these steps:

Let's apply these steps:

Therefore, the standard deviation is about 14.8.

Answer:

[tex]6x+7y+3=0[/tex]

Step-by-step explanation:

We are asked to find the equation of the line in general form, which has a of -6/7 and containing the point (10,-9).

We know that genera equation of a line is in form [tex]Ax+By+C=0[/tex], where, A, B and C are real numbers.

First of all, we will write our equation in point-slope form as:

[tex]y-y_1=m(x-x_1)[/tex], where,

m = Slope of line,

[tex](x_1,y_1)[/tex] = Given point on line.

[tex]y-(-9)=-\frac{6}{7}(x-10)[/tex]

[tex]y+9=-\frac{6}{7}x+\frac{60}{7}[/tex]

[tex]y*7+9*7=-\frac{6}{7}x*7+\frac{60}{7}*7[/tex]

[tex]7y+63=-6x+60[/tex]

[tex]6x+7y+63-60=-6x+6x+60-60[/tex]

[tex]6x+7y+3=0[/tex]

Therefore, our required equation would be [tex]6x+7y+3=0[/tex].

Answer:

Step-by-step explanation:

surface area=6*2.2²=6×4.84=29.04 m²

Answer:

29.04

Step-by-step explanation:

just took the test

Answer: To produce treatment groups with similar characteristics

Step-by-step explanation:

The purpose of this experiment is to determine that the treatments groups with similar characteristics are produced. Every groups is taking different amount of the supplement so this study ensures that by randomly assigning the supplements, we can check the cholesterol level in the blood. In this way, similar characteristics in groups are imparted so we can then make treatment groups of same characteristics.

The purpose of random assignment in experiments is to avoid bias, increase the research results' accuracy, help in producing treatment groups with similar characteristics, and control confounding variables. In this case, it ensures that all participants have an equal chance of receiving any level of omega-3 fatty acid or placebo.

The purpose of random assignment in this experiment is multifold. Firstly, it ensures all participants, regardless of their cholesterol levels, have an equal chance of being selected. This prevents bias in the sample selection. Secondly, it increases the accuracy of the research results by preventing skewness in the data. The random assignment ensures that every participant has an equal chance of receiving any level of the omega-3 fatty acid supplement or the placebo. This helps produce treatment groups with similar characteristics, which in turn allows for fair comparisons to be made. Finally, it aids in controlling confounding variables. These are factors other than the independent variable (in this case, omega-3 fatty acid supplements) that may affect the dependent variable (cholesterol level), and random assignment helps to equalize these among the groups.

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Answer:

Therefore the value of x are = -1 and -5 for which f(x)=g(x).

Step-by-step explanation:

Given,

f(x)=x²+6x+6    and    g(x)=1

f(x)=g(x)

⇒x²+6x+6=1

⇒x²+6x+6-1=0

⇒x²+6x+5=0

⇒x²+5x+x+5=0

⇒x(x+5)+1(x+5)=0

⇒(x+5)(x+1)=0

⇒x+5=0     or       x+1=0

⇒x=-5                     x=-1

Therefore the value of x are = -1 and -5.

To find the values of x for which f(x) equals g(x), we set the equations x² + 6x + 6 equal to 1 and solve. The quadratic equation factors to yield x = -1 and x = -5 as solutions.

To find the values of x for which f(x) equals g(x), we need to set the functions equal to each other and solve for x:

Given:
f(x) = x² + 6x + 6
g(x) = 1

We need to solve for x when:

x² + 6x + 6 = 1

Subtract 1 from both sides to set the equation to zero:

x² + 6x + 5 = 0

Next, we factor the quadratic equation:

(x + 1)(x + 5) = 0

Set each factor to zero and solve for x:

x + 1 = 0
x = -1

x + 5 = 0
x = -5

Thus, the values of x for which f(x) = g(x) are x = -1 and x = -5.

Answer: Anna eats 1/8 of pie

Step-by-step explanation: Let total pie =1

Mollie eats 1/4 of pie

Brandon eats half the amount of pie that Mollie eats i.e 1/2 of (1/4)

⇒1/8

Yuki eats 4 times as much as pie as Brandon i.e 4*(1/8)

⇒1/2

Total pie eaten by Mollie +Brandon+Yuki = 1/4+1/8+1/2

⇒7/8

Therefore Anna eats (1-7/8)

⇒ 1/8 of pie

Answer:

Step-by-step explanation:

Let us record the station number 1, 2 or 3 for each family member A, B or C.

I am attaching a table containing total outcomes. Outcomes are presented along rows while the assigned station to each member is written along columns. For ease of understanding, 1 3 2 in the table should be interpreted as family member A being assigned to station 1, member B to station 3 and member C to station number 2, respectively.

From table it is clear that the total outcomes possible are 27.

We know that, probability can be defined as,

[tex]PROBABITILY = \frac{NUMBER\;OF\;DESIRED\;OUTCOMES}{TOTAL\;NUMBER\;OF\;OUTCOMES}[/tex]

a) All Members Assigned to the Same Station.

Cases for all members being assigned to same station are as follows:

[1 1 1], [2 2 2], [3 3 3] (outcome number 1, 14 and 27 in the table).

Therefore,

[tex]PROBABILITY\;(Case\;a) = \frac{3}{27}\\\\PROBABILITY\;(Case\;a) = 0.111[/tex]

b) At Most Two Members Assigned to the Same Station.

It means that maximum of 2 members can have the same station. Cases for this situation are as follows:

[1 1 2], [1 1 3], [1 2 1], [1 2 2], [1 3 1], [1 3 3], [2 1 1], [2 1 2], [2 2 1], [2 2 3], [2 3 2],

[2 3 3], [3 1 1], [3 1 3], [3 2 2], [3 2 3], [3 3 1], [3 3 2]

(outcome number 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 25 and 26 in the table).

Therefore,

[tex]PROBABILITY\;(Case\;b) = \frac{18}{27}\\\\PROBABILITY\;(Case\;b) = 0.666[/tex]

c) All Members Assigned to a Different Station.

For this scenario, we have the following results:

[1 2 3], [1 3 2], [2 1 3], [2 3 1], [3 1 2], [3 2 1] (outcome number 6, 8, 12, 16, 20 and 22 in the table).

Therefore,

[tex]PROBABILITY\;(Case\;c) = \frac{6}{27}\\\\PROBABILITY\;(Case\;c) = 0.222[/tex]

Answer:

Blue M&M's

Step-by-step explanation:

Let the total M&M's bought be 100%.

If 1/3 of the M&M's is blue this means we have 1/3 of 100 of blue M&M's i.e 33.3% are blue.

If 1/4 were red, then we have 1/4 of 100 of red M&M's i.e 25% of reds

If 1/8 of the M&M's were yellow, this means there are 1/8 of 100% M&M's i.e 12.5% of yellow.

According to the results, Jordy have more of blue M&M's

Answer:

80 buses will be required for 1120 soldiers.

Step-by-step explanation:

Given:

Number of seats on One side = 12 seats.

Now Given:

five seats are reserved for equipment.

So we can say that;

Number of seats used by soldiers = [tex]12-5=7\ seats[/tex]

Number of soldiers on Each seat =2

So we will now find number of soldiers on each bus.

number of soldiers on each bus is equal to Number of seats used by soldiers multiplied by Number of soldiers on Each seat.

framing in equation form we get;

number of soldiers on each bus = [tex]7\times2 = 14\ soldiers[/tex]

Now we know that;

For 14 soldiers = 1 bus

So 1120 soldiers = Number of buses required for 1120 soldiers.

By Using Unitary method we get;

Number of buses required for 1120 soldiers = [tex]\frac{1120}{14} =80[/tex]

Hence 80 buses will be required for 1120 soldiers.

Answer:

a = 50 houses

b = 45 houses

Step-by-step explanation:

Given

Number of houses called Model A = a

Number of houses called Model B = b

Total of single windows = 1800

Total of double windows = 375

then we have the system of equations

18a + 20b = 1800  (I)

3a + 5b = 375     (II)

Solving the system by whatever method we prefer, we obtain

(I)     a = (1800 - 20b)/18

then (II)

3((1800 - 20b)/18) + 5b = 375

⇒ 300 - (10/3)*b + 5b = 375

⇒ (5/3)*b  = 75

⇒ b = 45 houses

then

a = (1800 - 20*45)/18

⇒ a = 50 houses

50 model A homes and 45 model B homes will be built.

To solve the problem, let's define our variables:

We then create the following system of equations based on the given information:

1. For single windows:

18A + 20B = 1800

2. For double windows:

3A + 5B = 375

We can solve this system using the substitution or elimination method.

Step-by-Step Solution:

The solution to the system is A = 50 and B = 45, meaning that the construction company plans to build 50 model A homes and 45 model B homes.

Answer:

The union of two event

Step-by-step explanation:

Addition law of probability  define that probability of two event  is total sum of probability of any event subtract the probability of both events

There are two rules  in addition law:

Addition law 1 -  when both event are mutually exclusive, then probability of either event is the sum of each event probability.

P( A or B) = P(A) +P(B)

Addition law 2 -  when both events are non mutually exclusive then there in addition to the individual probability there is some overlap .

P( A or B) = P(A) +P(B) - P(A and B)

It should be noted that addition law is potentially helpful when we are interested in computing the probability of The union of two event.

According to this question, we are to discuss about Addition law of probability.

As a result of this we can see that Addition law of probability  explain about probability for either of two mutually exclusive events which is occurring and also  the probability of two non-mutually exclusive events that is occurring.

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Answer: her regular hourly rate is $12.5

Step-by-step explanation:

Let x represent the regular payment that Sonya receives per hour for the first 40 hours of work. This means that her total pay for the first 40 hours of work is

40 × x = $40x

Sonya is paid time and a half for hours worked in excess of 40 hours. This means that her hourly pay for working more than 40 hours would be x + 0.5x = $1.5x

She worked for 52 hours. This means that the extra hours that she worked is

52 - 40 = 12 hours

Total pay for 12 extra hours is

12 × 1.5x = 18x

If she had gross weekly wages of $725, then

40x + 18x = 725

58x = 725

x = 725/58 = $12.5

To find Sonya's regular hourly rate, we need to calculate her overtime pay and then subtract it from her total weekly wages.

To find Sonya's regular hourly rate, we need to calculate her overtime pay and then subtract it from her total weekly wages. Sonya earned $725 for 52 hours worked. Since she is paid time and a half for hours worked more than 40, she worked 12 overtime hours (52 - 40 = 12).

Her overtime pay is calculated by multiplying her regular hourly rate by 1.5, so her overtime pay is 1.5 * regular hourly rate * 12 hours. Subtracting her overtime pay from her total wages gives us her regular wages, so we have the equation: $725 - (1.5 * regular hourly rate * 12) = regular wages. Solving for  regular hourly rate will give us the answer.

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Final answer:

Tesha's savings account balance was decreased by $91.00 after withdrawing $22.75 each week for four weeks to pay for piano lessons.

Explanation:

To calculate the change in Tesha's savings account balance due to payment for her piano lessons, we need to multiply the weekly withdrawal amount by the number of weeks. Tesha withdrew $22.75 each week for four weeks.

Answer:

Step-by-step explanation:

Let x represent the total number of red and blue beads

Angie has some red and blue beads. 40% of her beads were red. This means that the total number of red beads is

40/100 × x = 0.4x

The number of blue beads would be

x - 0.4x = 0.6x

When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. This means that

0.6x - 50 = 0.6x - 0.6x/3

0.6x - 50 = 0.6x - 0.2x = 0.4x

0.6x - 0.4x = 50

0.2x = 50

x = 50/0.2 = 250

The number of blue beads that Angie had initially is

0.6 × 250 = 150

The number of blue beads that Angie has left is

150 - 50 = 100 beads

The number of beads that Angie has in the end is

250 - 50 = 200 beads

Jack needs to correctly answer at least 28 out of the 30 questions to achieve a minimum of 92% on his science test.

To determine the minimum number of questions Jack must correctly answer to get at least 92% on his next 30-question science test, we can use the following calculation:

Minimum number of correct answers = 92% of total questions

= 0.92 × 30
= 27.6

Since Jack cannot answer a fraction of a question, he must round up to ensure the minimum percentage is met. Therefore, Jack must correctly answer at least 28 questions out of 30 to achieve a 92% score or higher.

Answer:

(C )  angle E = angle X; DF = XY

Step-by-step explanation:

a triangle is said to be congruent if SAS(two sides and included angle)

SSS (all the sides are equal), ASA (two angles and an included sides).

therefore,  if angle E and angle X are equal

line DF and line XY are also equal.

Answer:

[tex] a_{6} = - 11[/tex]

Final answer:

The 6th term in the recursive sequence with the first term 9 and each subsequent term decreasing by 4 from the previous term is -11.

Explanation:

To find the 6th term in the sequence described by the recursive formula given:

a1=9

an=an-1−4

We will apply the formula recursively to determine each term up to the 6th term.

First term (a1): 9

Second term (a2): a1 − 4 = 9 − 4 = 5

Third term (a3): a2 − 4 = 5 − 4 = 1

Fourth term (a4): a3 − 4 = 1 − 4 = -3

Fifth term (a5): a4 − 4 = -3 − 4 = -7

Sixth term (a6): a5 − 4 = -7 − 4 = -11

Therefore, the 6th term in the sequence is -11.

Answer:

87.5%

Step-by-step explanation:

64:64-8

64:56

56/64 *100 = 87.5%

Answer:

The second choice:

          [tex]\large\boxed{\large\boxed{1/x\cdot x=1}}[/tex]

Explanation:

The closure property on an operation means that the operation between two elements of a set produce one element of the same set.

In this case, the operation is multiplication and the set is the polynomials.

Then, the closrue property is that the multiplication of two polynomials will always produce a polynomial.

Since, [tex]1/x[/tex] is not a polynomial, the equation [tex]1/x\cdot x=1[/tex] does not support the fact that polynomials are closed under multiplication.

Slope of this line is -2.5

Step-by-step explanation:

Here, from the graph, x1 = -2, x2 = -4, y1 = 3, y2 = 8

⇒ m  = (8 - 3)/(-4 - -2) = 5/-2 = -2.5

Stratified sampling method - where population were divided into different groups called strata and the sample is then drawn from EACH group.

Systematic sampling method - sampling method using probability where elements are chosen from a target population.

Random sampling - each sample chosen has equal probability to be chosen.

Convenience sampling method - Not a random sampling method where the sample is being chosen as per ease of access.

Cluster sampling method - population were divided into different groups as known as clusters. The clusters were then chosen randomly as the samples. Each individuals in the clusters chosen are used as the samples.

Answer: E. Cluster sampling where selected towns refer to the clusters and were chosen randomly.

The type of sampling used by the researcher is cluster sampling.

Cluster sampling is a technique used when it becomes difficult to study the target population spread across a wide area and simple random sampling cannot be applied.

The researcher divides the entire population into sections or clusters. Then the researcher randomly selects a few clusters from the total clusters for the research.

In this case, the clusters are the five randomly selected towns. Everyone in these selected towns is included in the sample. This makes it a cluster sample.

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Subtract b from both sides: ax=c-b

Divide both sides by a: x=(c-b)/a

Hope this helped

Explanation:

To solve any equation that is linear in the variable of interest, you first look at what is done to the variable, using the Order of Operations as your guide.

Here, the variable is ...

You find the value of the variable by reversing these steps, starting from the last one on the list and working up the list.

To "undo" the addition of "b", we add its opposite (-b) to the equation. The rules of equality tell you that anything you do to one side of the equation must also be done to the other side, so we add -b to both sides:

  ax +b -b = c -b

  ax = c -b . . . . . . . . simplify

To "undo" the multiplication by "a", we multiply by its reciprocal. That is, we multiply by 1/a, or, equivalently, divide by "a". Again, we must do this to both sides of the equation:

  (1/a)ax = (1/a)(c -b)

  x = (c -b)/a . . . . . . . simplify

__

In short, we subtract the added constant (b) and divide by the multiplier (a).

Answer:

27

Step-by-step explanation:

       int x = 9;

       int y = 3;

       if (x >= y)

       if (y > 0)

       x = x * y;

       else if (y < 4)

       x = x - y;

First, the first if statement check for the value of x>=y which is true. The another if-statement check if y>0, which is true and it execute the statement x = x * y that is x = 9 * 3 and x = 27.

The else-if block is not executed because the if-statement attached to it has been executed already.

Answer:

output = n+3.

Step-by-step explanation:

input : 1  5   6    n

output: 4 8   9     -

Here   , 4= 1+3 , 8= 5+3  ,9 = 6+3

So,

output = input +3

When input =n

Then output = n+3.